William F. Tanner on environmental clastic granulometry

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Title:
William F. Tanner on environmental clastic granulometry
Portion of title:
Environmental clastic granulometry
Physical Description:
xii, 144 p. : ill., maps ; 28 cm.
Language:
English
Creator:
Tanner, William Francis, 1917-
Balsillie, James H.
Florida Geological Survey
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Florida Geological Survey
Place of Publication:
Tallahassee, Fla.
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Subjects

Subjects / Keywords:
Sediments (Geology) -- Analysis   ( lcsh )
Marine sediments -- Measurement   ( lcsh )
Coast changes -- Florida   ( lcsh )
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bibliography   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
non-fiction   ( marcgt )

Notes

Statement of Responsibility:
compiled by James H. Balsillie ; chief editor, William F. Tanner.
Bibliography:
Includes bibliographical references and index.
General Note:
Florida Geological Survey special publication number 40

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University of Florida
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University of Florida
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Full Text









William F. Tanner





Env ronmental


Clastic



GYranulometry


Florida Geological Survey
Special Publication No. 40



i _,^/ Compiled by:
James H. 'alsillie
"postal Engneeing Geologit-
he orida Geological S ey

... -:/ L ,. .


Dr. Wdlim Tanner
Regents Professor
Department of Geology
The Florida State University


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no.40


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State of Florida
Department of Environmental Protection
Virginia B. Wetherell, Secretary




Division of Administrative and Technical Services
Mimi Drew, Director of Technical Services




Florida Geological Survey
Walter Schmidt. State Gejologstand Chief





.IfL:": Special Publication No.. 40 'I:. i


S. Wiliam F Tannerii::::

Environmental Clastic Granulometry


::: -Compiled by: ... ::::: : :::
J ames H. Bais -.

-i ; .. C chief EdHditor:. .. ...........
Wilr.aii FTannner




RFlorida Geological Survey
Tallahassee, Florida
1995










LETTER OF TRANSMITTAL


Florida Geological Survey
Tallahassee



Governor Lawton Chiles
Florida Department of Environmental Protection
Tallahassee, Florida 32301

Dear Governor Chiles:

The Florida Geological Survey, Division of Administrative and Technical Services,
Department of Environmental Protection, is publishing "William F. Tanner on Environmental
Clastic Granulometry" as its Special Publication 40. This document shall be of use to the
State as a source of information related to sampling, analysis, and interpretation of the
significantly large volumes of sedimentary lithologies of Florida. Such work is a necessity and
is important to consider when addressing environmental concerns and issues on the behalf of
the welfare of the State of Florida.

Respectfully yours,


Walter Schmidt, Ph.D., P.G.
State Geologist and Chief
Florida Geological Survey


iii















































KEY WORDS:
Beach, Depositional Environments, Eolian, Grain Size, Granulometry, Fluvial,
Kurtosis, Lacustrine, Littoral, Moment Measures, Probability Distribution,
Settling, Sieving, Skewness, Suite Statistics, Wave Energy.



Printed for the
Florida Geological Survey

Tallahassee, Florida
1995

ISSN 0085-0640

iv









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


FOREWORD

Among his many other geological pursuits, Dr. William F. Tanner has over 45 years of
experience in sedimentologic studies and applications. He was chairman for the 1963 Society
of Economic Paleontologists and Mineralogists (S. E. P. M.) interdisciplinaryInter-Society Grain
Size Study Committee which established sedimentologic standards that remain the basis for
sedimentologic work. His combined experience and expertise is of a calibre not commonly
found at universities, let alone available for other instructional opportunities.

W. F. Tanner has persisted through the years in amassing information on modern
sedimentary environments, so that such information could be used in interpreting sedimentary
rocks of the geologic column. Hence, not only can ancient and classical geological
environments be addressed, but so can modern sedimentary environments that have recently
become of paramount importance concerning humankind's treatment of our planet.

It will become apparent that W. F. Tanner has amassed a veritable arsenal of published
works. Short of being a scholar of this published work, one might, however, be hard-pressed
to discover the motivation, the rationale, and the logic behind his sedimentologic pursuits. A
better, more revealing way in which to understand these things, to be able to place them into
perspective, is to have the researcher, himself, teach a course on the subject. His offer to
teach such a course at the Florida Geological Survey during the 1995 Spring semester
provided the opportunity, and motivated the compilation of this work. It is hoped that this
document will, to some extent, capture and place into perspective William F. Tanner's
approach to sedimentology and granulometry and its environmental ramifications.


James H. Balsillie
March 1995
45 MB


ACKNOWLEDGEMENTS

Lecture attendees completing this February-March, 1995, course included:

James H. Balsillie L. James Ladner
Paulette Bond Edward Lane
Kenneth M. Campbell Jacqueline M. Lloyd
Henry Freedenberg Frank Rupert
Ronald W. Hoenstine Thomas M. Scott
Ted Kiper Steven Spencer


Florida Geological Survey editorial staff that reviewed this volume were Jon Arthur,
Kenneth M. Campbell, Joel Duncan, Rick Green, Jacqueline M. Lloyd, Frank Rupert, Walter
Schmidt, and Thomas M. Scott. Their special attention, contributions leading to greater


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


clarity, and accelerated review are to be commended. During preparation of this document
the generous counsel of Kenneth M. Campbell was especially enlightening.

Compilation of this account was supported by funding from cooperative studies
between the Florida Geological Survey (FGS) and the United States Geological Survey
(agreement number 37-05-02-04-429) entitled the Florida Coastal Wetlands Study, and
between the FGS and the Minerals Management Service (agreement number 37-05-02-04-
422) entitled the East-Central Coast of Florida Study.

Copyrighted material appears in this work for which permission to publish was granted
from several sources. Acknowlegements are extended to the journal of Sedementloogyfor the
document:

Socci, A., and Tanner, W. F., 1980, Little known but important papers on
grain-size analysis, Sedimentology, v. 27, p. 231-232,

to the journal Transactions of the Grlf Coast Association of Geological Societies for the
document:

Tanner, W. F., 1990, Origin of barrier islands on sandy coasts: Transactions
of the Gulf Coast Association of Geological Societies, v. 40, p. 90-94,

and to the Jornal of Sedimentary Petrology (now the Journalof SedarnentaryResearch) for:

Tanner, W. F., 1964, Modification of sediment size distributions: Journal of
Sedimentary Petrology, v. 34, no. 1, p. 156-164,

and the abstract of:

Doeglas, D. J., 1946, Interpretation of the results of mechanical analyses:
Journal of Sedimentary Petrology, v. 16, no.2 1, p. 19-40.

Certain illustrations (figures 19, 20, 21, 22, 23, and 35 of this text) and two papers
(in which the illustrations were originally published) appear in this document. The papers are:

Tanner, W. F., 1991, Suite statistics: the hydrodynamic evolution of the sediment
pool: [In] Principles, Methods and Application of Particle Size Analysis, (J. P.
M. Syvitski, ed.), Cambridge University Press, Cambridge, p. 225-236,

and:

Tanner, W. F., 1991, Application of suite statistics to stratigraphy and sea-level
changes: [In] Principles, Methods and Application of Particle Size
Analysis, (J. P. M. Syvitski, ed.), Cambridge University Press,
Cambridge, p. 283-292.


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


This published material was copyrighted by Cambridge University Press in 1991, and is here
reprinted with the permission of Cambridge University Press.


Lecture Notes vii James H. Balsilie


Lecture Notes


vii


James H. Balsillie







W. F Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


COENENTS


LETTER OF TRANSMITTAL ..........
FOREWORD ....................
ACKNOWLEDGEMENTS ............
INTRODUCTION..................

PARTICLE SIZE AND NOMENCLATURE
ANALYTICAL CONSIDERATIONS .....

Laboratory Do's and Don'ts ....
Sieving Time ..........
Balance Accuracy ......
Splitting .............
Sieve Sample Size ......
Sieve Interval .........

Analytic Graphical Results .....
The Bar Graph .........
The Cumulative Graph ...
The Probability Plot .....
Settling-Eolian-Littoral-Fluvia
Environmental Identif
Line Segments versus Components
The Key to Probability Distributions
Sieving Versus Settling ........
Moments and Moment Measures .

How Not to Plot An Example ...

DETERMINING THE TRANSPO-DEPOSITIO
The Sediment Sample and Samplini
Suite Pattern Sampling ........
The GRAN-7. Program ........
Example 1: Great Sand Dun
Example 2: St. Vincent Isla.
Example 3: The German Dai
Example 4: Florida Panhand
Exam De 5: Florida Archeolo


Page
. iii


..........................,
..........................
..........................























Il (SELF) Transpo-Depositional
ication ....................
and Plot Decompositi........




NAL ENVIRONMENTS..........
Unit.......................


es, central Colo .............
d, Florida..................

















rss..........................
e Offshore Data..........................
S(SELF) Transpo-Deposit ionale
ication ....................
, and Plot Decomposition .......


. . . . . . . .
. . . . . . . .
. . . . . . . .


Unit .....................
. . . . . . . .







le Offshore Data .............
gical Site ..................


Letr oesvi ae H asli


....~l 5: FlrdvAce


Lecture Notes


viii


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995



Example 6: Origin of Barrier Islands ........................... 23
Sample Suite Statistical Analysis .................................. 24
Tail of Fines Plot ........................................ 24
The Variability Diagram .................................... 25
Skewness Versus Kurtosis Plot .............................. 25
Diagrammatic Probability Plots .............................. 25
The Segment Analysis Triangle .............................. 26
Approach to the Investigation .................................... 27
The Field Site .......................................... 27
The Paleogeography ...................................... 28
Hydrodynamics ......................................... 28
The Kurtosis ................................................ 28
Kurtosis and Wave Energy Climates ........................... 29
Case 1. The Lower Peninsular East and West Coasts of Florida .. 29
Case 2. Denmark .................................. 29
Case 3. Captiva and Sanibel Islands, Lower Gulf Coast of
Florida ..................................... 30
Case 4. Dog Island, eastern Panhandle Coast of Northwestern
Florida ..................................... 30
Case 5. Laguna Madre, Texas ......................... 31
Kurtosis versus Seasonal and Short-Term Hurricane Impacts ......... 31
Kurtosis and Long-Term Sea Level Changes ..................... 32
St. Vincent Island, Florida, Beach Ridge Plain .............. 33
St. Joseph Peninsula Storm Ridge ....................... 34
Beach Ridge Formation Fair-Weather or Storm Deposits? ........... 34
Texas Barrier Island Study Conversation with W. Armstrong
Price .......................................35
Transpo-Depositional Energy Levels and the Kurtosis; and an
Explanation ........................................... 35
Importance of Variability of Moment Measures in the Sample Suite .......... 36
Application of Suite Statistics to Stratigraphy and Sea-Level Changes ........ 36
Cape San Bias, Florida .................................... 36
Medano Creek, Colorado ................................... 37
St. Vincent Island Beach Ridge Plain .......................... 38
The Relative Dispersion Plot ................................ 38


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


The SUITES Program .......

Example 1. Great Sand [

Example 2. Storm Ridge,

Example 3. The Railroad


)unes, Colorado .............

St. Joseph Peninsula, Florida .

Embankment, Gulf County, Florida


The Storm Ridge versus the Railroad Embankment and the Z

Example 4. The St. Vincent Island Beach Ridge Plain ....

Spatial Granulometric Analysis .........................

Review ..........................................

1. The Site ..................................

2. Paleogeography ............................

3. Kurtosis and Hydrodynamics ...................

4. Sand Sources ..............................

5. Tracing of Transport Paths .....................

6. Sea Level Rise .............................

7. Seasonal Changes and Storm/Hurricane Impact ......

PLOT DECOMPOSITION: MIXING AND SELECTION ...............

Sim ple M ixing .....................................

Non-Zero Component ...........................

Case I ................................

Case II ................................

Zero Component ..............................

Selection........................................ ..

Censorship ..................................

Type I Censorship ........................

Type II Censorhip..........................

Truncation ..................................

Filtering ....................................

Sum m ary ...................................


. . . .. G

.......... 39

.......... 39

.......... 44

-Test ...... 45

.......... 46

.......... 5 1

.......... 52

.......... 52

.......... 53

.......... 53

.......... 53

.......... 53

.......... 54

.......... 54

.......... 54

.......... 55

.......... 55

.......... 55

.......... 55

.......... 57

.......... 57

.......... 57

.......... 57

.......... 57

.......... 58

.......... 58

..........59


Determination of Sample Components Using the Method of Differences ....

Case 1. Two Components with Means Unequal, Standard Deviations

Equal, and Proportions Equal ........................

Case 2. Two Components with Means Unequal, Standard Deviations

Unequal, and Proportions Unequal ................... .

CARBONATES .................................................

REFERENCES CITED AND ADDITIONAL SEDIMENTOLOGIC READINGS .........


Lectur Note JamesH. Basilli


... 59


... 60


... 62

... 63

... 66


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


INDEX ........................................ ........143


APPENDICES
Appendix I. Little Known But Important Papers on Grain-Size Analysis ............ 71
Appendix II. Guidelines for Collecting Sand Samples ......................... 75
Appendix Ill. Laboratory Analysis of Sand Samples .......................... 79
Appendix IV. Example Calculation of Moments and Moment Measures for Classified
Data ...................................................... 83
Appendix V. The Darss ............................................. 87
Appendix VI. Origin of Barrier Islands on Sandy Coasts ....................... 95
Appendix VII. Suite Statistics: The Hydrodynamic Evolution of the Sediment Pool 101
Appendix VIII. Application of Suite Statistics to Stratigraphy and Sea-Level
Changes .................................................. 115
Appendix IX. Sedimentologic Plotting Tools ............................ 127
Appendix X. Modification of Sediment Size Distributions ..................... 133


Lecture Notes James H. Balsillie


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Lecture Notes xii James H. Balsilile


Lecture Notes


xii


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995




WILLAM F. TANNER


on


ENVIRONMENTAL CLASTIC GRANULOMETRY



Compiled by
James H. Balsillie, P. G. No. 167
Coastal Engineering Geologist
The Florida Geological Survey


Chief Editor
William F. Tanner, Ph.D., Regents Professor
Department of Geology
The Florida State University



INTRODUCTION

Sedimentology encompasses the scientific study of both sedimentary rocks and
unconsolidated sedimentary deposits. Sedimentology is defined by Bates and Jackson (1980)
as the ...scientific study of sedimentary rocks and of the processes by which they are formed
... and ... the description, classification, origin, and interpretation of sediments. They also
define granulometry to be the ... measurement of grains, esp. of grain sizes. It should be
apparent, therefore, that granulometry is a pursuit that, while appearing to be more
specialized, has significant impacts on the success of more generalized sedimentologic
endeavors.

Unconsolidated sedimentary particles range in size from boulders (e.g., glacially
produced products) to colloids. This work deals with quartzose sediment sizes ranging from
about -2.0 0 (4 mm) to about 5.0 0 (0.0313 mm), that is, those sediments whose bulk is
comprised of sand-sized material.

At the outset, it is important to understand that the majority, perhaps 90% or more,
of sand-sized siliciclastic sediments have been transported and deposited by water. In a
recent paper on suite statistics (i.e., a collection of correctly obtained samples from a discrete
sedimentologic body), W. F. Tanner (1991 a) identified an historical paradigm and asked certain
questions pertinent to the objectives of this account.


Lecture Notes


James H. Balsillie








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


For a century or so the purpose of making grain size measurements was
to determine the diameter of a representative particle. This is useful when one
is studying reduction in grain size along a river (e.g., Sternberg, 1875). But it
is a simplistic approach, and one is entitled.to ask: Is the mean diameter the
only information that we wish to get? Or does the simplicity of this first step
make us think that we have now described the sand pool?

When we measure grain size, what do we really want to know? This
does not refer to whether we measure the long axis or the short axis of a
nonspherical particle, or whether we approximate the diameter by measuring a
surrogate (such as a fall velocity). Rather, we ask this question in order to get
a glimpse of how far research has come in understanding transport agencies or
conditions of deposition, and of the degree to which we might reasonably
expect to improve our methods of environmental discrimination.

Does a set of parameters describing a size distribution for a sample set from a discrete
sedimentary deposit allow us to compare the set with some other, that we might recognize
a different transport agency or depositional environment? An answer or answers to this
question constitutes an underlying objective of this account. However, the question also
engenders complexity of the kind that would pique the interest of any researcher.
Unfortunately, most of us (even if we were so motivated) are not afforded the luxury to pursue
such matters. Rather, we must be content to apply any answers to such a quest in a
practical, a practicable, a pragmatic manner, which also constitutes an underlying objective
of this work.

In 1795,James Hutton proposed the Uniformitarian Principle, stating that ...the present
is the key to the past. If this is so, then the corollary that the past is the key to present must
also hold true. In addition, a second corollary must be true that the present is the key to the
future. It might be submitted, therefore, that in this day-and-age of environmental concern,
we might well have a responsibility to place at least equal importance on the corollaries as on
the principal. It would appear to be so critical, in fact, that at no time in the history of the
discipline has, not just the investigation, but the application of "now geology" or "now earth
science" been more important.

This document, while available for unlimited distribution, has not been designed to be
a general information document tailored for the layman. It is a quite specific account, which
requires some considerable familiarity with granulometry, sedimentology, and statistics
associated with probability distributions. It is, therefore, designed for those who require
specific information in their approach to environmental concerns, i.e., it is a professional peer
group educational/reference document.

One might feel that there is an apparent lack of references to the work of others who
have published countless papers on sedimentological matters. Please understand that this
document is the result of a short course documenting contributions of one researcher. W. F.
Tanner is adamant about giving credit where credit is due. While recording of many references
might not be apparent in the following account, they certainly are in his published works to
which the reader is referred (e.g., see the appendices).


Lectur Note JamesH. Basilli


Lecture Notes


James H. Balsillie







W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995



PARTICLE SIZE AND NOMENCLATURE

In sedimentologic endeavors particulate matter can cover a significant range in size.
One scheme, for example encompasses a minimum of five orders in magnitude (Table 1).
Note, also, that there is a consistent non-linear progression (square or square-root depending
upon where the origin lies) in size and corresponding
nomenclature. Using another scale, that of Wentworth
Table 1. Basic Paricle Size- (1922), a similar although somewhat different
Nomeclature Distinctions. nomenclature-size scale is espoused and commonly
used (see Table 2).
Boulders
----- 256 mm
Cobbles Table 2. Size Conversions and
CA ob Pticde Nomendature.


Sand Boukmer
---- 1/16 mm 256.00 -8.00 com
Silt 64.oo -.oo.00
-- 1/256 mm
Clay 5.60 -2.s0 Pebbe Onve
4.75 -2.25
4.00 -2.00
3.35 -1.75
2.80 -150 Gnnulb
This course addresses sand-sized 2.00 -1.00
particles, or in the case of the Wentworth 1.68 -0.75 very
Scale sand- and granule-sized particles. 1.1 0.50 coraM
1.19 -0.25 Sand
1.00 0.00
In addition, this course.deals primarily 0.84 0.25 coUM.
with siliciclastics (i.e., quartz particulate 0.71 0.50 Sand
0.69 0.75
matter). For instance, heavy mineral-laden o.so 1.00
sediments (e.g., magnetite) behave 0.42 1.25 MtdBim
0.25 1.5 Saud Saud
differently than quartz to forcing elements, 0.30 1.75
and granulometric interpretations will be 0.26 2.00
quite different. Carbonate sediments also 0.21 2.256 F
0.177 2.50 8S8d
produce different results, not because of 0.15 2.75
mass density differences but because of 0.125 3.00
carbonate grain shape divergences. The 0.10o 3.256 V.
0.088. 3.50 FkI
latter, however, because of the 0.074 3.75 Sand
preponderance of CaC03 sediments in south 0.0625 4.00
Florida will receive attention throughout this 0.0426 4.25
COUrse. 0.0372 4.75
0.0313 5.00 81
0.0263 S.25
Numerical representation of 0.0263 5.50
sediments is often given in millimeters (mm).
There are, however, compelling reasons to .o0039 8.00
use the phi (pronounced "fee") convention. o.0002 12.00
Correct terminology is phi units, the phi co
scale, orphi measure. Phi units, denoted by


Pebbles
---- 4 mm


Immsen Im Urie Weamtmr iCbhMlhlam
(-) I)_


James H. Balsillie


Lecture Notes







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


the Greek symbols 0 (lower case) or Q (upper case) are numerically defined by:
= -log2 d(mm)

where d(mm) is the particle diameter in mm. Conversely,

d(mm) = 2-*

Computational equations for the above which can be easily (e.g., Hobson, 1977) programmed
or evaluated using a hand-held calculator, are given by:
S= -1.442695 In d(mm)
and

d(mm) = INV In (-0.69315 4) = e-0o.631s


This course uses and promotes universal use of the phi measure. Reasons for its
adoption were forthcoming from the
1963 S.E.P.M. Inter-Society Grain Size
Study Committee. They were published Table 3. Reasons for Adoption of the Phi
by Tanner (1969) and are listed in Table Scale (from Tanner 1969).
3.
(1) Evenly-spaced division points, facilitating
ANALYTICAL plotting.
CONSIDERATIONS (2) Geometric basis, allowing equally close
inspection of all parts of the size spectrum.
Sand-sized particulate matters of (3) Simplicity of subdivision of classes to any
such dimension that it responds in a precision desired, with no awkward numbers.
timely manner to aero- and (4) Wide range of sizes, extending
hydrodynamic forces (i.e., wind, waves, automatically to any extreme.
astronomical tides, currents, etc.). (5) Widespread acceptance.
Conversely, therefore, such sediments (6) Coincidence of major dividing points with
can reveal information about how they natural class boundaries (approximately).
were transported and, hence, the (7) Ease of use in probability analysis.
paleogeography. See, for instance, (8) Ease of use in computing statistical
Socci and Tanner (1980) and text parameters.
reference to De Vries (1970) of (9) Amenability to more advanced analytical
Appendix I. methods.
(10) Fairly close approximation to most other
There are, however, several scales, allowing easy adoption.
considerations with which to contend. (11) Phi-size screens are already available
First, field sampling and laboratory errors commercially.
do occur. Second, many samples, ...
i.e., sample suites, ... are required to No other scale is even close to matching this
verify transport and depositional list; most other scales do not have more than
interpretations and results (e.g., W. F. three or four of these advantages.


Lecture Notes


James H. Balsillie






W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Tanner has analytical results for over 11,000samples from a multitude of transpo-depositional
environments each comprised of many sample suites). Third, standardized laboratory and
analytical procedures are crucial in order to realize accurate interpretations.

Laboratory Do's and Don'ts

Guidelines for the collection of sand samples are given in Appendix II. Procedures for
laboratory analysis of samples are given in Appendix Ill. The following, however, identify
certain issues that deserve special, concerted attention.

Sieving Time

A minimum of 30-minutes is recommended for siliciclastic sediments (longer sieving
time is a matter of diminishing returns); see the work of Mizutani as referenced in Socci and
Tanner (1980).

Balance Accuracy

Weigh to 0.0001 grams, then round to the nearest 0.001 g.

Splitting

Splitting is "bad news". It is recognized that splitting might be a necessity under some
circumstances. However, there should be no more than one split, and to "do without" is even
better. See the work of Emmerling and Tanner (1974) referenced in Socci and Tanner (1980).

Sieve Sample Size

Introduce no more than 100 g to the -2.0 0 or finer sieve. A larger mass or size will
introduce overcrowding. An introductory sample size of 45 g is ideal, but can range from 40
to 50 g.

For instance, for a sample containing 50% quartz and 50% carbonate material, a 100
g sample (maximum size allowable) needs to be sieved first. The CO3 is then removed with
HCI and the siliciclastic fraction resieved. Simple subtraction of the quartz distribution from
the total distribution will yield the CaCO, distribution.

Sieve Interval

Without reservation, it is recommended that 1/4-phi sieve intervals be used in
granulometric work.

Analytic Graphical Results

The Bar Graph

The bar graph (Figure 1) is not a rigorous analytical tool; it is for the layman. It is not
sufficient to "tell the story" for analytical purposes. There is a better graphical method,

Lectue Noes Jmes H Ba/i/li


James H. Balsillie


Lecture Notes








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


however, that "tells the story" with
standardized clarity. The bar graph,
however, can be presented to facilitate a
communicative link leading to the proper
form of graphical presentation.

The Cumndative Graph

This form of graphing (Figure 2) using
various types of graph paper (e.g., linear, log
cycle, etc.) is too indefinite. Data and paper
plotting ordinates may not be evenly spaced
leading to possible multiple interpretations
(e.g., fitted lines A and B) that can each
have significantly high correlation
coefficients.


3.875 I
3.625
3.375 C
3.125
2.875
2.625
2.375
2.125
1.875
1.625
1.375
1.125
0.875 4
0.625 ]
0 2 4 6 8 10 12 14 16 18 20 22 24
Frequency %


Figure 1. The bar graph.


The Probabiity Plot

This form of plotting (Figure 3)
uses arithmetic probability paper. Such
paper assures that points will be equally
spaced. Ensuing interpolation can then
be accomplished with assurance. Such
assurance is not always possible using
other types of graph paper. Non-
parametric parameters, such as the F
median (50th percentile value), can be
located with a good deal of precision.
Arithmetic probability paper also allows for
later. Moreover, statistical application


Coarse



Phi



Fine


0.1%


50%


Figure 3. The arithmetic probability plot.


100%



100 P



0%



igure 2


Finer


. The cumulative graph.


the procedure of decomposition to be discussed
and arithmetic probability paper constitutes a
standardized approach for
sedimentologic work. The line on the
graph is a true Gaussian (after K. F.
Gauss) distribution because it plots as a
straight line on probability paper.

It is more realistically the case,
however, that the cumulative
distribution for sand-sized siliciclastic
samples are comprised of multiple line
99.9% segments (Figure 4). Each segment, in
fact, commonly represents a different
transpo-depositionalprocess orsediment
source.


RULE: a minimum of three (3) consecutive points are required to identify a segment


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


with assurance.


Coarse



Phi



Fine


0.1%


50%


99.9%


Figure 4. The segmented arithmetic probability
plot.


It is to be recognized that some
transport processes, such as landslide
debris and fluvial flooding, are so rapid that
granulometric results are not afforded the
time to become Gaussian. However, most
eolian and littoral processes provide
sufficient time relative to sand-sized range
response that analytical granulometric
results are allowed to become Gaussian.
Hence, transpo-depositional processes can
be identified.


Coarse



Phi



Fine
0.1%



Figure 5. Effect of high
depositonal processes.


Coarse



Phi



Fine


0.1%


50% 99



energy transpo-


50%


High energy fluvial sediment data
might appear as plotted in Figure 5. Note
that the general trend of the slope of a
straight line fitted to the erratic
granulometric results is steep, indicating
poorly sorted sediments.

However, both eolian and littoral
.9% sediment data provide similar results ...
they are very well sorted, i.e., along the y-
axis the distributions encompass very few
1/4-0 units, and line slopes are low. Note:
parallel lines of Figure 6 indicate identical
sorting, even though sample A has a
coarser average size than sample B.

In the example of Figure 7, sample
B is better sorted than sample A, even
though sample B has a coarser mean.


Coarse


99.9%


Figure 6. Finer and coarser distributions with
identical sorting.


Fine


0.1%


50%


99.9%


Figure 7. Coarser and finer distributions with
different sorting characteristics.


Lecture Notes James H. Balsillie


A

1/ i
1/4 Phi Units

I


BI


A

B



--- ____ i------


Lecture Notes


James H. Balsillie








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Sett n-Eolan-Littoral-Fuvial (SELF) Transpo-Deposiional Environmental Identification

Relative relationships of adjoining line segments require relative consideration when
interpreting probability plot results, which J. H. Balsillie has termed the WFTmethod of SELF
determination. Consider the generalized plot of Figure 8 for possible combinations of
interpretative results. Interpretative descriptions are given in Table 4.
High Energy
Comer


Coarse -



D
Phi


Se
ne
Fine -
0.1%


50%


Possible Curve
Combinations


99.9%
Low Energy
Comer


AEF
AEG
BEF
BEG
CEF
CEG
DEF
DEG


Figure 8. Basic line segments on arithmetic probability paper.


Table 4. Rudiments of WFT method of SELF determination for lne segments of Figure 8.
Segment(S) Description of Interpretation
AEF The Gaussian distribution.

Indicates that the operating transpo-depositional force element is wave activity; point
a, relative to segment E, is termed the surf-break. This slope, which is gentle,
represents beach sand ... it occurs no where else ... it is definitive! The higher the
B slope of segment B, the higher the wave energy. Note that for sand-sized material,
the surf-break normally appears for low- to moderate-energy wave climates. For
high-energy waves, point a moves off the graph (to the left) and segment B
disappears (i.e., the wave energy is over-powering even to the coarsest sand-sized
sediment fraction available (Savage, 1958; Balsillie, in press)).

D Indicates eolian processes; point a is termed, relative to segment E, the eobr
hump.

Represents fluvial energy ... has a steep slope, the greater the slope the higher the
C energy expenditure. This segment is termed the fluvia coarse ta, or may represent
a pebbly beach.

E Central portion of the distribution.
Is the low energy tail termed the setthg tat and, if present, may indicate lowering
G of energy for the total distribution or component distributions of the coarser
sediments.


Lecture Notes


James H. Balsillie






W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Figures 6 and 7 have illustrated how
one can identify finer and coarser distributions
with different standard deviations (i.e.,
sorting). For future reference, what of
skewness and kurtosis? Figure 9 illustrates
how skewness appears on the arithmetic
probability plot. Figures 10a and 10b illustrate
the effect of kurtosis.

These plots represent simple examples,
..., more complicated results are certainly
possible.

It is often advantageous to view
concepts using a different approach.
Regarding moment measures, consider the
following (refer to preceding figures if
necessary). First, the mean or average simply
locates the central portion of the distribution.
Second, the standard deviation on arithmetic
probability paper is the slope of the line
representing the distribution. Third, the
skewness is 0 if the distribution is truly
Gaussian (i.e., the often used normal or bell-
shaped curve terminology, terms which should
be dropped from usage) and, therefore, as
much of the distribution lies to the left of the
50th percentile as to the right. Fourth, if the
distribution plots as a straight line it is a true
Gaussian distribution with a Kurtosis value of
K = 3.0. There is published work that
identifies the Gaussian kurtosis as 0 or 1;
these, however, are but arbitrary definitions
determined by subtracting 3 and 2,
respectively, from the calculated 4th moment
measure.


Line Segments versus
Components, and
Plot Decomposition


Coarse



Phi



Fine


0.1%


99.9%


Figure 9. Appearance of skewness on arithmetic
probability paper.


Coarse



Phi



Fine


0.1%


50%


99.9%


Figure 10a. Appearance of kurtosis on arithmetic
probability paper; plot is for a flat-topped
(platykurtic) distribution.


Coarse



Phi


0.1%


50%


99.9%


Figure lOb. Appearance of kurtosis on arthimetic
probability paper; plot represents a peaked
(leptokurtic) distribution.


When dealing with plotted
sedimentologic data on arithmetic probability paper, one often sees multiple line segments
(e.g., Figures 4 and 8). These segments represent, as we have learned, different transpo-
depositional processes. They are not distributions in their own right.


LecureNoes ams H B/sili


Positive
Sk


Negat.ve
Sk


James H. Balsillie


Lecture Notes







W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


There is a common belief espoused




- Component A

Combined Curve
Component B
Component B


0.1%


50%


99.9%


Figure 11. Example of plot decomposition yielding
two samples with equal standard deviations and
unequal means.


in the literature that one can lift out a line
segment and examine it on its own to
determine low- or mid-level traction loads
or suspended load. Such advocates do
not understand the aero- or
hydrodynamics involved.

Where a probability plot has
multiple line segments there are true
component distributions or components
that can be identified using the process
of decomposition. For instance the
combined distribution of Figure 11 (multi-
segmented curve) is comprised of two
components (not three).


The Key to Probabiity Distributions

There is a property associated with the Gaussian (or any other) Distribution that is not
widely known nor appreciated. However, it is so important that it deserves special
identification here. To understand this property will lead to greater clarity as to how statistical
distributions are to be viewed, treated, and understood.

It is the tails of the distribution which dictate the shape of the
central portion of the distribution.


Most folks
assume it is the
central portion of the
distribution which
determines the
behavior of the tails ...
an assumption that is
incorrect. This was
first demonstrated to
J. H. Balsillie in 1973
by W. R. James (a
statistician and
geologist, and student
of W. C. Krumbein).
Doeglas (1946), in an
essentially unknown
paper, understood this
property ... see the
underlined text in his
abstract (Figure 12).


JoURNAL. o SEDInMETARX PBTIOLOUY, VOL. 16, NO. 1, Pr. 19-40
FIGs. 1-30, TABLK 1, APRIL, 1946

INTERPRETATION OF THE RESULTS OF MECHANICAL ANALYSES1
D. J. DOEGLAS
Laboratorium N.V. De Bataafsche Petroleum Maatschappij, Amsterdam

ABSTRACT
Mechanical analyses of deposits of various sedimentary environments have been made by
means of a new type of sedimentation balance for grain sizes from 500 to 5 p. The results have
been plotted on arithmetic probability paper. Well-sorted sands give on this paper straight
lines proving that they have a symmetrical size frequency distribution when an arithmetic
grade scale is used. The size frequency distribution of the sand and silt grades of argillaceous
sediments commonly is a part of a symmetrical one.
The arithmetic probability paper enables us to study the phenomena caused by the dif-
ferentiation of the transported detritus. Three main types of frequency distribution called
R-, S-and T-types ocur in sedimentary deposits due to the sorting of the transporting medium.
The characteristic features of a sedimentary size frequency distribution are found in the
e temes and not in the central halt of the distribution. Statistical values based on quartiles.
threlore do not ive satisfactory results.
The claracterstic shape of the extremes of the distributions caused by the differentiating
action are frequently blurred by later mixing of material due to variations in the capacity of
the transporting medium. Composite frequency distributions, however, are commonly recog-
nized if the results ar plotted on the probability paper.
As far as analyses by means of the sedimentation balance have been made sedimentary
environments can be recognized by the predominance or alternation of certain frequency
distributions.
Figure 12. The Doeglas abstract (reprinted with permission).


Lecture Notes James H. Ba/si/lie


Coarse



Phi



Fine


James H. Balsillie


Lecture Notes







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Sieving Versus Settling

Settling tubes have gained popularity because of their time saving capability and,
hence, are most often referred to as Rapid Sediment Analyzers (RSA's). There are, however,
serious problems associated with RSA's such as drag interference with side walls, and effects
of sediment introduction into the fluid, etc. The most serious defect of RSA's, however,
involves the production of von Karmbn vortex trails by the settling grains.

Theodore von KBrmbn was born in Hungary in 1881. He was trained as an engineer
and became a U. S. citizen in 1936. He was a noted aeronautical engineer and consultant to
the U. S. Air Force during the late 1930's and the 1940's. He was recently honored with a
U. S. postage stamp.

For an automobile or boat wake the von
Up Karm6n effect is two-dimensional. For a grain
falling in water it is three-dimensional. Each
Vortex vortex "kicks off" at different times. They are
W+ Trail spaced at less than 120 degrees (say 106 to
108 degrees) which causes the entire system to
spiral to the bottom (see Figure 13). These
vortexes or vortices (latteral effects are 2 to 3
Times the sediment grain diameter) affect other
G. ni grains much in the same manner as the
Grain -' tailgating effect is used in auto racing. The net
result is that larger grains entrain smaller trailing
0 grains, increasing the fall velocity of the smaller
-108 grains; hence, the smaller grains appear to be
larger than they actually are. At the same time,
the smaller entrained grains slow the settling
velocity of the larger grains, making the latter
Figure 13. The von Kanrmn vortex train appear smaller than they actually are.
phenomenon.
Bergman (1982) investigated the sieving
versus settling problem by not only using sieve and settling tube results, but also microscope
size determinations, and he verified the above results. His findings are recounted in Figure 14.

It is also important to note that sieves, at least in the U. S., are standardized. RSA's,
however, can significantly vary in equipment type, dimensions, fall velocity mathematics
applied, etc. A most serious problem between RSA's, is that they are not calibrated from
laboratory-to-laboratory. Hence, there is no standardized RSA.

The bulk of the literature concerning the issue, supports sieving over settling devices.
The U. S. Army Corps of Engineers, regarding marine sediments and beach restoration design
work, recognizes the problems with RSAs. Hobson (1977), in a Coastal Engineering Research
Center document, lists some of the common problems as:

(a) Failure of the fall velocity equations to account for the effects of varied
particle shapes and densities, interference of falling particles with each other,


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995



Abstract

A comparison of the grain size data derived from sieving and settling techniques of sixty
samples from modern sedimentary environments indicates that there exist important differences in
the way grain size distributions are perceived by the two methods. A third method of analysis,
microscope grain size determination, supports the results of the sieve analysis, indicating that the
settling tube has inherent properties which makes it less dependable for grain size studies.

In comparisons of moment measures sievingg vs. settling tube) significant differences were
found. The settling tube perceives fine grain sizes coarser than they actually are, and coarse grain
sizes finer that they actually are. A compression of the overall distribution of values results. This
compression also occurs in individual samples, as indicated by studies of the probability plots. The
settling tube fails to detect certain tails (in the distribution) that are indicated by the sieving results.
This compression of samples is apparent in the standard deviation sieving vs. settling comparison.
The settling tube consistently perceives the samples to be better sorted (lower standard deviation)
than is indicated by the sieving results. Results of the skewness and kurtosis comparisons indicate
the settling tube is not capable of detecting these small differences in the grain size distribution.

The compression phenomenon caused by the settling tube is thought to have two possible
sources. The first, a physical truncation of the distribution by sampling technique, is of varying
significance. The second, a hydrodynamic "truncation", occurs in all samples but may be
accentuated with certain changes in the distribution.


Figure 14. Bergman's (1982) Masters Thesis Abstract on grain size determinations.

and water turbulence; (b) drag interference between the cylinder walls and the
settling particles; (c) the divergent difficulties of accurately timing the rapid fall
of larger particles; and (d) various problems associated with introducing the
sediment into the fluid.

Hobson concluded that for practical beach engineering problems, sieve data are the most
reliable and reproducible, especially among different laboratories. He also reported that
granulometric results from the two techniques (i.e., sieving and RSAs) are not to be mixed.

Moments and Moment Measures


Except for the first moment and the moment measure termed
there is a difference between moments and moment measures.
measures are calculated from numerical consideration of moments.


the average or mean,
Specifically, moment


The first moment about zero (m,) is also the mean or average (pu or M,) calculated
according to:

0 = MN = M, = fn


where x is the class midpoint grain size, f is its frequency (weight percent), and n is the
number of classes. Higher orders of moments are computed about the mean as a


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


transcendental progression of the form:

M, Ax mly
mra=
n-1


where p is an integer, and mp is the pth moment about the mean.

Moments required for the evaluation of moment measures are:

Sfx m,)2
m2
n-1



I(x- m,)3
m =
n-1

and

4 f(x- m,)4
n-1


where m2 is the second moment, m3 is the third moment and m4 is the fourth moment.

The second moment is actually the variance, and the standard deviation moment
measure, a,, becomes:




The skewness moment measure, Sk,, is calculated by:


S(m2)1


and the kurtosis moment measure, K,, is calculated according to:

Sm
(m2)2


An example of moment and moment measure calculations is given in Appendix IV.

It is critically important to understand that higher moment measures progressively
describe more about the behavior of the tails of the distribution, as illustrated in the example


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995



of Figure 15. The figure illustrates that the higher moment measures are zero near the center
of the distribution, whereas non-zero values appear only as the tails of the distribution are
approached.


This is MOM-DEMO. Data source: Keyboard.. SampleTVER X-46. 02-06-1995
S114 % sieves)


Example of calculation of moment measures:


f(i) ProdMn MnDev ProdSD ProdSK ProdKu Prod6th Prod8th ProdlOth
(grams)
.0021 .001 -1.46 .004 -.007 8.999999E-03


.0455
.2664
1.6031
5.1485
13.4455
19.1243-
10.8556
3.8318
.4658
.0613
.0168
.0063
.0033


.039 -1.21
.299 -.96
2.204 -.71
8.366 -.46
25.21 -.21
40.639- .04--
25.782 .29
10.058 .54
1.339 .79
.191 1.04
.056 1.29
.022 1.54
.012 1.79


.066
.245
.805
1.084
.587
.032-
.919
1.121
.291
.066
.028
.014
.01


.02 .043 .092
-.081 .097 .142 .207 .303
-.235 .225 .207 .19 .175
-.572 .405 .203 .102 .051
-.498 .228 .048 01 .002-
-.123 .025--.001 0 0
.001 0 0 0
.267 .07 .006..0 0
.606 .328 .096 .028"-'.008_
.23 .182 .114 .071 .044
.069 .071 .078 .084 .091
.036 .046 .077 .129 .216
.023 .035 .084 .2 .475
.018 .033 .108 .349 1.12


Sums: n 54.93g. 114.224
Mean is 2.084 114.224/54.93
[0.236 mm]


5.272 -.266


1.761 1.184 1.413 2.577


Figure 15. Higher moment measures describe the behavior of the tails of the distribution.


For the higher moments, the even moment measures are more meaningful than the odd
moment measures. Odd moment measures address asymmetry of the distribution, about
which we know relatively little. A comprehensive list of the higher moments and
corresponding moment measures (e.g., m5 is the 5th moment, and mm, is the 5th moment
measure; there are no descriptive names for mm, and higher moment measures) are:


Moment


Corresponding Moment Measure


Sf (x- m1)6
n-i

fn m,



m n-
n-1


Sf(x-m,)7
n-1


mm, = -
(1m)2 o0


mm6-
(f7)


m77 n7y
mm,7
(m2)u o7


Lecture Notes James H. Balsillie


MidPt

.625


.875
1.125
1.375
1.625
1.875
2.125-
2.375
2.625
2.875
3.125
3.375
3.625
3.875


Lecture Notes


James H. Balsillie







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Sf (x- mr)
m- -
n-1


m, m,
mm, n
(m)4 a


How Not to Plot An Example

Figure 16 illustrates a "bad blunder". First, just what is meant by the "third moment"
is uncertain. Second, the meaning of "zone of 2-way beach flow" is open to question. Third,
the plotted data are certainly not definitive in delineating the two regions shown. By design
or default, the figure certainly does not convince the student that statistics can work. One
lesson is that we must be precise in our use and application of analytic numerical
methodologies and data presentation. A second lesson is that "single sample" data are
commonly contradictory.


1.5


1


0.5


0


-0.5


-1


-1.5


i
0 Zoe of 2- ay Flow on ,eaIhe

S Bar ks of 1-Way Flo N Channels of Rveri






0






I I I



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.


5


Standard Deviation

Figure 16. The Friedman and Sanders (1978) plot (replotted). Some 250 individual sample
results were originally plotted; only those which disagree with the arbitrary set division (bold
dashed ine) are replotted here. The area of uncertainty may contain multiple river sample
results (unclear from the original figure).


- -~-


5


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


DETERMINING TRANSPO-DEPOSITIONAL ENVIRONMENTS

Rather than occupying careers as scientists purely for the sake of pursuing scientific
discovery, most of us occupy positions where there is a limiting constraint of practicality or
pragmatism. Let us apply this to the study of granulometry as it applies to sedimentology and
environments of deposition.

Should we be given a siliciclastic sediment sample of unknown or uncertain origin, can
we ascertain its transpo-depositional environment? We can certainly address it. Although
there is no certainty that we can always provide a solution, in most cases we can. One of
the basic issues concerns the hydrodynamics or aerodynamics associated with conditions of
sediment transport and deposition.

The Sediment Sample and Sampling Unit

An underlying assumption with such sedimentologic studies is that the field sample we
collect is a laminar sample. This is the sedimentation unit of Otto (1938, p. 575) defined as
...that thickness of sediment which was deposited under essentially constant physical
conditions. Similarly, Apfel (1938, p. 67) defined a phase as ... deposition during a single
fluctuation in the competency of the transporting agent (the reader is also referred to the later
work of Jopling, 1964). The sedimentation unit constitutes a narrowly defined event. For
instance, it is not deposited by a flood occurring over a period of 3 weeks, but it might be
deposited by one energy pulse, with each pulse occurring over-and-over during the flood. It
is not known what a sedimentation unit, lamina, or bedding plane is in terms of physical
principles. But we can recognize them to some extent. Regardless of the unknowns, we
should strive to collect sedimentation unit samples.

In indurated rocks, e.g., sandstones, ground water staining can cause features that
appear to be laminae. Drilling can turbidate sediment, causing mixing and disruption of
sedimentation units. In many cases, in the field one cannot see the laminae. At other times
we can see or sense the laminar bedding in the field, but cannot define it. Where one cannot
see the laminae, samples can be taken in a plane parallel to the existing surface if it is
determined the surface is the active depositional bedding plane. At other times, a momentary
glimpse of bedding planes (due to moisture content, evaporation and associated optics) might
occur to aid in sample selection clues. Sampling a sedimentation unit can often be a matter
of estimation. However, a multitude of samples termed the sample suite can aid in assuring
sampling completeness.

Suite Pattern Sampling

A suite is a collection of samples that represents a deposit from one transporting agent
under one set of conditions and, therefore, must have certain geometric relationships. For
instance, it is not practical that 5 samples taken 100 km apart would represent a suite. Do
five samples from one river bank or point bar, one beach, or one sand dune that are
immediately adjacent to one another (i.e., touching) constitute a suite? By definition, the
answer would be yes. However, the preceding two examples are the extremes. Suite
samples must be far enough apart to show variation, and yet not spaced far enough apart to


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


represent factors that are not wanted or not related. One can look for the transporting-
depositional agent involved and adjust the suite sampling procedure/schedule accordingly.

The number and pattern of suite samples is not etched in stone. For instance, road
cuts are where you find them, they are not laid out in advance on a grid. Multi-level,
hierarchical sampling schemes are not always possible or the best choice.

One can also collect suite samples as a time series in the rock record "vertical"
sequence, although in cross-bedded rocks it can be difficult. In "more recent" unconsolidated
sediments comprising a fluvial point bar or beach ridge plain, the time sequence will be in the
horizontal direction.

The GRAN-7 Program

While the computer programs W. F. Tanner has developed could be copyrighted as
intellectual property, for various reasons he has not, and provides copies of software to all
those making request for its use. The GRAN-7 program is based on a program that James P.
May wrote a number of years ago called GRANULO. GRAN-7 has been modified and extended
in its analytical capability.

Example 1: Great Sand Dunes, central Colorado (Figure 17)

On the first line KIRK identifies the graduate student (Kirkpatrick), the GSD signifies the
locality for the Great Sand Dunes in central Colorado. The extension DT$ means that the
sample number contains both numeric (DT) and alpha ($) code.

The first panel is the Table of Raw Data. The 5th and 6th columns are the decimal
weight percentages or probabilities. That is, multiply by 100 to obtain the values in per cent.
These have been computed to 5 decimal places.

The 2nd panel lists moment measures in phi units. They are not graphic measures
(which are no longer suitable for use). With the advent of the programmable calculator and
Personal Computers, there is no excuse to not use the method of moments and moment
measures. In fact, even 40 years ago when we did not have the computing power of today,
graphic measures may have not been appropriate in many applications. The 2nd column lists
moment measures excluding the pan fraction. The pan, however, may contain various
sediments including clay sizes. One may wish to process these using the settling tube. While
there are various pan sizes listed, the literature suggests a standard pan size of 5 0 for low
percentages of the fine fractions (column 3). The 7 0 pan (column 6) can significantly weight
the pan fraction. NOTE: the GRAN-7 program allows for saving this output so that it can be
used in other ensuing software applications.

The relative dispersion (or coefficient of variation) is oI/M,. The smaller the value of
the relative dispersion, the "tighter" the distribution. Also, "tail of fines" is the percent of the
sample containing the 4 0 and finer fraction of the sample. If it is a relatively high percentage,
then fluvial sediments are indicated. If it is relatively low, beach or dune sediments are
indicated.


Lecture Notes


James H. Balsillie










W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995




Panel 4 is the frequency histogram; panel 5 is the cumulative probability plot with the
eolian hump. Note that the cumulative probability plot is much clearer in providing for
identification of the eolian properties of the sample than the frequency plot.


Example 2: St. Vincent Island, Florida (Figure 18).


The sample is from St. Vincent Island, taken along the central profile. Note in panel
1 there is no pan fraction. The modal class listed in panel 2 is always the primary mode.


At the 5 0 pan, the standard deviation (panel 3) is 0.416 0. This value is not


This is GRAN-7. The data source is kirk-gsd.dt$.
Panel 1


02-24-1995


This is GRAN-7. File: kirk-gsd.dt$. Sample: M-09. Table of raw data:


MidPt(phi)
.625
.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
PAN
MidPt(phi)


Sieve(phi)
.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4

Sieve (phi)


Wt. (g.)
.018
.397
4.059
15.989
16.016
19.894
16.369
14.007
8.514
2.766
1.514
.351
.071
.013
.025
Wt. (g.)


CumWt(g.)
.018
.415
4.474
20.463
36.479
56.373
72.742
86.74901
95.26301
98.02901
99.54301
99.894
99.965
99.978
100.003
CumWt(g.)


Wt(Dec.)
.00017
.00396
.04058
.15988
.16015
.19893
.16368
.14006
.08513
.02765
.01513
.0035
.0007
.00012
.0002
Wt(Dec.)


Cum.Wt(D)
.00017
.00414
.04473
.20462
.36477
.56371
.72739
.86746
.9526
.98026
.9954
.9989
.99961
.99974
.9999
Cum.Wt(D)


Cumulative weight, including pan (if any): 100.003 grams.

Panel 2

Results calculated by GRAN-7. File: kirk-gsd.dt$. Sample: M-09
Several versions are given below, with the pan fraction either
omitted, or located at different places on the phi scale. A
widely-used procedure (for moment measures) is to put it at 5 phi.
The relative dispersion is standard deviation divided by the mean.
The mean, std. dev., etc., are MOMENT (NOT graphic) measures.
Median size: 1.91 phi. Modal class: 1.75 to 2 phi.


Exclud.Pan P
Means: 1.948 1
Std.Dev.: .476
Skewness: .329
JPMaySk: .164
Kurtosis: 2.674 3
Fifth Mom.: 2.793 5
Sixth Mom.: 12.37 2
Relative dispersion: .244
Dec.Wt. 4 phi & finer: .00032
For pan fraction placed at
SD/Ku: .1577037 .1429424 .
Pan weight (grams; decimal


an @ 5
.949
478
384
192
.031
.334
8.751
.246


Pan @ 5.5
1.949
.479
.418
.209
3.351
8.244
53.089
.246


Coarsest sieve (phi):
5 phi, and at 5.5 phi:


Pan @ 6
1.949
.48
.464
.232
3.841
13.294
101.48
.246
.75


Mn/Ku: .6430221 .5816174
fraction; %): .025 ; .0002


Pan @ 7 phi
1.949
.482
.594
.297
5.52
33.886
15 338.903
.248
No. of sieves: 14


.02


Figure 17. Example of granulometic output from GRAN-7 for sample M-09 from
the Great Sand Dunes, central Colorado.


Lecture Notes


James H. Balsillie










W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


On the histogram,
The column on the
0 10
Phi
+
1+
+


2

+
3
+
+
4+
PN +
0 10
The column on the


Panel 3
values > 69% show as 69%. File: kirk-gsd.dt$. Sample; M-09
left shows screen sizes, not mid-points, in Phi.
20 30 40 50 60 %


+
+






20 30 40 50 60 %
left shows screen sizes, not mid-points, in Phi.


PAN


Panel 4
Next: Probability (decimal wt. vs Phi size). File: kirk-gsd.dt$.
The column on the left shows screen sizes, not mid-points, in Phi.
0.1 1 2 5 10 20 30 50 70 80 90 95 98 99
: : : : : ~:: : :


Sample: M-09

99.9 %


-Eolian Hump


PAN

0.1 1 2 5 10 20 30 50 70 80 90 95 98 99 99.9


This is GRAN-7.
Coarsest sieve:


Sieve interval: .25 File: kirk-gsd.dt$. Sample: M-09
.75 phi. Pan contents (g., %): .025 .0002


Figure 17. (cont.)



particularly good for a mature beach sand. Mature beaches have ao values of from 0.30 to
0.50 0; the lowest ao value WFT has seen is about 0.260.


The cumulative probability plot of panel 4 shows the surf-break. The surf-break
inflection point moves with time ... the plot, therefore, is a snapshot in the history of the
evolution of the sample. With high enough wave energy or with sufficient time, the inflection
point will move to the left and off the plot. Note, also, that there is a tail of fines. Hence, the
sample is one reflecting low wave energy. The surf-break occurs at about 4.5% with the
settling curve comprised of less than 1 % of the sample. Hence, we are looking at only about
5% of the sample. By looking at a multitude of samples we can attempt to clarify our


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995




interpretations.


Example 3: The German Darss


The Darss, a German federal nature preserve, is located in Germany fronting on the
Baltic sea, just to the east of the old East-West German border. It is attractive to study
because it is not subject to open Atlantic Ocean waves. A series of 120 to 200 ridges
comprise the plain, although it is not possible to count all the ridges because wind work has
been pervasive. The feature has been interpreted by many investigators (-20) to represent




I .


This is GRAN-7.


This is GRAN-7.

MidPt(phi) Si
.375 .5
.625 .7
.875 1
1.125 1.
1.375 1.
1.625 1.
1.875 2
2.125 2.
2.375 2.
2.625 2.
2.875 3
3.125 3.
3.375 3.
3.625 3.
3.875 4
4.125 4.;
MidPt(phi) Si


The data source is stv-wei.dt$.


File: stv-wei.dt$.


eve (phi)

5

25
5
75

25
5
75

25
5
75

25
eve (phi)


Wt. (g.)
.021
.146
.348
1.003
3.543
8.487
10.821
13.819
7.208
3.383
1.579
.311
.066
.017
.013
.034
Wt. (g.)


Panel I
Sample: Centr.16.

CumWt(g.)
.021
.167
.515
1.518
5.061
13.548
24.369
38.188
45.396
48.779
50.358
50.669
50.735
50.752
50.765
50.799
CumWt(g.)


02-24-1995


Table of raw data:


Wt(Dec.)
.00041
.00287
.00685
.01974
.06974
.16707
.21301
.27203
.14189
.06659
.03108
.00612
.00129
.00033
.00025
.00066
Wt(Dec.)


Cum.Wt(D)
.00041
.00328
.01013
.02988
.09962
.26669
.47971
.75174
.89363
.96023
.99131
.99744
.99874
.99907
.99933
1
Cum.Wt (D)


Cumulative weight, including pan (if any): 50.799 grams.

Panel 2

Results calculated by GRAN-7. File: stv-wei.dt$. Sample: Centr.16
Several versions are given below, with the pan fraction either
omitted, or located at different places on the phi scale. A
widely-used procedure (for moment measures) is to put it at 5 phi.
The relative dispersion is standard deviation divided by the mean.
The mean, std. dev., etc., are MOMENT (NOT graphic) measures.
Median size: 2.01 phi. Modal class: 2 to 2.25 phi.


Exclud.Pan Pan @ 5 Pan a 5.5 Pan 6 6
Means: 2.004 2.004 2.004 2.004
Std.Dev.: .416 .416 .416 .416
Skewness: .08 .08 .08 .08
JPMaySk: .04 .04 .04 .04
Kurtosis: 3.806 3.806 3.806 3.806
Fifth Mom.: 2.208 2.208 2.208 2.208
Sixth Mom.: 33 33 33 33
Relative dispersion: .208 .208 .208 .208
Dec.Wt. 4 phi & finer: .00092 Coarsest sieve (phi): .5 No.
For pan fraction placed at 5 phi, and at 5.5 phi:
SD/Ku: .1093011 .1093011 Mn/Ku: .5265371 .5265371
Nothing in pan.


Pan @ 7 phi
2.004
.416
.08
.04
3.806
2.208
33
.208
of sieves: 16


Figure 18. Example of granulometic output from GRAN-7 for sample Centr. 16
from St. Vincent Island, Roida.


Lecture Notes


James H. Balsillie










W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


On the histogram,
The column on the
0 10
Phi :

S+
+
1
+


2


3 +
-+

4+
+
PN +
0 10
The column on the


values > 69% show
left shows screen
20 30


Panel 3
as 69%. File: stv-wei.dt$. Sample; Centr.16
sizes, not mid-points, in Phi.
40 50 60 %


20 30 40 50 60 %
left shows screen sizes, not mid-points, in Phi.


PAN


Panel 4


Next: Proba
Centr.16
The column
0.1


ability


(decimal wt. vs Phi size). File: stv-wei.dt$. Sample:


on the left shows screen sizes, not mid-points, in Phi.
1 2 5 10 20 30 50 70 80 90 95 98 99


99.9 %


Surf-Break


PAN

0.1 1 2 5 10 20 30 50 70 80 90 95 98 99 99.9 %

This is GRAN-7. Sieve interval: .25 File: stv-wei.dt$. Sample: Centr.16
Coarsest sieve: .5 phi. Pan contents (g., t): 0 0


Figure 18. (cont.)


a dune field. Ul'st (1957) trenched the Darss ridges and found low-angle, fair-weather, beach-
type cross-bedding and concluded that they were beach ridges (i.e., wave deposited) with a
top layer of eolian decoration. Zenkovich (1967), in his text Processes of Coastal
Development, noted that Ul'st investigated the Darss ridges, but persisted to view them as
dunes. [Aside: one should be very careful when using this textbook ... it is written in such
a manner that one can be easily misled.] Many of the dune proponents visually examined only
the surface and, of course, found eolian evidence. Harald Eisner, at W. F. Tanner's request,


Lecture Notes


James H. Balsillie









W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


sampled the ridges where eolian reworking appeared minimal then trenched 30 to 50 cm deep
where the samples were taken. A total of 16 samples were sent to W. F. Tanner for analysis,
the results of which are described in detail in Appendix V. Of the 16 samples, 12 had the
definitive surf-break. Only one had the eolian hump. Not one sample plotted showed fluvial
conditions, 5 samples plotted as swash, and 7 as settling. The features are, therefore, beach
ridges and not dunes.

Example 4: Florida Panhandle Offshore Data

Arthur et al. (1986) reported on offshore sediments along the northwestern panhandle
Gulf Coast of Florida. Samples were taken from 1 to 15 km offshore. Can the surf-break be
found in sediments found in fairly deep offshore coastal waters? There are two important
considerations here: 1. How deep can storm waves affect bottom sediments? and 2. Has
sea level rise during the last 15,000 to 20,000 years resulted in an onshore shoreline
transgression? The offshore sand sample data were analyzed and the surf-break inflection
was found for most of the samples (see Tanner, 1991b, Appendix VIII, p. 118).

Example 5: Florida Archeological Site

W. F. Tanner was asked to assess sediment from an archeological site on U. S. 90just
west of Marianna, FL, where there are several "Indian mounds". The State Archeologist
wanted to know why they were composed of 98% quartz sand, since such mounds are
normally comprised of shell material. The mounds were trenched. No bedding was found.
Sample analysis showed the surf-break. The mounds probably represent marine terrace
deposits reworked by eolian processes. That is, some degree of eolian reworking may not
always destroy the surf-break character of the sediments. Such destruction of the indicator
would require higher energy levels and/or time.

Example 6: Origin of Barrier Islands (Appendix VI)

Much of the work on the origin of barrier islands is in error (refer to Appendix VI
entitled Origin of Barrier Islands on Sandy Coasts (Tanner, 1990a; Appendix VI). Tanner
(1990a; Appendix VI, p. 96) presents a list and discussion of common origin hypotheses.
Felix Rizk (Appendix VI, p. 97, 2nd column, 2nd paragraph down) trenched and took 10 or
more samples from each of the two nuclei (i.e., initial vestiges of island formation). Means
of the samples from the nuclei were 0.24 mm and 0.22 mm with a slight coarsening trend in
one direction. It is generally homogenized sand, all of which looks alike. Standard deviations
(Appendix VI, p. 97, col. 2, paragraph 4) for the two areas were statistically the same.
However, these numbers which have typical values for beach sand are a little larger than the
adjacent, younger non-nuclei sediments. Hence, the sorting of the younger non-nuclei sand
has improved with time. We can draw the inference that this area has been reworked by
waves. With assurance, neither nucleus was a dune, nor was it deposited by a river.
Skewness values (Appendix VI, p. 97, col. 2, paragraph 5) are slightly negative. These values
are typical of beach or river sand deposits, but rivers can be ruled out by the above. They are
absolutely not dunes or deposits settling from water. Kurtosis values (Appendix VI, p. 97, col.
2, paragraph 6) are low to moderate, indicating low to moderate wave energy levels.
Altogether, (Appendix VI, p. 97, col. 2, paragraphs 6 and 7) the nuclei were formed by the
same agencies that formed everything else, that is, by wave activity.


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


This account is not advocating that barrier island formation, in isolated cases, cannot
occur for some of the hypotheses listed, for example, drowning of dunes. However, the
above example and data for other locales (e.g., St. Vincent Island (Appendix VI, p. 99, figure
1), and Johnson Shoal off of Cayo Costa (Appendix VI, p. 99, figure 2)) suggest that for the
majority of cases, barrier island formation occurs because of small sea level changes of one
or two meters and accompanying wave and swash activity.

Sample Suite Statistical Analysis

Please refer to Appendix VII entitled Suite Statistics: The Hydrodynamic Evolution of
the Sediment Pool (W. F. Tanner, 1991 a, [In] Principles, methods, and application of particle
size analysis. Cambridge University Press).

Let us assume that we have 20 samples taken 10 m apart and representing some
depositonal time frame, say, 10 years. Do not mix Cambrian with Devonian samples and
expect to make sense of the results.

For years in statistical pursuits large sampling statistics required the number of
samples, n, to be 30 or more. That is not required in granulometric work. For instance, n =
15 or n = 8 may be quite enough. There is a way of checking the required value of n so that
we do not have to be uncertain about it. A desirable number of sediment samples for a suite
is commonly from 15 to 20 samples.

Also, what is a reasonable sampling distance? There is a no specified distance, except
for the absurd. But, again, bear in mind that the field worker is a "prisoner" of what is
available ... one does the best that he or she can.

Suite statistics, for our 20 samples above, might, for instance, yield 20 means, 20
standard deviations, 20 skewness values, 20 kurtosis values, 20 fifth moment measures, 20
sixth moment measures, and the tail of fines. This encompasses 140 data points. If we use
the same parameters in a suite analysis, 49 suite statistics will result, more if we recombine
the original individual sample data. Therefore, there are many data with which to work.

What we are interested in is a way to examine the behavior of sample suites relative
to the individual samples. The plot of Figure 16 is an example of horrible scatter (see Tanner,
1991; Appendix VII, p. 104, second column for further discussion). There are procedures
available to permit one to break a large number of samples into smaller groups. In addition,
one can conduct repetitive recombinations of groups in order to inspect for improved grouping
of one or more of the descriptive moment measures (e.g. mean, std. dev. ... 6th moment
measure, etc.).

Please review from Appendix VII:

last paragraph of page 102,
Control factors air versus water of page 103,
Trapping phenomena beginning on the last paragraph, 1st column of page 103,
Bivariate plots on page 104.


James H. Balsillie


Lecture Notes









W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Tailof Fnes Plot: [Appendix VII, p. 105, figure
16.1].
0001 001 01 I 10
This is a plot of the suite means, p, and T. F CLOS
suite standard deviations, a, of the weight WT% I BASw,
percent that are 4 0 and finer (Figure 19). o-

The Tail of Fines Plot is successful /
because it is dependent on the aero- and o/
hydrodynamics. The suite mean separates a
large, new sediment supply (i.e., river or closed T-UE
basin sediments) from winnowing or sorting BACH
products (i.e., beach and dune sediments). The
suite standard deviation separates BAFS (i.e., Figure 16.1. The tail-of-fnes diagram. The means
mature beach and near-shore sediments) and and standard deviations of the weight percent on
large mass density differences (i.e., dune the 4 screen and finer are shown here. Four fairly
sediments) from settling and winnowed distinct number fields appear, as labeled above.
with relatively little overlap. Many suites plot
products. It is sensitive enough to distinguish neatly in a single field. In certain other cases the
between mature beach and mature dune sands, apparentambiguity may be useful; for example, a
because the number of transport events for point at a mean of 0.01 and a standard deviation of
beaches is 10s or 106 times as large as it is for 0.017 mightindicate either dneormature beach.
and not formed in a closed basin. This diagram
dunes during the annual period, commonly gives a "river" position when in fact
the river was the "last-previous" agency, but not
The Vanabity Diagram: [ Appendix VII, p. 105, the final one.
figure 16.2]. Figure 19. Tag-of-ines Plot. (From Tanner
1991a).
This plot is also based on suite statistics
(Figure 20) where:
0 1 I
o, = standard deviation of the individual sample
means, and 05 OFFSHORE S
WAVE
oa = standard deviation of the individual sample 02 SH
standard deviations. Oe / GRA
TRM.
Why is the lower-left to upper-right band so
broad? One might argue that there is lot that we do
not know about this diagram. Richard Hummel of the DUNE
Alabama State Survey has done some very good
work with this plot, and suggests we are missing Figure 16.2. The variability diagram, showing the
some transporting agencies. suite standard deviation of the sample means and
of the sample standard deviations. Except for the
extremes, the plotted position indicates two possi-
The diagonal lines stop in the middle. ble agencies (such as swash or dune). The decision
Samples can, therefore, overlap and one may not between these two can be made, in most instances,
Sw ic a is t i i by consulting other plots (such as Fig. 16.1). This
know which agency is the primary transporting diagram considers specifically the variability, with.
agent. Other plotting tools, therefore, would have to in the suite, from one sample to the others.
be consulted to clarify which is the transporting
mechanism. Figure 20. The Variabity Diagram.
(From Tanner, 1991a).


,


Lecture Notes


James H. Balsillie






W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Skewness Versus Kurtosis Plot: [Appendix VII, p. 106, figure 16.3].


Figure 163. Skewness vs. kurtosis. The suite
means of these two parameters are used. Positive
skewness, as used here, identifies a geometrically
distinctive fine tail; if there is also a distinctive
coarse tail, it is the smaller (weight percent) of the
two. The closed basin (settling) environment typi-
cally produces an obvious fine tail. much more so
than beach or river sands. Eolian sands commonly
have, instead of a well-developed fine tail, a feature
called the eolian hump (cf. Fig. 16.5), which the
skewness indicates in the same way as it does a
distinctive fine tail. Therefore the two tend to plot
together. Negative skewness identifies a distinctive
coarse tail, either fluvial coarse tail (large K) or
surf"break" (=kink in the probability plot; K in
the range of 3-5 or so). Many river and beach
suites appear in the same part of the diagram but
are ordinarily easy to identify by using this fig-
ure first and then the tail-of-fines diagram (Fig.
16.1).
Figure 21. Skewness vs. Kurtosis Plot. (From
Tanner, 1991a).


Table 5. Talying the granulometric results.
River Beach Settling Dune

X
x x
x x
xX X
X


Diagrammatc Probabty Plots: [Appendix VII, p. 108, figure 16.5].

These plots are for individual samples (Figure 22). Note the eolian hump of sample 2.
Question: the swash zone sand dries out and a relatively strong wind removes the top layer


Suite averages for the skewness (Sk)
and Kurtosis (K) are plotted in this diagram
(Figure 21).

River .......
Beach
Eolian & Settling -------

Beach and river sands tend to be
skewed to the coarse, i.e., Sk < 0.1.

Settling tail or closed basin sediments
are skewed to the fine, i.e., Sk > 0.1.
Eolian sands also occur for Sk > 0.1 as
explained in text (Appendix VII, p. 106, last
paragraph, 1st column).

There is no guarantee that this plot
will produce definitive results. That is why
a number of different plotting diagrams for
process identification have been compiled.
Collective consideration of them together
will more nearly allow one to ferret out the
most plausible explanation. Using these
plots one can tally the results, for example
see Table 5. While confusing results can
certainly occur, it is generally the case that
the tally is never close, such as identification
of the beach transpo-depositional
mechanism above.


James H. Balsillie


Lecture Notes








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


and transports it 4 m down the beach where it is deposited. At what split second in time did
it quit being beach sand to become eolian material? That is, is there any place where one can
identify a point in time between the two deposits where the sediment changed from beach to
eolian sand? The answer should clearly be NO! There is no razor-sharp demarcating line or
point ... it is gradational. Wind tunnel laboratory results confirm the process. In fact, the
results are normally clearer than one might expect, given that the philosophical concerns are
not clear. One has to realize that the previous transpo-depositional history of a sample is
bound to characterize any sample and to show up in these plotting tools. Even so W. F.
Tanner has been delighted with the success of these analytical diagrams.


Figure 165. Diagrammatic probability plots. (1) The Gaussian, rare among sands. (2) The distinctive eolian
hump (E.H.) is common, but not universal, in dune sands, and so far has not been observed in other sands that
did not have any previous eolian history. (3) The surf break (S.B.) has been demonstrated to form in the :urf
zone, as the sorting improves. (4) The fluvial coarse tail is geometrically distinctive, but cannot be distin-
guished in every case from the surf break. (5) This curve has both a fluvial coarse tail and a fluvial fine tail;
the central segment (C.S.) is the line between the two small squares. However, it is not the modal swarm (see
text). (6) The modal swarm (a grain size concept, not a graphic one) obtained by subtraction from the original
distribution; it shows the actual size distribution of the central segment (graphic device) of line 5. Lines of
these kinds help one visualize the effects summarized in the bivariate plots.
Figure 22. Diagrammatic Probabity Plots. (From Tanner, 1991a).



Aside: sampling of marine sediments is not easy. It is highly difficult to sample laminae.
Grab samples from ship board are really not ideal. Rather, an experienced bottom diver is
required.

The SegmentAnalysis Tiangle: [Appendix VII, p. 106, figure 16.4].

This is a very powerful tool. It cannot be plotted by computer program; data must be
subjectively determined and then plotted (see Figure 23). Values are determined from the
probability plot (see Figure 24) for each sample. There must first be identified a centrally
located absolutely Gaussian, straight-line segment. Now, we want to identify the weight
percentages for the coarse tail (CT) and fine tail (FT). The value to be plotted on the Segment
Analysis Triangle, SA,,,, is calculated as:


Lecture Notes James H. Ba/si/lie


James H. Balsillie


Lecture Notes







W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995




NO SA, = B- A
TAILS

SEGMENT.I, Eon o* where A and B are the respective weight
ANALYSIS, Ealion
T.% percentages.

o. Labels on the Segment Analysis Triangle
/ include SI for river silt and CL for river clay, or a
RIVER closed basin such as an estuary, lake or lagoon,
Sl.OCSEC....LO etc. Note that the river SI and CI and closed basin
BASIN sediment field overlaps the dune sediment field. If
FINE i 0 0 CO"ARSE the eolian hump does not show up in the
TA'. .n TA L probability plots of the samples, it is unlikely that
the suite represents dune sediments.
Figure 16.4. The segment analysis triangle. The
procedure for picking segments and obtaining the
necessary numbers is outlined in the text. The apex Coarse
is characterized by very small or negligible distinc-
ive tails C'no tails"), and the base (not shown) Must be an absolutely
connects distinctive coarse tail (to the right) with straight-line segment
distinctive fine lail (to Ihe left). Four diftcrcnt en-
vironments are distinguished reasonably clearly, Phi
except for one area of overlap in thiareara one ex-
amincs the probability plots for the colian hump
in order to see which of the two is indicated.
OT Fr
Fine -CT,
Figure 23. The Segment Analysis 0.1% A 50% B 99.9%
Triangle. (From Tanner, 1991a).
Figure 24. Determination of values for A and B for
evaluation of the Segment Analysis Triangle.



Approach to the Investigation

It should be obvious to the geologist with any experience that he or she needs all the
help that he or she can get. There are often no easy answers in pursuing matters of a
technical nature, particular when we first are introduced to the field locatity that might be
of interest. There are, when undertaking such an investigation, some questions that we would
like to address.

The Field Site:

The first endeavor is to try to identify just what we are dealing with. Examples might
include:

B Beach
MB Mature Beach
ED Eolian Dune (or ash, loess, etc.)
GLF Glacial-Fluvial Deposit


Lecture Notes


James H. Balsillie






W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


S Settling Basin
U Unknown

The stratigraphic column, both the target and non-target stratigraphy, can often be
useful to provide clues to the problem at hand. Classical geology dictates that the present is
the key to the past. In many cases, the corollaries that the past is the key to the present and
both the past and present are the key to the future yields successful results. It is also
important that any non-recognizable aspects of the stratigraphy are noted.

The Paleogeography:

The second pursuit is to make a statement or statements about the paleogeography of
the site, if that is at all possible. For example, if the deposit is identified as beach material it
would be highly useful to discern in which direction lay the upland and in which direction lay
the sea. Other similar determinations should be made depending upon the paleoenvironment
identified.

Cross-plots, such as those of Figure 19 through 23, are useful tools to identify transpo-
depositional sediments such as those above, ..., e.g., B, MB, ED, GLF, and S.

Hydrodynamics:

It is straightforward procedure to plot our data using a geological mapping format (e.g.,
grain size, heavy mineral content, etc.). Remember, however, that when dealing with sand-
sized sediments, the central portion of the distribution tells us little about the sample. It is,
rather, the tails of the distribution that provide us with useful information.., a lesson Doeglas
taught some 50 years ago!

By way of contrast, envision the scenario of the western flank of the Andes Mountains
in which a talus slope near the upper base is comprised of 1 to 2 meter diameter boulders.
Farther to the west and down-slope on the river fan, sediment size diminishes greatly. The
sediment size gradient, therefore, is highly significant. For our endeavors, however, such a
gradient is not available, since we are working within the sand-sized range. If we take our
clue from Doeglas and what we have learned about the tails of the sand-sized distribution and
moment measures, we need to be looking at the 3rd moment measure or skewness, and the
4th moment measure or kurtosis. Specifically, as it relates to hydrodynamics, let us look at
the kurtosis.

The Kurtosis

The bulk of the work on the relationship between hydrodynamics and kurtosis has been
conducted on beaches, in particular, Florida beaches. Specifically, kurtosis and
hydrodynamics can be related in terms of the energy levels associated with the
hydrodynamics. Hydrodynamic force elements inducing a sedimentologic response include
characteristic wave energy levels for coasts, long-term sea level rise, seasonal changes, and
short-term storm tide and wave impact events.


Lecture Notes James H. Balsillie


Lecture Notes


James H. Balsillie







W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Kurtosis and Wave Energy Climates:

Let us denote average wave energy in terms of wave height which, according to
classical Airy or Small Amplitude wave theory, is given by:

E= H2

Gulf "' "
Guf Atlantic
of --" Ocean in which E is the wave energy
Mexico density per unit surface area,
Mexico. pf is the fluid mass density, g

H s 0.5 m "H v 1.0 m is the acceleration of gravity,
S .and H is the average wave
K > 3.5 height. Hence, simply put for
3.0 < K < 3.5 2
S3.0 < < 3 diagrammatic uses, E cH 2.
Let us also denote the kurtosis
/ as K. Consider the following
five (5) example cases.
Figure 25. Characteristic average wave heights and kurtosis Case 1. The Lower
values for the coasts of lower peninsular Florida. Peninsular East and West
Coasts of Florida. The
prevailing wind direction for the lower peninsula of Florida is from the east. Noting that the
Atlantic has a larger fetch (i.e., length over which the wind acts to generate gravity water
waves) than the Gulf of Mexico, we
would expect to find larger waves
along Florida's east coast, lower ;
waves along the lower Gulf Coast '
(Figure 25). In fact, the average Nwy 1 ,I
wave height along the east coast is
typically about 1 m. Along the swe
lower Gulf Coast (Tampa to Naples)
waves are generally 0.5 m or less. Skagerak
Kurotsis values for the east coast
range from 3.0 (perfectly Gaussian)
to 3.5, while along the lower Gulf K Nort Sm.ler
is greater than 3.5. Sea Larg K
Larger H Kattega
Case 2. Denmark. The fetch SmK D ark
is narrow for the Kattegat (Figure
26) separating Denmark and Sweden
and characteristic wave heights are
smaller than for the North Sea where u
the fetch is only slightly sheltered by
the British Isles but not from Figure 26. Characteristic average wave height and
northwest winds. The result is that kurtosis conditions for opposing coasts of Denmark.
Danish east coast sediments have a


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


larger characteristic
kurtosis value (lower wave
energy) than the Danish
west coast beach
sediments (higher wave
energy).

Case 3. Captiva
and Sanibel Islands, Lower
Gulf Coast of Florida.
Cases 1 and 2 represent
coastal reaches of regional
extent. Let us look at
some specific cases
representing more localized
coastal reaches.


I Mexico K > 20.0| There are no
Figure 27. Wave energy kurtosis behavior for the Captiva- quantified wave height
Sanibel Island coastal reach. data for the Captiva-
Sanibel Island coastal
reach. Wave refraction
analyses, however, show that wave heights along the northern portion of the reach are
largest. As the coastal curvature trends to the southeast and east, sheltering occurs and


characteristic wave heights significantly
diminish (Figure 27). Corresponding
response of the kurtosis is also
significant (see Tanner (1992a, fig. 1)
for quantitative details of the kurtosis
data). It is to be noted that beach
sediments along Sanibel and Captiva
can be comprised totally of carbonate
material. Care was taken, therefore,
that the samples for this study were
comprised of as much siliciclastic sand
as was possible.

Case 4. Dog Island, eastern
Panhandle Coast of Northwest Florida.
This example is for a reach located
immediately adjacent to the classical
zero energy Big Bend coast of Florida
(Tanner, 1960a), located at the eastern
end of the northwestern Panhandle Gulf
Coast of Florida. Wave heights and
energy are low. Results should,
therefore, be quite sensitive regarding
the interaction of wave forces and


Island

I HE
I \

V
*1 I
*/ \ .
/
K .

DD= drift divide '
HE = highest energy
Figure 28. Correlation between kurtosis and wave
energy in terms of longshore transport energies for
Dog Island, Florida. (After Tanner, 1990b).


Lecture Notes James H. Balsilie


Wave height b e
diminishes from
NW to SE; K increases --


\
Lowest Waves


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


divergence or "drift divide" near the eastern central portion of the island (Figure 28). A
combination refraction-longshore transport analysis confirms that lowest wave energy occurs
at the drift divide (point DD). Highest energy levels occur at point HE. The refraction analysis
attenuates shoaling waves, while the longshore transport equations are wave height driven.
Forty-four lower beach sand samples were collected and analyzed (Tanner, 1990). Once again,
kurtosis values are largest for the low wave energy portion of the island, and are smallest for
the higher wave energy portion of the island.

Case 5. Laguna Madre, Texas. The southern part of Laguna Madre is located near
Boca Chica east of Brownsville, Texas. This part of the lagoon is separated from the Gulf of
Mexico by a long, narrow, sandy peninsula. Two modern beach samples collected from the
lagoon side had a kurtosis of 4.11, and 10. Adjacent and slightly older lagoon-side beach
samples had kurtosis values of 4.2 or greater. Samples from beaches fronting on the Gulf of
Mexico, however, had an average kurtosis of 3.39. The peninsula is a product of high-energy
processes, as is indicated by the lower kurtosis.

Kurtosis versus Seasonal and Short-Term Hurricane Impacts:

While we should certainly desire more data on seasonal effects and extreme
climatological impacts, there are not much data yet amassed. Even so, the following should
pique one's interest!


Rizk (1985) studied beach
sediments along Alligator Spit,
located to the south of
Tallahassee, FL and some few
kilometers to the northeast of .
0.8
Dog Island. Again, overall wave
energy is not high for the reach. 0.6
In addition, the beaches of 0K
Alligator Spit had not experienced 0.4
the effects of hurricane impact in
9 years. Rizk found a correlation 0.2
between kurtosis and wave
energy levels, the latter being 0
higher during the spring than the
summer. Hence, kurtosis can
distinguish seasonal effects. In Figure 29.
addition, Figure 29 indicates that effects an
the standard deviation of the Kurtosis v
suite of samples, aK, also deviation
correlates with extreme event kurtosis. i
energy conditions, being smaller
in value during higher energy
conditions, ..., larger during lower energy con'


No
Hurricanes
in
9 Years


(3.72)^\Sunmmer
/ I
/ I (
OSpring I
(3.13)



/
I


(3.41).
/3.39)
/
/
/
413.39) -


H. Elena H. Kate
Aug Sep Late Nov
1985 1985
Time
Kurtosis data versus energy levels for seasonal
d hurricane impacts for Aigator Spit, Forida.
values are in parentheses, oK is the standard
of the kurtosis values of the sample suite
After Tanner, 1992a).


i \
I (
/ (
d(3.25)


Two successive hurricanes impacted the area in 1985 (see Figure 29), and ensuing
sedimentologic response was monitored by Rizk and Demirpolat (1986). During high energy


James H. Balsillie


Lecture Notes







W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


sedimentologic response was monitored by Rizk and Demirpolat (1986). During high energy
conditions of Hurricane Elena kurtosis values were low compared to conditions weeks after
the event. Note that shore-incident storms or hurricanes, not only produce exceptionally high
waves, but also storm tides (which being a super-elevated water surface) allow for even higher
waves (since waves are depth limited) closer to shore. Kurtosis values immediately after
impact of Hurricane Kate and several weeks later are not different. Why this is so, is not
clearly understood. Even so, standard deviations of the sample suites, oK, do show a
correlation. Hence, UK is an additional tool that can provide valuable information.

Kurtosis and Long-Term Sea Level Changes:

Beach ridges are formed by small couplets of mean sea level rise and fall (10 to 30 cm).
In order to appreciate how beach ridge formation occurs, there must be some understanding
of coastal, beach, nearshore, and offshore dynamics. First, in the topographic sense, slopes
for nearshore and offshore profiles are very gentle. Relief of any proportion at all does not
occur until the shoreward portion of the nearshore, the beach, and the coast are encountered.
Second, where shore-propagating waves begin to be attenuated due to drag effects with the
bed is a function of the wave length. The deep water wave length, Lo, in meters is given by
Lo = 1.56 T2 where T is the wave period. The water depth where drag effects begin to occur
is approximately given by L, /2. Third, farther nearshore, waves are depth-limited. That is,
waves will distort and break according to db = 1.28 Hb where db is the water depth at
breaking and Hb is the height of the breaking wave. Finally, where breaking is represented by
final shore-breaking (i.e., the breaking waves cannot reform and again rebreak) swash runup
mechanics are important in inducing final sedimentologic transport.

Let us look at the case where there is a drop of several meters in sea level as
illustrated in Figure 30a. For the pre-sea level drop case let us suppose that waves begin to
experience bed drag at point A. There is, then, the distance a-A over which the waves will
attenuate to eventually shore-break with a breaker height of Hb. However, when sea level
drops these same deep water
waves will begin to experience
bed drag at point B which
continues for the distance b-B, a
distance that is much greater C Near-
Coast Beach Shore ( Offshore
than distance a-A. That is, theShore
longer the distance, the greater
the attenuation of the wave
height. Hence, where shore-
breaking, Hbb, occurs for the sea b A
level drop scenario, Hbb will be b H ubb B
smaller than Hb. Hence, breaker
energy levels will be less, at least
initially (i.e., a readjustment
period of approximately 2 or 3 Pre-SeaLel DropProfile
centuries might be appropriate
for the Gulf of Mexico), when
sea level drops. Figure 30a. The ittoral and offshore profile and effect of
sea level drop on wave energy levels.


James H. Balsillie


Lecture Notes









W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Let us inspect the case for
sea level rise, illustrated in Figure
30b. Just the opposite
occurs for sea level rise,Nea
compared to the sea level drop Coast Beach Shore Ofshore
scenario. The distance a-A for
the pre-rise sea level is longer
than for the b-B distance b Hbb 8
following sea level rise. a ba A
Moreover, shore-breaking wave
heights Hbb will be larger than
Hba.

If we have learned our
lessons from previous Pre-Sea LeveRiseProle
experience, it should be clear
that kurtosis values for a sea
level drop should be large and Figure 30b. The lttoral and offshore profie and effect of
kurtosis values for a sea level sea level rse on wave energy levels.
rise should be small.

St. Vincent Island, Florida, Beach Ridge Plain. St. Vincent Island, a federal wildlife
refuge, is located south of the town of Apalachicola along the eastern part of the northwestern
panhandle coast of Florida. It is comprised of a sequence of beach ridge sets ranging in age
from set A (oldest) to set K (youngest) as illustrated in Figure 31. Sets A, B, and D stand low.
Three dates are available for the island: an archeological date of older than 3,000 3500
years B. P. (before present) is found on the northwest; a C14 date of 2110 130 years B. P.
near the east coast, and historical records of pond closure of approximately 200 years for the
southern coast. Each
SVincent Sound beach ridge has been
St Vincent Sound .
repetitively surveyed and
p sampled for granulometric
2110 analysis, by different
+130 investigators. Laminar
KM o B. P samples for the seaward
0 2 4 face of each ridge (one
-' '" -- sample each) were taken
S3,000B.P- at depths of from 30 to 40
>3,000 B. -- cm. The different
Investigators did not know
G where the others had
,SP conducted work. Results
were statistically identical
GULF OF MEXI 200 B.P. for the 59 individual ridges
along the profile.
Figure 31. The St. Vincent Island beach ridge plain. (After We should expect
Stapor and Tanner, 1977). that when sea level drops,


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


A& I C
Ridge Number


Oldest


E I


10 20 30
HIGH
LEVEL



1 / \


F IG K

40 50 Youngest


LITTLE
ICE
AGE_


LOW
SEA
LEVEL


3000 2000
Approximate date (B.P) Time -
Figure 32. Plot of kurtosis versus time for sedimentologic
data from the St. Vincent Island Beach Ridge Plain.
Letters at the top of the figure identify location of beach
ridge sets of Figure 30. (After Tanner, 1992a).


for additional details). There are two (2) conclusions:


kurtosis values should increase
and when sea level rises kurtosis
should decrease. This is
precisely what happens as
illustrated by Figure 32. Time
spacing between points is
approximately 50 years. Note
that the beach ridge sets (sets are
comprised of multiple beach
ridges) each represent a different
sea level stand and differ from
one another in topographic height
by about 1 or 2 meters. Also
note that the ordinate is inverted
to simulate 1/K to directly
correlate with hydrodynamic
energy levels. Sea level changes
range from 1 to 2 meters, and the
plot includes 4 rises and 3 drops
in sea level (see Tanner, 1992a,


1. Whether there are topographic data or not, one can (based on the kurtosis),
identify when sea level rise occurred or when it fell.

2. Based on the kurtosis values, not a single value represents a storm. That
is not to say that there are not laminae where K would represent storm activity,
just that none were found. Certainly, there were storms in its 3,000-year
history ... none have as yet been isolated.

St. Joseph Peninsula Storm Ridge. However, Felix Rizk in work along St. Joseph
Peninsula, not too far to the west of St. Vincent Island, found a storm produced ridge,
amongst a beach ridge set, which is called the Storm Ridge. It's relief is about 4 meters, 20
to 25 m wide at the base. There are results for some 40 sand samples from the ridge, which
is composed of uniform bedding sloping at from 18 to 20 degrees downward in the seaward
direction. Granulometry indicates storm depositional conditions. This is the ONLY storm ridge
(not a lamina or a berm, but a complete ridge) in a beach ridge set that W. F. Tanner has
found along the coastal northeastern Gulf of Mexico. What are the chances of a storm ridge
being preserved here? Undoubtably it is much less than 1%, and one might venture it is on
the order of 0.01%.

Beach Ridge Formation Fair-Weather or Storm Deposits?:

Of all the hundreds of beach ridges investigated, only one isolated beach ridge formed
by a storm (preceding paragraph) has been identified by W. F. Tanner. However, in the
popular textbook literature there is espoused the notion that each modern beach ridge we see
today has been produced by a single storm event. In these same texts, however, it is without
exception, noted that storms erode beaches and coasts. These are diametrically opposed


3.00
K
3.25


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


outcomes. Beach ridges are, with rare exceptions, fair-weather swash deposits. They are
formed by small sea level rise followed by a small sea level drop occurring over a period of
from 10 to 50 or so years. Runup from final shore-breaking waves plays an important role,
where higher runup (larger breakers) forms the ridges and small runup (smaller breakers) forms
the swales.

Texas Barrier Island Study Conversation with W. Armstrong Price. A number of years
ago, W. A. Price had a summer contract to survey by plane table barrier islands and their
lagoonal beaches between Brownsville and Corpus Christi, Texas. Two or so months into their
work, Price and his survey crew noticed (having not been in that particular area for some time)
a beach ridge on the lagoon side of a portion of the locale. This discovery brought a halt to
field work while they re-checked their maps in order to determine if they had originally missed
the feature. Confident in their work, it was decided the beach ridge was a new feature.
Based on prevailing literature that each beach ridge is the product of a single storm, Price
checked the records and found no such occurrence. How the beach ridge formed in a month
or two is not known. However, it was not storm-produced.

Transpo-Depositional Energy Levels and the Kurtosis; and an Explanation:

From the preceding examples we can 100
draw some general conclusions. In general,
kurtosis and transpo-depositional energy
levels can be related. A diagrammatic so II Increased Settling
representation is suggested by Figure 33,
for which the energy, E, is related to the
kurtosis, K, according to:
2 Combined
K fn [E-l] K Processes
10-

where for waves E ac H2, where H is the
wave height. -- ----------
I. Representative Wave Energy
3 _K Values
Tanner and Campbell (1986) found Val
K values ranging from 3.7 to 13 for II. Mixing
beaches of some Florida lakes, which Zero High
Energy Energy
represent a combination of low wave e ed rel n etee
energy and settling mechanics. 3. G
energy levels and kurtosis.
A consistent algebraic expression
relating K and energy levels, in particular, wave energy for sand-sized and finer sediments, has
not been discovered.

What, then, is the explanation for the inverse relationship between kurtosis and energy
levels? Let us use the littoral zone as an example, one characteristically experiencing, say,
low to moderate wave energy levels. Suppose that normal wave conditions are operating
wherein shore-propagating waves break once at the shoreline. It is well known that sediments


Lecture Notes James If. Balsillie


James H. Balsillie


Lecture Notes








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


just shoreward of the breaker position (e.g., plunge point and foreshore slope) are the coarsest
sediments found along the beach and offshore profile. This occurs because finer sediments
are sorted out, and transported alongshore and offshore. The result is that the sedimentologic
distribution is compressed, leading to a peaked or leptokurtic kurtosis (K > 3.0). Suppose
that a storm makes impact. Now, energy conditions are greatly increased due to both an
increase in the water level (storm tide) and larger incident waves. In fact, because of fully
aroused seas, waves are breaking across the entire littoral zone which is significantly wider
than under normal conditions, affecting not only the nearshore, but also the beach. The result
is a significantly wide high energy expenditure zone where sediment mixing occurs. That is,
more sediment is added to the tails of the distribution, resulting in a reduction of the kurtosis
relative to normal conditions, and reaching a value of K = 3.0.

Importance of Variabity of Moment Measures
in the Sample Suite

Refer to the Friedman-Sanders plot (Figure 16). The apparent reason of this figure is
to convince the reader that such comparison does not work as an analytical tool. Let us
assume their samples were correctly taken, etc. In addition, let us look, for the moment, at
the hydrodynamic differences between beaches and rivers.

Uprush and backwash on beaches are characterized by a thin layer or "sheet" of water
1 to 5 cm thick. Hydrodynamically, this condition should be represented by very small
Reynolds numbers ( A) and very large Froude numbers ( F). River channels, on the other
hand, with much greater depths and unidirectional flow conditions, should have large X 's and
very small I's. These differences are great enough that the beach and river points of Figure
16 should not overlap. Why the overlap? There is a basic principal that requires observance:
the hydrodynamic information we obtain from granulometry is the result of the variability from
sample-to-sample within the sample suite. If the same level of energy of a force element (e.g.,
waves) is the same day-after-day-after-day, the variability between sand samples representing
daily samples should be very small. However, this is almost never the case. Rather, there is
not only turbulence but multi-story turbulence; that is, turbulence on quite different scales due
to different energy levels and features. Hence, it is desirable that there should be some degree
of variablity between parameters such as the mean or kurtosis, etc., for samples comprising
the sample suite. Therefore, Friedman and Sanders should have used averages of sample suite
parameters.

Application of Suite Statistics to
Stratigraphy and Sea-Level Changes

Refer to Appendix VIII entitled Application of Suite Statistics to Stratigraphy and Sea-
Level Changes (W. F. Tanner, 1991, Chapter 20, [In] Principals, Methods, and Application of
Particle Size Analysis. Cambridge University Press). Discussion of the rationale for Chapter
20 (i.e., Appendix VIII, this work) is given by Chapter 16 (i.e., Appendix VII, this work).

Cape San Bias, Florida [Appendix VIII, p. 116, 3rd paragraph].

The beach sands of Cape San Bias provide simple and straightforward granulometric


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


interpretations (see the reference). Let us look at a more complicated case.

M6dano Creek, Colorado [Appendix VIII, p. 116, last paragraph].

This locality was selected for study to avoid the charge of looking only at simple or
easy examples. It is not an easy example.

M6dano, pronounced MED (as in ED)
- ANO, is Spanish for "sandy place".
M6dano Creek, located in central Colorado, PrevallingWInd
flows through Great Sand Dunes National
Monument in a southerly direction along the
eastern side of the sand dunes (Figure 34).
The dunes have a relief of some hundreds of sai
Rocks
feet. To the east of the creek lies an area of W Gre Sand Dunes Cryalln E
crystalline rocks. The creek bed, which is
very flat because it is composed of quartz
sand with no binding fines (i.e., silts or Mdano reek
clays), is about 20 meters wide with water
depths of only about 2 cm. Prevailing
winds from west to east provide one source Fgure 34. Conceptualzed cross-section of
of sediments to the creek. The other is the the Great Sand Dunes and M6dano Creek
creek itself. (drawing not to scale).

Sand samples (23, which is a large
number of samples, rarely are this many needed) from the Great Sand Dunes, using plotting
techniques of Figure 19 through 23, confirm eolian transport and deposition. Note also, using
the diagrammatic probability plot (Figure 22), only 1/4 to 1/2 of the plots need to show the
eolian hump to confirm eolian processes. The creek samples show a faint but sharply
developed fluvial coarse tail. If the creek sands were lithified and sampled in section, the
environmental intrepretation would probably be dune, but some minor fluvial influence should
be evident... remember, this is a very shallow creek not a river of consequential dimensions.
Hence, we should be looking for subtleties. One might consider these to be coastal dunes.
However, homogeneity of parameters for the suite of samples is greater than one would find
in coastal environments, and they should be recognized as non-coastal eolian sediments.
Greater homogeniety for eolian transport should occur because of the greater mass density
differential between air and quartz, than it is between water and quartz. Even so, swash zone
sediments do also show remarkable homogeneity due to the number of uprush and backwash
events that occur.

Note also the Tail-of-Fines Diagram (Appendix VIII, p. 117, figure 20.1) and The
Variablity Diagram (Appendix VIII, p. 117, figure 20.2). Do these plotting techniques (i.e.,
Figures 19 through 23) plot with 100% assurance? Note that the river, R, suite results
misplot on figure 20.2 (Appendix VIII, p. 117). So, they do not always plot with total
success. Individual plotting tools appear to have maximum success rates of from 80% to
90%. However, taken all together, the diagrams have a success rate of from 90 to 95%.

The Suite Skewness Versus Suite Kurtosis Plot (Appendix VIII, p. 120, figure 20.3)


James H. Balsillie


Lecture Notes






W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


does not allow one to distinguish fluvial from beach sands, but does allow one to distinguish
between eolian and hydrodynamic influences.

St. Vincent Island Beach Ridge Plain

Figure 20.4 of Appendix VIII, page 121, is an example from computer program LINEAR
for sediment samples from beach ridges 1 through 37 (the older ridges) for St. Vincent Island.
The plot comprised of $ represents a 3-point floating average for 1/K. The program identifies,
based on a mean/kurtosis quotient of 0.68, where sea level should be low by the "LOW?"
designation which can be confirmed from topographic data for beach ridge set elevations.
Other parameters which also correlate with changes of sea level stands are the quotients
mean/kurtosis and standard deviation/kurtosis, and differences of the standard deviations.
Beach ridge set sedimentologic means and set means of the standard deviation also provide
information. These are discussed on page 120, 2nd column of Appendix VIII.

The Relative Dispersion Plot

The Sediment Analysis Triangle is again discussed on page 121 of Appendix VIII. An
additional interpretative aid is provided by the Relative Dispersion Plot (Appendix VIII, p. 122,
figure 20.6) shown here as Figure 35. The relative dispersion, R. D. (also known variously as
the coefficient of variation), is given by:

R.D. = Standard Deviation __
Mean M# 10


If the standard deviation is large because the mean is large, one does not want to interpret the
result in terms of the scatter. The relative dispersion eliminates this effect. Two parameters
are calculated for use in the Relative Dispersion Plot. The relative dispersion of the means,
p*, is given by:


003 005 O.I 02
04 "\ r- B
// in which o, is the standard deviation of the
0 / means of the suite samples, and p, is the
S S mean of sample averages comprising the
ci / suite. The relative dispersion of the standard
." deviations, a*, is evaluated by:

o*
Figure 20.6. Relative dispersions of means and /a
standard devimaionsshowing settling (S), river (R),
beach, and don areas. There is a wnal overlap a
two places. See Figure 20.1 for key. where oa is the average standard deviation of
figure 35. The Relative Dispersion Plot. (From the sample standard deviations comprising
Tanner 1991b. the suite, and pr is the mean value of the


James H. Balsillie


Lecture Notes






W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


standard deviations of the suite samples.

Note from Figure 35 that there are some small regions that overlap. Even so, the
Relative Dispersion Plot provides an additional and useful analytical tool. Again, these plotting
tools ... Figures 19 through 23 and Figure 35 and computer tools such as GRAN-7 ... when
the results are tallied, have never resulted in a tie between transpo-depositional agencies. A
predominant mechanism has always surfaced to identify the last mode of the depositional
environment. Copies of these working plotting tools (and a few others which have merit) are
provided in Appendix IX.

The SUITES Program

The SUITES computer program, written by W. F. Tanner, provides the means for
computing suites statistics and for assessing the results. The program requires stored output
generated by the GRAN-7 computer program. Following are examples.

Example 1. Great Sand Dunes, Colorado.

Figure 36 represents SUITES output for the Great Sand Dunes just to the west of
M6dano Creek, Colorado. There are 21 samples. Notice from panel 1 that the samples are
so "clean" that there is no tail-of-fines. Inspect the 2nd panel entitled "suite homogeneity".
Plotted values are much less than 0.5 a. This is marvelously good homogeneity. Good
homogeneity would occur near 0.5 a. Even for excellent or good homogeneity outliers are
possible. Consistently poor homogeneity, or heterogeneity, e.g., from high energy rivers,
glacial-fluvial deposits, etc.), would exceed 0.5 a. In panel 3, the vertical columns contain
the basic parameters that we are summarizing in the SUITES program. The horizontal lines
are suite means, standard deviations, kurtosis, etc. of the basic data. The last (4th) panel
provides an environmental analysis. It states the procedures used and assesses 6 commonly
encountered sedimentologic depositional environments, i.e., dune, mature beach (MB), river
(Riv), settling from relatively still water (Sett), tidal flats (TFlat), and glacio-fluvial (GLF). A
capital X signifies assured environmental identification of the transpo-depositional
environment, a lower case x indicates less assured identification. The highly diagnostic eolian
hump is identified from the probability plot and interactively noted in the data entry portion of
the SUITES program. The overwhelming evidence identifies that the deposit is, indeed, eolian.

Example 2. Storm Ridge, St. Joseph Peninsula, Florida.

Felix Rizk found the St. Joseph Peninsula Storm Ridge locality. W. F. Tanner sampled
the deposit. This storm deposited ridge described previously (p. 34) is located along the
central portion of St. Joseph Peninsula (see Figure 41 for an approximate location). Suite
results are given by Figure 37. Rizk took his samples in a vertical direction (14 or 15
samples), which meant that they represented the difference between the upper and lower
portions of the swash resulting from final shore-breaking storm wave activity. W. F. Tanner,
however, re-sampled (21 samples) the ridge in a horizontal direction to look at the middle or
central portion of swash/runup force element activity. The results provided more continuity.
Panel 2 indicates very good homogeneity, internal to which there is variability and, therefore,
a good suite of samples. [NOTE: the computer file extension .5P5 indicates that the original
data source generated from GRAN-7 contained 5 parameters with the pan fraction


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995





This is SUITES. Data source: kirk-gsd.7p5. No. of Samples: 21 02-24-1995

This program produces suite, or group, statistics for a suite, or set, of
samples, presumably all representing the same depositional environment.
Panel

Tabulation of data:


Mean
2.18
2.161
2.214
2.14
2.167
2.218
2.208
1.929
1.949
1.872
1.938
1.966
2.032
2.039
1.856
1.825
1.835
1.88
1.877
1.94
1.967
Mean


Std.Dev. Skewness Kurtosis
.477 .5 4.321
.518 .337 3.128
.486 .632. 4.527
.434 .39 4.936
.514 .636 4.644
.511 .528 4.264
.494 .537 4.413
.5210001 1.092 7.138
.478 .384 3.031
.499 .592 3.051
.504 .501 3.107
.451 .541 3.556
.445 .283 3.047
.486 .446 3.208
.425 .677 4.043
.431 .638 3.498
.378 .766 3.573
.466 .277 2.728
.477 .489 2.904
.409 .397 2.894
.434 .168 2.967
Std.Dev. Skewness Kurtosis

Panel 2


5thM.M.
10.369
3.139
11.631
14.224
12.728
10.513
10.842
32.523
5.334
6.356
5.79
7.2
2.583
6.01
6.289
5.567
6.642
2.204
3.611
2.9
1.453
5thM.M.


6thM.M.
62.935
19.1
67.575
106.378
71.723
60.682
65.12
189.064
28.751
28.967
27.861
39.116
16.771
32.501
33.716
21.791
24.372
11.996
14.221
14.759
14.104
6thM.M.


T.of F.
.00257
.00104
.00257
.00109
.00305
.00264
.00226
.00451
.00032
.00043
.00038
.00031
.00001
.00041
0
0
0
0
0
0
0
T.of F.


Suite homogeneity, in terms of departures of sample means and
standard deviations from the suite mean values (of means & std.devs.)
as an evaluation of uniformity. Crosses represent numbers on far right.
Mean and Std. Dev. of Means: 2.009 .135 and of Std.Devs.: .468 .038


Dep.of Std.D.
.053
.05
.046
.042
.036
.031
.025
.018
.018
.009
.009
.009
-.003
-.017
-.024
-.035
-.035
-.038
-.043
-.059
-.091
Dep.of Std.D.


Dep. of Mean
-.082
.15
.157
.208
-.072
-.138
.197
.203
.028
-.062
-.134
.171
-.13
-.044
.023
-.044
.13
-.186
-.154
-.071
-.175
Dep. of Mean


-.5


Evaluation of homogeneity. Crosses represent numbers on far right.
Outliers, if any, should be obvious. Data Source: kirk-gsd.7p5
If any point needs to be removed from the suite, the program should
be run again with a reduced number of samples.

Figure 36. Example of SUITES output for the Great Sand Dunes, central Colorado.


Lecture Notes James H. Balsillie


Sample
T-01
T-02
T-03
T-04
T-05
T-06
T-07
M-08
M-09
M-10
M-11
M-12
M-13
M-14
B-15
B-16
B-17
B-18
B-19
B-20
B-21
Sample


Std.Dv.
.521
.518
.513
.51
.504
.499
.493
.486
.486
.477
.476
.476
.465
.451
.444
.433
.433
.43
.425
.409
.377
Std.Dv.


James H. Balsillie


Lecture Notes










W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


This is SUITES. Results: ane3

The sequence of results, for each parameter such as the mean, is:
six moment measures, then percent on the 4-phi-sieve-and-finer.
That is, the first line refers to the mean of the means, mean of
the standard deviations, mean of the skewnesses, etc.


Source of data kirk-gsd.7p5.

Means Std.Dev.
Mean of the: 2.009 .468
Stnd. Dev.: .135 .038

Skewness: .316 -.541

Kurtosis: 1.585 2.452

Fifth Mom.: .879 -3.408

Sixth Mom.: 2.883 9.721
18.495
Rel.Disp.: .067 .082


N= 21

Skewn.
.514
.193

.908

4.688

10.218

35.484

.376


SSamples, 1 to

Kurtos. 5th.M.M.
3.76 7.995
1.005 6.547

1.74 2.404

6.388 9.579

20.345 35.047

68.628 131.71

.267 .818


21

6th.M.M.
45.309
40.347

2.202

8.048

27.651

98.046

.89


T.Fines
.001
.0013

1.155

3.195

7.165



1.268


Invrtd.R.D.: 14.838 12.184 2.657 3.74 1.221 1.122 .788
StdDev/Ku. = .124 Kurt./Mean = 1.871 .
T.of F. Mns & StdDevs as Percent: .1 ; .13
Mn & StdDev of Mn/Ku & of SD/Ku: .534 .108 .124 .028

The Relative Dispersion (or Coefficient of Variation) is the
Standard Deviation divided by the Mean.
Panel4

The primary use of the next display is to minimize the weight of certain
interpretations (e.g., no X's). Of those that are left, a single line
with 2 X's must not be taken to demonstrate either one alone; FIRST,
identify SINGLE-X lines and their site meanings. NOTE that the
Tail-of-Fines tends to identify the last-previous agency.
For best results, plot numerical data by hand on proper bivariate charts.

MB=Mature Bch; Sett=Settling (Closed Basin); Tflat=Tidal Flat; GLF=Glacio-Fluv.
Parameter (below) Environment: Dune MB Riv Sett TFlat GLF
Procedures giving 1 or 2 answers: . . . . .

Mean of the Skewness: x x
Variability diagram: x x
Procedures generally giving one answer: . . . .
RelDisMn vs RelDisStdDev: X
Mean of the Tails-of-Fines: X
StdDev of Tail-of-Fines: X
Tail-of-Fines diagram: X
Inverted RelDisp (Sk vs K; Min. usefulness): x
Eolian hump (definitive!): X


This is SUITES. Data source: kirk-gsd.7p5.

The End.


N 21 1 to 21 02-24-1995


Figure 36. (cont.)


Lectue Noes Jmes H Ba/i/li


Lecture Notes


James H. Balsillie









W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995





This is SUITES. Data source: stormrdg.5p5. No. of Samples: 21 02-27-1995

This program produces suite, or group, statistics for a suite, or set, of
samples, presumably all representing the same depositional environment.
Panel

Tabulation of data:


Sample
SJ89-20
SJ89-21
SJ89-22
SJ89-23
SJ89-24
SJ89-25
SJ89-26
SJ89-27
SJ89-28
SJ89-29
SJ89-30
SJ89-31
SJ89-32
SJ89-33
SJ89-34
SJ89-35
SJ89-36
SJ89-37
SJ89-38
SJ89-39
SJ89-40
Sample


Mean
2.012
2.039
1.973
1.88
1.932
2.114
2.043
2.247
2.085
1.914
2.253
2.239
2.158
2.068
2.036
1.951
1.88
2.105
2.067
2.08
2.109
Mean


Std.Dev.
.338
.317
.347
.29
.302
.256
.338
.286
.274
.34
.289
.269
.261
.337
.342
.354
.327
.293
.346
.345
.332
Std.Dev.


Skewness
.061
.143
-.01
.124
.085
.192
.057
.063
-.038
-.187
-.087
.039
.162
-.081
.113
-.033
.127
.051
-.1
-.195
-.014
Skewness


Kurtosis
3.399
3.744
3.797
3.974
3.745
4.359
3.033
3.533
3.837
3.264
3.507
3.771
4.015
3.308
2.765
3.066
3.147
3.727
3.341
3.263
3.358
Kurtosis


5thM.M.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5thM.M.


6thM.M.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6thM.M.


Panel 2

Suite homogeneity, in terms of departures of sample means and
standard deviations from the suite mean values (of means & std.devs.)
as an evaluation of uniformity. Crosses represent numbers on far right.
Mean and Std. Dev. of Means: 2.056 .108 and of Std.Devs.: .313 .031


T.of F.
.00029
.00031
.00036
.0002
.00021
.00024
.00019
.00017
.00014
.00012
.00019
.00017
.00027
.00028
.00016
.00017
.00012
.0003
.00015
.00013
.0002
T.of F.


Dep.of Std.D.
.041
.034
.032
.032
.029
.027
.025
.025
.024
.018
.013
.004
-.012
-.02
-.024
-.024
-.027
-.04
-.044
-.052
-.057
Dep.of Std.D.


Dep. of Mean
-.106
-.083
.009
.023
-.02
-.143
-.044
-.015
.012
.052
-.176
-.018
-.124
.048
-.176
.196
.189
.028
.182
.101
.057
Dep. of Mean


-.5


Evaluation of homogeneity. Crosses represent numbers on far right.
Outliers, if any, should be obvious. Data Source: stormrdg.5p5
If any point needs to be removed from the suite, the program should
be run again with a reduced number of samples.

Figure 37. Example of SUITES output for the Storm Ridge deposit of St. Joseph
Peninsula, Florida.


Lecture Notes James II. Balsillie


Std.Dv.
.354
.347
.345
.344
.342
.34
.337
.337
.337
.331
.326
.317
.301
.293
.289
.289
.286
.273
.268
.261
.256
Std.Dv.


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995







This is SUITES. Results: Pane 3

The sequence of results, for each parameter such as the mean, is:
six moment measures, then percent on the 4-phi-sieve-and-finer.
That is, the first line refers to the mean of the means, mean of
the standard deviations, mean of the skewnesses, etc.
Source of data stormrdg.5p5. N= 21 Samples, 1 to 21

Means Std.Dev. Skewn. Kurtos. 5th.M.M. 6th.M.M. T.Fines
Mean of the: 2.056 .313 .022 3.521 0 0 .0002

Stnd. Dev.: .108 .031 .106 .374 0 0 0
Skewness: .166 -.431 -.45 .132 0 0 .601
Kurtosis: 2.335 1.702 2.344 2.62 0 0 2.295

Fifth Mom.: .984 -1.646 -2.393 1.047 0 0 3.015

Sixth Mom.: 6.327 3.934 7.511 10.114 0 0 7.957

Rel.Disp.: .052 .1 4.751 .106 0 0 .324
Invrtd.R.D.: 18.937 9.989 .21 9.41 0 0 3.082
StdDev/Ku. = .088 Kurt./Mean = 1.712
T.of F. Mns & StdDevs as Percent: .02 ; 0
Mn & StdDev of Mn/Ku & of SD/Ku: .583 .063 .089 .017

The Relative Dispersion (or Coefficient of Variation) is the
Standard Deviation divided by the Mean.
Panel 4
The primary use of the next display is to minimize the weight of certain
interpretations (e.g., no X's). Of those that are left, a single line
with 2 X's must not be taken to demonstrate either one alone; FIRST,
identify SINGLE-X lines and their site meanings. NOTE that the
Tail-of-Fines tends to identify the last-previous agency.
For best results, plot numerical data by hand on proper bivariate charts.

MB=Mature Bch; Sett=Settling (Closed Basin); Tflat=Tidal Flat; GLF=Glacio-Fluv.
Parameter (below) Environment: Dune MB Riv Sett TFlat GLF
Procedures giving 1 or 2 answers: .........

Mean of the Skewness: x x
Variability diagram: x x
Procedures generally giving one answer: .......
RelDisMn vs RelDisStdDev: X
Mean of the Tails-of-Fines: X
StdDev. of Tail-of-Fines: X
Tail-of-Fines diagram: X

The Storm Ridge on St. Joseph Peninsula, FL. Tall ridge.
This is SUITES. Data source: stormrdg.5p5. N = 21 1 to 21 02-27-1995

The End.
Figure 37. (cont.)



arbitrarily set at 5 P.]

Panel 4 indicates that the deposit is a high energy mature beach. It is the additional
field information that suggests it is storm produced.

It may be of interest to note that while storms and hurricanes are primarily erosive
agents, Balsillie (1985, p. 33-34) found from 249 first quadrant (in terms of event impact)


Lecture Notes


James H. Balsillie








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995




beach and nearshore profiles for 3 hurricanes and 2 storms that, on the average, 16% of the
area impacted by the extreme events resulted in accretion. The standard deviation for these
data was only 0.059%! It is also interesting that the volume of sand accreted during the
storms was 27% of the eroded volume (i.e., TYPE I erosion where accretion was not even
considered). This is a rather large volume considering that but 16% of the impacted areas)
experienced accretion. Furthermore, there is no singular area within the 1st quadrant where
accretion occurs; rather, it appears to be random.


Example 3. The Railroad Embankment, Gulf County, Florida.


The Railroad Embankment is located in Gulf County just to the east of Cape San Bias
(see Figure 41 for an approximate location locale RREMB). It is a ridge with 4 or 5 meters
of relief, and is comprised of parallel to sub-parallel, low-angle, cross-bedding planes sloping
6 to 8 degrees down in the seaward direction. It, again, shows good homogeneity (Figure 38)



This is SUITES. Data source: rr-emb$.5p5. No. of Samples: 11 03-01-1995

This program produces suite, or group, statistics for a suite, or set, of
samples, presumably all representing the same depositional environment.
Panel 1

Tabulation of data:


Sample
RR-1
RR-2
RR-3
RR-4
RR-9
RR-13
RR-19
RR-20
RR-7n
RR-6n
RR-3n
Sample


Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M. T.of F.


2.782
2.583
2.158
2.703
2.463
2.545
2.422
2.583
2.195
2.262
2.44
Mean


.32
.389
.473
.333
.375
.325
.382
.353
.434
.398
.341
Std.Dev.


-.211
-.176
.113
-.163
-.093
-.128
-.018
-.128
-.204
-.201
-.172
Skewness


3.882
3.177
2.416
3.117
3.523
3.461
3.196
3.24
3.1
3.414
3.52
Kurtosis


1
1
1
1
1
5thM.M.


1
1
1
1
1
1
1
1
1
1
1
6thM.M.


0
.0001
.0001
0
.0001
.0001
.00001
0
.0001
.0001
.0001
T.of F.


Panel 2
Suite homogeneity, in terms of departures of sample means and
standard deviations from the suite mean values (of means & std.devs.)
as an evaluation of uniformity. Crosses represent numbers on far right.
Mean and Std. Dev. of Means: 2.466 .191 and of Std.Devs.: .374 .045


Dep.of Std.D.
.098
.059
.023
.014
.007
0
-.022
-.034
-.042
-.05
-.055
Dep.of Std.D.


Dep. of Mean
-.309
-.273
-.204
.115
-.046
-.005
.115
-.028
.236
.078
.314
Dep. of Mean


Evaluation of homogeneity. Crosses represent numbers on far right.
Outliers, if any, should be obvious. Data Source: rr-emb$.5p5
If any point needs to be removed from the suite, the program should
be run again with a reduced number of samples.

Figure 38. Example of SUITES output for the Rairoad Embankment.


Std.Dv.
.472
.433
.398
.388
.381
.375
.352
.34
.333
.324
.319
Std.Dv.


Lecture Notes


James H. Balsillie









W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995





This is SUITES. Results: Pane

The sequence of results, for each parameter such as the mean, is:
six moment measures, then percent on the 4-phi-sieve-and-finer.
That is, the first line refers to the mean of the means, mean of
the standard deviations, mean of the skewnesses, etc.
Source of data rr-emb$.5p5. N= 11 Samples, 1 to 11

Means Std.Dev. Skewn. Kurtos. 5th.M.M. 6th.M.M. T.Fines
Mean of the: 2.466 .374 -.126 3.276 0 0 0
Stnd. .Dev.: .191 .045 .092 .35 0 0 0
Skewness: -.134 .731 1.481 -.82 0 0 -.577
Kurtosis: 2.02 2.654 4.295 4.16 0 0 1.343

Fifth Mom.: -.277 4.131 10.234 -6.667 0 0 -1.372
Sixth Mom.: 4.657 10.105 26.508 22.244 0 0 2.175
Rel.Disp.: .077 .121 -.74 .107 0 0 .727
Invrtd.R.D.: 12.901 8.235 -1.353 9.338 0 0 1.374
StdDev/Ku. = .114 Kurt./Mean = 1.328 .
T.of F. Mns & StdDevs as Percent: 0 ; 0
Mn & StdDev of Mn/Ku & of SD/Ku: .752 .071 .114 .029

The Relative Dispersion (or Coefficient of Variation) is the
Standard Deviation divided by the Mean.
Panel 4
The primary use of the next display is to minimize the weight of certain
interpretations (e.g., no X's). Of those that are left, a single line
with 2 X's must not be taken to demonstrate either one alone; FIRST,
identify SINGLE-X lines and their site meanings. NOTE that the
Tail-of-Fines tends to identify the last-previous agency.
For best results, plot numerical data by hand on proper bivariate charts.

MB=Mature Bch; Sett-Settling (Closed Basin); Tflat=Tidal Flat; GLF=Glacio-Fluv.
Parameter (below) Environment: Dune MB Riv Sett TFlat GLF
Procedures giving 1 or 2 answers: . . . . .

Mean of the Skewness: x x
Variability diagram: x x
Procedures generally giving one answer: . . .
RelDisMn vs RelDisStdDev: X
Mean of the Tails-of-Fines: X
StdDev. of Tail-of-Fines: X
Tail-of-Fines diagram: X
Inverted RelDisp (Sk vs K; Min. usefulness: x

Railroad Embankment, near Cape San Blas, FL. Tall. ridge

This is SUITES. Data source: rr-emb$.5p5. N = 11 1 to 11 03-01-1995

The End.

Figure 38. (cont.)


according to panel 2 of the SUITES program. The environmental interpretation of panel 4
indicates, with no question, that the deposit is mature beach. [NOTE: probability plots did
show the highly diagnostic surf-break which was not interactively logged in the SUITES data
entry section.] The Railroad Embankment is a fair-weather swash/runup deposit, or beach
ridge.


The Storm Ridge versus the Railroad Embankment and the Z-Test.


Interpretation of granulometric results of the SUITES program clearly identifying both
deposits to be mature beach. Additional field evidence, as we have seen (e.g., bedding types


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995



and slopes), indicate that they are different. Is there any other way that would indicate a
difference? Yes, probability applications can be employed. Results from a Z-Test are listed
in Table 6. The Z-Test determines the degree of difference between averages, in this case
suite means for the first 4 moment measures. The number of samples for the Storm Ridge
(STORMRDG.5P5) was 21, with 11 samples comprising the suite representing the Railroad
Embankment (RR-EMB$.5P5). Input data are listed under the heading "summary of means and
standard deviations". The column with the header "Z VALUE" lists the Z value results; the
larger the Z value, the greater the statistical difference between averages tested. Exceedence
probability and significance of the Z-Test results are shown by the Z and P rows near the
bottom of the table. Moment measures for a, p, and the tail-of-fines (T of F) are significantly
different to the less than 0.00005 confidence level, K is significantly different to less than the
0.05 confidence level. Hence, the two deposits are not the same.


Table 6. Z-Test for the Storm Ridge (STORMRDG.5P5) and Railroad
Embankment (RR-EMB$.5P5) deposits of Gulf County, Florida.

This is Z-TEST Data sources: STORMRDG.5P5. RR-EMB$.5P5 N = 21 11
Summary of means and-standard deviations:
File Mn and SD, STORMRDG.5P5. File Mn and SD, RR-EMBS.5P5.
Variable 1: A 2.056429 .1085852 2.466909 .1912094
Variable 2: o .3134762 3.138014E-02 .3748182 4.551521E-02
Variable 3: Sk .0224762 .1067845 -.1255455 9.283353E-02
Variable 4: K 3.521572 .3742375 3.27691 .3508905
Variable 5:TofF 2.080952E-04 6.751506E-05 6.454546E-05
4.697459E-05
If these are sedimentological data, the variables MAY BE the mean,
standard deviation, skewness and kurtosis. The values given above
are means & standard deviations of the variables for each datafile.

Z VALUE Std Err Degr.Freedom
First Variable: p 6.585459 6.233131E-02 30
Second Variable: o 3.999623 1.533693E-02 30
Third Variable: Sk 4.064234 3.642056E-02 30
Fourth Variable: K 1.830617 .13365 30
Fifth Variable: T. of F. 7.024088 2.0436793-05 30
If the degrees of freedom > 25-to-30, then large-sample procedures
are appropriate. T of F
K o
P is theJ.probability of exceeding Z by chance:
Z: 1.645 2.054 2.170 2.326 2.576 3.090 3.290 3.719 3.891" 4.265
P: 0.05 0.02 0.015 0.010 0.005 0.001 0.0005 0.0001 0.00005 0.00001

This is Z-TEST. Sources: STORMBDG.5P5, RR-EMBS.5P5 02-15-1995. The End.



Example 4. The St. Vincent Island Beach Ridge Plain.

It would be remiss if we did not show SUITES results for the classic St. Vincent Island
Beach Ridge Plain. Results for all 59 individual ridges for the plain are given by Figure 39.
Again, the homogeneity (panel 2) is very good. Panel 4 overwhelmingly indicates that the


Lecture Notes


James H. Balsillie










SW. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


This is SUITES. Data source: stvin-ak.4p5. No. of Samples: 59 03-01-1995

This program produces suite, or group, statistics for a suite, or set, of
samples, presumably all representing the same depositional environment.
Panel 1

Tabulation of data:


Sample
AB1
AB2
AB3
AB4
AB5
AB6
AB7
C1
C2
C3
C4
C5
C6
C7
D1
D2
D3
D4
D5
D6
El
E2
E3
E4
E5
E6
E7
E8
E9
E10
Ell
E12
E13
E14
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
Fl
G1
G2
G3
G4
G5
G6
K1
K2
K3
K4
K5
K6
K7
K8
Sample


Mean Std.Dev. Skewness
2.318 .378 -.072
2.362 .38 -.135
2.274 .387 -.133
2.346 .379 -.109
2.23 .468 -.141
2.381 .37 -.093
2.392 .407 -.133
2.445 .38 -.137
2.473 .427 -.266
2.338 .43 -.153
2.434 .433 -.165
2.315 .415 -.052
2.303 .379 .01
2.297 .411 -.011
2.34 .38 .03
2.29 .43 .04
2.21 .42 -.09
2.14 .42 .1
2.43 .34 -.08
2.31 .4 -.11
2.42 .37 -.22
2.2 .47 -.24
2.42 .35 -.21
2.37 .36 -.13
2.43 .4 -.32
2.45 .36 -.2
2.52 .36 -.16
2.24 .43 -.02
2.47 .37 -.08
2.53 .37 -.14
2.47 .39 -.11
2.35 .39 -.09
2.46 .37 -.15
2.57 .37 -.16
2.19 .45 -.18
2.23 .36 -.15
2.19 .38 -.17
2.39 .36 -.14
2.43 .36 -.12
2.45 .42 -.32
2.56 .37 -.22
2.32 .37 -.11
2.28 .33 -.11
2.1 .44 -.09
2.21 .5 -.11
2.28 .39 .01
2.22 .45 -.01
2.14 .38 -.08
2.05 .41 .03
2.12 .4 -.03
2.24 .35 -.02
2.21 .37 -.01
2.52 .38 -.01
2.31 .39 -.03
2.34 .41 -.09
2.4 .34 -.04
2.43 .38 -.07
2.43 .38 -.04
2.14 .43 -.07
Mean Std.Dev. Skewness


Kurtosis
3.928
3.578
3.728
3.158
3.459
3.658
3.403
3.355
3.266
2.861
3.019
3.048
3.455
3.33
3.92
3.54
3.41
3.84
3.82
2.9
3.45
2.99
2.39
3.2
3.74
3.26
3.12
2.8
2.92
3.14
2.9
2.96
3.15
3.33
2.93
3.71
3.52
3.24
3.1
3.75
3.06
3.33
3.4
3.01
2.86
3.14
2.85
3.46
3.57
3.75
3.47
3.78
3.01
2.96
3.2
3.39
2.95
2.84
2.89
Kurtosis


5thM.M.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5thM.M.


6thM.M.

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6thM.M.


Figure 39. Example of SUITES output for the St Vincent Island Beach Ridge Plain.


I


T.of F.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T.of F.


Lecture Notes


James H. Balsillie








W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995







Panel 2

Suite homogeneity, in terms of departures of sample means and
standard deviations from the suite mean values (of means & std.devs.)
as an evaluation of uniformity. Crosses represent numbers on far right.
Mean and Std. Dev. of Means: 2.334 .122 and of Std.Devs.: .393 .034


Std.Dv.
.5
.469
.467
.449
.449
.439
.432
.43
.43
.43
.43
.426
.419
.419
.419
.414
.411
.409
.409
.407
.4
.4
.4
.389
.389
.389
.389
.386
.379
.379
.379
.379
.379
.379
.379
.379
.379
.379
.377
.37
.37
.37
.37
.37
.37
.37
.37
.37
.36
.36
.36
.36
.36
.36
.349
.349
.34
.34
.33
Std.Dv.


+.5


-.5


Dep.of Std.D.
.106
.076
.074
.056
.056
.046
.039
.037
.037
.037
.037
.033
.026
.026
.026
.021
.018
.016
.016
.013
.006
.006
.006
-.004
-.004
-.004
-.004
-.007
-.014
-.014
-.014
-.014
-.014
-.014
-.014
-.014
-.014
-.014
-.016
-.024
-.024
-.024
-.024
-.024
-.024
-.024
-.024
-.024
-.033
-.033
-.033
-.033
-.033
-.033
-.044
-.044
-.054
-.054
-.063
Dep.of Std.D.


-.5 .0. +.5


Dep. of Mean
-.125
-.136
-.105
-.116
-.145
-.235
.098
-.195
-.046
.003
-.095
.137
.115
-.195
-.125
-.02
-.038
-.285
.004
.057
.094
-.216
-.026
.014
-.055
.135
-.026
.062
.094
.094
.145
.185
.027
.109
.195
.004
.01
-.033
-.018
.234
-.125
.125
.194
.015
.224
.135
.085
.046
.185
.115
.035
.094
.054
-.105
.085
-.095
.064
.094
-.055
Dep. of Mean


Evaluation of homogeneity. Crosses represent numbers on far right.
Outliers, if any, should be obvious. Data Source: stvin-ak.4p5
If any point needs to be removed from the suite, the program should
be run again with a reduced number of samples.


Figure 39. count. )


+
+
+
4
+
+
+
+
+
+


Rgum 39. (cont.)


Lecture Notes


James H. Balsillie










W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


This is SUITES.


Results:


Panel 3


The sequence of results, for each parameter such as the mean, is:
six moment measures, then percent on the 4-phi-sieve-and-finer.
That is, the first line refers to the mean of the means, mean of
the standard deviations, mean of the skewnesses, etc.
Source of data stvin-ak.4p5. N= 59 Samples, 1 to 59


Mean of the:
Stnd. Dev.:
Skewness:
Kurtosis:
Fifth Mom.:
Sixth Mom.:
Rel.Disp.:
Invrtd.R.D.:


Means
2.334
.122
-.195
2.318
-1.116
7.499
.052
19.111


StdDev/Ku. =
T.of
Mn & StdDev of Mn/Ku


Std.Dev. Skewn. Kurtos. 5th.M.M
.393 -.104 3.274 0
.034 .084 .336 0
.775 -.258 .06 0
3.383 3.222 2.409 0
6.332 -2.368 -.692 0
20.873 15.594 9.385 0
.087 -.817 .102 0
-11.374 -1.225 9.718 0
.12 Kurt./Mean = 1.402
F. Mns & StdDevs as Percent: 0 ;
& of SD/Ku: .712 0 .12 0


The Relative Dispersion (or Coefficient of Variation) is the
Standard Deviation divided by the Mean.
Panel4
The primary use of the next display is to minimize the weight of certain
interpretations (e.g., no X's). Of those that are left, a single line
with 2 X's must not be taken to demonstrate either one alone; FIRST,
identify SINGLE-X lines and their site meanings. NOTE that the
Tail-of-Fines tends to identify the last-previous agency.
For best results, plot numerical data by hand on proper bivariate charts.

MB=Mature Bch; Sett=Settling (Closed Basin); Tflat=Tidal Flat; GLF=Glacio-Fluv.
Parameter (below) Environment: Dune MB Riv Sett TFlat GLF
Procedures giving 1 or 2 answers: . . . .


Mean of the Skewness:
Variability diagram:
Procedures generally giving one answer:
RelDisMn vs RelDisStdDev:
Mean of the Tails-of-Fines:
StdDev. of Tail-of-Fines:
Tail-of-Fines diagram:
Inverted RelDisp (Sk vs K; Min. usefulness:


x x
x x
S . . . .
X


St. Vincent Island, FL beach ridges.

This is SUITES. Data source: stvin-ak.4p5. N = 59 1 to 59 03-01-1995

The End.
Figure 39. (cont.)



suite of samples represents a mature beach deposit. The majority of probability plots did show
the surf-break, although it was not interactively so noted in the SUITES program.


The relationship between 1/K and relatively small sea level changes (1-2 m) for all St.
Vincent Island beach ridges is illustrated by Figure 40. Sets are identified depending upon
whether sea level was low or high and, therefore, sets were correspondingly low or high.


Lecture Notes James H. Balsillie


6th.M.M.
0
0
0
0
0
0
0
0


T.Fines
0
0
0
0
0
0
0


.





.


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995




This is MOVAVG. N= 62 Width of window: 6 .
Grand Mn, SD; Grd Mn +/- .5tSD: .307 .032 .323 .291
The number in the first column is located at the center of the window.
Data source: STVIN.4AL. Variable No. 4 out of 4 Inverted.

GrMn-SD/2; GrMn; GrMn+SD/2: L $
I Sum(I) Mn(I) 1/K
3 1.408066 .281 0 # 3
4 1.426856 .285 4 4
5 1.441229 .288 W f 5
6 1.471051 .294 6
7 1.46058 .292 7
8 1.521007 .304 a 8
9 1.578869 .315 9
10 1.613095 .322 10
11 1.604468 .32 # 11
12 1.598584 .319 S 12
13 1.504157 .3 4 13
14 1.455408 .291 0 14
15 1.420579 .284 L # 15
16 1.39156 .278 0 16
17 1.35304 .27 4 17
18 1.442765 .288 W # 18
19 1.450134 .29 # 19
20 1.491328' .298 j 20
21 1.649321 .329 # 21
22 1.700041 .34 | 22
23 1.622593 .324 4 23
24 1.639486 .327 24
25 1.625551 .325 25
26 1.564284 .312 26
27 1.59425 .318 27
28 1.645341 .329 4 28
29 1.68342 .336 4 29
30 1.700746 .34 4 30
31 1.661063 .332 4 31
32 1.618897 .323 4 32
33 1.641723 .328 4 33
34 1.566437 .313 1 34
35 1.51269 .302 4 35
36 1.503872 .3 3 36
37 1.526152 .305 4 37
38 1.451522 .29 38
39 1.508778 .301 39
40 1.524987 .304 40
41 1.510463 .302 4 41
42 1.520108 .304 42
43 1.603092 .32 43
44 1.594766 .318 4 44
45 1.645343 .329 45
46 1.640242 .328 # 46
47 1.588129 .317 47
48 1.505145 .301 4 48
49 1.474858 .294 # 49
50 1.383048 .276 L 50
51 1.368003 .273 Q 51
52 1.376909 .276 52
53 1.374792 .274 W 53
54 1.418834 .283 6 54
55 1.497604 .299 55
56 1.536132 .307 56
57 1.542099 .308 57
58 1.616532 .323 # 58
59 1.636419 .327 4 59
60 1.644602 .328 # 60
I Sum(I) Mn(I)
GrMn-SD/2; GrMn; GrMn+SD/2: *

Data source: STVIN.4AL. N= 62 Variable No. 4 out of 4 Window: 5 .
Grand Mn, SD; Grd.Mn +/- .5SD: .307 .032 .323 .291 .

This is MOVAVG. Number of items: 62 Data source: STVIN.4AL.
Width of the window is 5 Date: 08-03-1990. The End.

Figure 40. Plot of 1/K for sedinent samples from each of the St. Vincent Island beach
ridges; data identifies set vertical position changes and, hence, sea-level changes.


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995



Spatial Granulometric Analysis


Probability applications can also be employed to identify geographic distribution of
sediments. Pairs of sample suites can be statistically compared using the Z-Test as discussed
in the previous section. For example, in Figure 41, fourteen suites of samples have been so
analyzed. Analysis of one of the pairs has already been presented in Table 4 for the Storm
Ridge versus the Railroad Embankment (RREMB) in which it has been demonstrated that they
are two different types of deposits. They have not been deposited by the same transpo-
depositional processes. Another interesting pair is found on St. Vincent Island where the
classic beach ridges and ridge sets of Figures 31 and 32 are quite different from a set of


( Dog Island
SSt George I
SLittle St Ge
SCape StGe
SSt. Vincent
@ Cape San B


stand
orge Island
orge Shoal
Island
las x


Storm Ridge
2.056
0.313 .
0.022
3.52


2.467
0.375
0.126
Numbers are Averages for 3-277
Suite Statistics in
Following
Order: A

Sk
K



GULF OF MEXICO


St Joseph Peninsula
Apalachicola Bay


I I
Figure 41. Z-test results for phi averages of suite parameters for mean grain size (p),
standard deviation (a), skewness (Sk), and kurtosis (K) for wester panhandle Florida Gulf
coast sediments. Paired site means were tested using the Z-test; bold dashed Enes
represent statistical significant difference between mean values to the standard 0.01
confidence level actuallyy to the 0.0001 level). Offshore islands have been shifted to the
south (narrow vertical Ene and arrows) to facitate Estings of data.


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995



smaller ridges (labelled small ridges in Figure 41) found along the southeastern tip of the
island. Table 7 shows that suite averages for both a and K are significantly different to less
than the 0.005 confidence level. This should be enough evidence to suggest that these ridge
sets are different. Sediments from these small ridges are not different from sediment from
Little St. George Island. Hence, the small ridges have been deposited by essentially the same
depositional agencies that formed Little St. George Island which, in turn, represents a different
depositional regime than eastern St. George Island.

The bold dashed lines delineate where areas are different. Z-Test probabilities that
these sediment deposits are the same are negligible.


Table 7. Z-Test for St. Vincent Island Beach Ridge Plain (STVIN.4EK) and the
southeastern small ridges of St. Vincent Island (CLARK.5P5), Florida.

This is Z-TEST Data sources: STVIN.4EK. CLARK.5P5. N = 39 13
Summary of means and standard deviations:
File Mn and SD, STVIN.4EK. File Mn and SD, CLARK.SP5.
Variable 1: p 2.335384 .1386392 2.300923 7.652164E-02
Variable 2: o .388718 3.638637E-02 .4141539 2.594015E-02
Variable 3: Sk -.1130769 8.397658E-02 -6.907693E-02 .1802351
Variable 4: K 3.19282 .3166097 3.936308 .6842861
If these are sedimentological data, the variables MAY BE the mean
standard deviation, skewness and kurtosis. The values given above
are means & standard deviations of the variables for each datafile.
Z Value Std Err Degr.Freedom
First Variable: p 1.122053 .0307127 50
Second Variable: a 2.747476 9.257903E-03 50
Third Variable: Sk .8499909 5.176528E-02 50
Fourth Variable: K 3.784773 .1964417 50
If the degrees of freedom > 25-to-30, then large-sample procedures
are appropriate. o
P is the probability of exceeding Z + chance:
Z: 1.645 2.054 2.170 2.326 2.576 3.090. 3.290 3.719 3.891 4.265
P: 0.05 0.02 0.015 0.010 0.005 0.001 0.0005 0.0001 0.00005 0.00001
This is Z-TEST Sources: STVIN.4EE, CLARK.5P5 10-24-1989. The End.
Ok



Review

Employing the granulometric methods that have been presented, we can accomplish
at least 7 tasks. These are:

1. The Site:

Although, from time-to-time, it has been requested, one cannot (based on granulometry
alone), identify the location where a sample was taken, that is, the beach name, river name,
or latitude-longitude.


Lecture Notes


James H. Balsillie






W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


2. Paleogeography:

Granulometric suite OPEN SEA
statistics and the inherent Non-cross-bedded alternating shales.
variability within is nds & limestone > 100 marine
variability within is invertebrate species
correlative with
paleogeographic evidence. ARRIE
For instance, Tanner ISLAND H cross-beddedsandsupto
(1o988, d ontrabbles, several species of fresh water
(1 988), demonstrated the gastropods, micro-fossils, fossil tree
correlation for ancient branches & trunks and organic matter,
correlon for ancient beach granulometry
lithified late Pennsylvanian DELTA
- early Permian Fuvil N
sedimentary rocks of granuometry LAGOON
central Oklahoma (Figure
l Oa ( Fine-grained sediments, approx 12
42). non-marine species. 4 rare trilobite species,
settling granulometry
3. Kurtosis and
Hydrodynamics:

If we can identify a Figure 42. Paleogeography and granulometry for a late
mature beach, then the Pennsylvanian early Pennian coastal complex in central
kurtosis will tell us about Oklahoma. The sediment source for the complex was the
the wave energy levels at Arbuclde Mountains lying southeast of the study area.
the time the beach was
formed.

4. Sand Sources:

The sand source, in terms of its depositional environment, can be determined, and we
can distinguish one sediment pool from another. For example, see Figure 41 for the
Apalachicola area and the Z-Test.

5. Tracing of Transport Paths: Ccudimns- Dee i Mac
igneous rocks (e g. of 1he
Firm wdimnrt$ "Sugaoart type o future)
The coast of Brazil in the vicinity of
Rio de Janeiro is characterized by hills of Po
deeply weathered Mesozoic igneous rocks
with pocket beaches lying between (see
Figure 43). The question has been asked as
to the direction of longshore sediment c
transport. At the outset one would expect C
to find coarser sediment at the updrift end of
a longshore transport cell, becoming finer in
the downdrift direction. The subject pocket ATLANTIC OCEAN
beaches, however, have finer sediments at
the central portion of the beaches, and Fgure 43. Granulometry and sediment
coarser sediments at the ends of the transport paths.
beaches. Granulometric evidence suggests


James H. Balsillie


Lecture Notes






W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


that little, if any, sand is escaping from beach-to-beach in the longshore direction.

6. Sea Level Rise:

Kurtosis correlates inversely with even small changes in sea level (rise and fall). This
applies to long-term sea level changes, as well as to extreme event impacts (i.e., hurricanes
and storms).

7. Seasonal Changes and Storm/Hurricane Impact:

In the northern hemisphere, astronomical tidal levels are slightly depressed during the
winter months relative to summer months. In addition, wave energy levels are normally higher
during the winter months. Storm and hurricane impacts result in both high storm tides and
wave energy levels. Again, there appears to be an inverse correlation between energy levels
for these two examples and the kurtosis, as illustrated by Figure 29. The term "appears" is
used because there are not'much data available to quantify the relationship, and the reader
is encouraged to pursue the collection of such information.


PLOT DECOMPOSITION: MIXING AND SELECTION

On probability paper, quartzose sediment distributions commonly plot as zig-zag lines.
Even so, the hypothesis that the basic distribution is Gaussian (i.e., mean = mode = median
or 50th percentile) and will, therefore, plot as a straight line remains valid. It is departure from
the Gaussian that provides additional characterization of the sediments. Each segment on
probability paper is important to consider because it is indicative of a process or processes
leading to its appearance. That such identification can be made relating force and response
elements using probability paper is not commonly understood. Again, a segment and a
component are not the same, although it has been so stated in the literature; a segment must
be recalculated to 100% to be a component. Multi-segmented, zig-zag, or multi-component
sand distributions have been discussed by a multitude of investigators. However, in a series
of papers, Tanner (1964; Appendix X, p. 134) found that zig-zag modifications of the straight-
line plot include mixing and selection which, in turn, can be subdivided as follows:

Mixing: Non-zero component
*Zero component

Censorship
Selection: *Truncation
Filtering

In reality, when we obtain a sand sample it is usually already a mixture of components.
In order to determine the components, the distribution must undergo the process of
decomposition. It is easier, however, to understand decomposition using the reverse process,
e.g., the simple mixing of known component distributions and then determining the resulting
total distribution.


Lecture Note JaesH Blili


James H. Balsillie


Lecture Notes






W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Many sedimentologists/soil scientists do not utilize probability paper in the manner
presented in this work. They most often use it in a manner that suppresses the very details
that we wish to observe. It is W. F. Tanner's opinion that they have not seriously nor
carefully thought the issue through.

Simple Mixing

In order to discuss mixing, it helps to specify some conditions such as proportions of
mixtures (P), means (p), and standard deviations (a).


Non-Zero Component:


Coarse


Case 1. Let us inspect the case
for two component mixing where the
proportions are equal, the means differ,
and the standard deviations are
identical, i.e.,

P1 = P2
, pY 2 [i.e., Pi > #2]
o, = a2

Plotted components and the resulting
mixed distribution are illustrated by
Figure 44.

The resultant distribution is
calculated by adding percentages
for each size class and dividing by
two. An example for Figure 44 is
given by Table 8.

If proportions change, then
the combination of curves plotted
in Figure 44, will slide either to
the right or to the left.

Case 2. Let us make a
change in the component
characteristics where:

P1 P2
1p, P2 [i.e., p, < p2]
a, ao2 [i.e., a, < o'

Component 1 might represent a
beach sand, and component 2 a
river sand (although it is not


0.1%


99.9%


Figure 44. Case 1 example of two-component
simple mixing.




Table 8. Example calculation of component
mixing illustrated in Figure 44.
Combined
Component 1 Component 2 Combined
Curve
0 Cumulative Cumulative C
Cumulative
Percent Percent
Percent
0 0.1 0 0.05
0.25 1.0 0 0.5
0.5 6.0 0 3.0
0.75 21.0 0 10.5
1.00 50.0 0 25.0
1.25 78.0 0 39.0
1.50 94.0 0 47.0
1.75 99.0 0.1 49.55
2.00 99.9 1.0 50.45
2.25 100.0 6.0 53.0
2.50 100.0 21.0 60.5
2.75 100.0 50.0 75.0
3.00 100.0 78.0 89.0
3.25 100.0 94.0 97.0
3.50 100.0 99.0 99.5
3.75 100.0 99.9 99.95


Lecture Notes James H. Balsillie


i


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


normally possible to have a Gaussian
distribution for a fluvial sediment).
Would it be possible in nature to have
two components of fluvial sediments?
The answer is certainly yes; for
instance, where two streams meet and
one of them has a higher gradient and/or
flows across a different lithology than
the other, the sediment loads might very
well be different. Component 1,
however, would more nearly be
representative of a beach sand.

Note for cases 1 and 2, that 2
components result in a distribution
comprised of 3 segments. There is one
instance where 2 components cannot be
distinguished from one another ... that
occurs where p, = P2 and a, = 02, or
multiples of such components,
regardless of the proportions involved.
Now then, if one component is quartz
and the other is something different, say
olivine, that is a different matter (i.e.,
chemistry must be considered); or if one
is quartz and the other is composed of
calcium carbonate shell fragments, then
grain shape will affect the outcome. In
general, however, the above discourse
constitutes the basic preliminary rules
for the treatment of simple mixing.


Coarse



Phi



Fine
C


50%


99.9%


Figure 45. Case 2 example of two-dimensional
simple mixing.


Coarse



Phi



Fine


0.1%


50%


99.9%


Figure 46. Two component simple mixing with
usjointed component cistributions.


Let us inspect the case where the components to be mixed are disjointed samples.
That is, for the sake of discussion, component 1 is a Gaussian sample of particles ranging in
size from baseballs to ping-pong balls,
and component 2 is a Gaussian sample
ranging in size from marbles to beads. coarse
Simple mixing results in a distribution \ Components
illustrated in Figure 46. The vertical**
segment of the resulting distribution is -.
a zero sediment segment (the gap) and Phi Compon. ibuon
contains no sediment particles.

An example of simple mixing Fine
.,. = .F.. ..


with 3 components is illustrated in
Figure 47. For natural sands, 2 to 4
component mixing is common.


0.1%


50%


99.9%


Figure 47. An example of simple three-component
mixing.


Lecture Notes James H. Balsihie


\ 1Component2
SResulting
Distribution

Component 1 \ >


'CP-- entl

Gap
ent --


.1%


James H. Balsillie


Lecture Notes






W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Zero Component:
5
Sediments cannot have a zero
component, since as a response element
the sediment is either available or it is Hb
not present. However, it is important to (m) '
realize that there are natural
distributions that can have a zero
component, such as ocean waves which o
constitute a force element that induces 0.1% 50%/ 99.9%
sedimentologic response. For instance,
along the lower Gulf Coast of Florida, Fgure 48. An example of a distribution with a
seas are calm for about 30% of the
seas are calm for about 30% of the zero component, in this case ocean waves.
annual period. In fact, for beach sands,
wave heights somewhere in the range of
from 3 to 5 cm no longer have the competence to transport significant, if any, quantities of
sand, and may be considered to be a part of the zero wave energy component. An example
is illustrated by Figure 48.

Selection

Simple mixing is not the only way of combining components, or of distorting the
distribution. Three additional methods, described as "statistical selection", are censorship,
truncation, and filtering. Selection examples can be explained by laboratory procedures or by
natural processes.

Censorship:
Coarse
Censoring involves the ,
suppression of all the data of one variety Censored Point
within a certain range of values. The j
missing data normally occurs in the tails Phi
of the distribution, but can occur in the *
central portion. There are two types of
censorship. Fine
0.1% 50% 99.9%
Type I Censorship: This occurs
where the number of suppressed phi size Figure 49. Example of Type I censorship .
classes is known. An example is
illustrated by figure 49, where one data
point (i.e., one sieve) is missing. However, we know the total sample weight (which we
measured prior to sieving), and the percentages for the other data points. Hence, we should
be able to recover the entire characteristics of the distribution.

Type II Censorship: This occurs where the number of suppressed measurements is
known, but the numerical values to be assigned to the individual items (e.g., diameters for the
screens lost) are not known. For instance, the finest sieve used in the 1/4-phi interval sieve
nest was 3.5 0. Hence, data for the 3.75 0 and finer sieves are missing. However, the pan


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


collects the total not retained by the missing sieve fractions. Again, the total weight of the
sample is known, and the bulk of the weight data for the missing fractions is available.

Censorship is the mildest form of selection. In some cases, more than 50% of a
sample can be missing without impeding successful analysis. In fact, many published
sediment curves show simple censorship. Censorship is seldom serious because it does not
generally alter the appearance of the probability curve.

Truncation:
Coarse
Truncation occurs where there is a
total loss of information for a number of ,.
Point of Truncation (PoT)
adjacent missing 1/4-phi classes, or for a Phi, t-o
number of missing items (i.e., n number of
sand grains within a 1/4-phi size class).
Generally, this occurs in one or both of the
tails of the distribution. The result is more Fine
0.1% 50% 99.9%
serious than censorship. For instance, if
we did not have the total weight of the
sample before sieving and, for some Figure 50. Example of single truncation.
reason, the pan fraction were lost, then
the total weight of the sample represents
only those sieves in which sediment was Coarse
retained. origin
---- Truncated
Truncated probability curves are Phi
difficult to handle and may require trial- Po --
and-error tessellation in order to find the
original distribution (see Tanner, 1964;
Appendix X, p. 139). However, one Fine 0.% 50% 99.9%
should at least be able to readily identify
when truncation has occurred. It is
characterized by typically smooth, gentle Figure 51. Example of double truncation.
curves on probability paper; no inflection
points occur unless some other modifications have also taken place. The truncated tail has
better sorting because it plots as a flattened line compared to the rest of the curve. Either tail
can be truncated to result in single truncation (see Figure 50), or both tails can simultaneously
be truncated (see Figure 51).

Fitering:

Filtering is more problematic than either censorship or truncation. It is not relegated
to a continuous segment (i.e., several sieves or size classes in numerical order), but the
removal of, say, some sediment (varying amounts) from each of any number of random sieves
or size classes, for which we have no quantitative information. Viewed in some ways, filtering
is negative mixing, i.e., component 1 plus component 2 for mixing, component 1 minus
component 2 for filtering. One might assume that the filter is Gaussian and that a negative
component added to the filtered distribution will result in the original straight-line probability


Lecture~ Notes Jmes H. alsilli


Lecture Notes


James H. Balsillie





W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


distribution. An example is illustrated in
Figure 52, where the standard deviations
of the filter and the original sample are
identical. An example where the
standard deviations of the filter and
original distribution are unequal is
illustrated by Figure 53.

There are no guidelines to correct
for filtering in order to determine the
original distribution. It is prudent to
assume that filtering has not occurred
unless there is no other explanation.

Summary


Employing Occam's Razor, the
simplest procedure is probably the best
procedure. A practicable endeavor might
be to ignore the effects of censorship
(since it does not generally alter the shape
of the probability curve), to reject an
hypothesis of filtering unless other
evidence compels one to do so, and to
distinguish through inspection of the
probability curve any difference between
truncation and simple mixing. The latter
should not be difficult, inasmuch as the
two processes normally produce quite
different and distinguishable results. Once I
interpretive decisions have been made, the
task of resolving the components can be
undertaken... including the identification
of points and agencies of truncation, if any.


Coarse



Phi



Fine


99.9%


Figure 52. Example of fitering where the fiter
mean is coarser thanth he original istrbution and
standard deviations are equal.


Coarse



Phi



Fine


0.1%


50%


99.9%


Figure 53. Example of ftering where the after
mean is coarser than the original stibutio and
standard deviations are unequal.


Deternination of Sample Components
Using the Method of Differences

The preceding section dealing with plot decomposition has demonstrated the process
using, for example, simple mixing of components. In reality, however, we usually have a
complete sieved sample with identificable line segments that we might wish to decompose
into its constituent components. In order to do so, we can employ the Method of Differences
(Tanner, 1959), which constitutes an approximation to the method of derivatives. The method
is one that applies to the decomposition of any probability distribution, not just one dealing
with sediments. Such work could have important implications, assisting in identifying force
and response element relationships that might not otheriwse be possible to identify.

As an example, let us select an original sedimentologic distribution that is comprised


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Table 9. Cumulative and frequency per-
centages, and first and second differences.
1 2 3 4 5

S Feq. 1st 2nd
% Diffs Dffs

0 0.3 0.3
[0.125] [0.95] -1.0
0.25 1.6 1.3 +1.3
[0.375] [3.4] -2.3
0.5 5.2 3.6 + 1.9
[0.625] [9.1] -4.2
0.75 13.0 7.8 0
[0.875] [19.0] -4.2
1.00 25.0 12.0 -7.2
[1.125] [30.5] +3.0
1.25 36.0 9.0, +2.0
[1.375] [40.0] +1.0
1.50 44.0 8.0 -1.0
[1.625] [47.0] +2.0
1.75 50.0 6.0 +1.0
[1.875] [52.5] +1.0
2.00 55.0 5.0 +5.0
[2.125] [59.5] -4.0
2.25 64.0 9.0 -2.0
[2.375] [69.5] -2.0
2.50 75.0 11.0 -1.0
[2.625] [81.0] -1.0
2.75 87.0 12.0 -5.0
[2.875] [91.0] +4.0
3.00 95.0 8.0 -0.7
[3.125] [96.65] +4.7
3.25 98.3 3.3 +2.8
[3.375] [99.0] +1.9
3.50 99.7 1.4 +0.78
[3.625] [99.8] +1.15
3.75 99.95 0.25
NOTE: Numbers in [ are interpolated values for plotting
purposes.


of two Gaussian components (Table 9).
Initially, from the cumulative probability
distribution percentages (Table 9, column
2), the inner differences or frequency
percentages are determined (column 3).
First differences are determined from the
frequency percentages and are listed in
column 4. Second differences are
determined from column 4 and listed in
column 5.

Results of Table 9 are then
plotted as in Figure 54. Important points
identifying the character of the
distribution and its components occur
where first differences (solid line) equal
zero. That is:

e Where first differences equal
zero and second differences are
negative, approximate means
appear.

Where first differences are
zero and second differences are
positive, approximate proportions
appear.

Hence, Figure 54 confirms that
the total or original distribution is
comprised of 2 means, and 2 proportions
or components. Proportions are 54% for


the first component and 46% for the
second. However, because of the
approximating nature of this method (e.g., we are using 1/4-phi intervals), we can assume that
the proportions are 1:1.

The degree of complexity involved in decomposing distributions depends on whether
means, standard deviations, and proportions are equal or not. Let us look at two cases.

Case 1. Two Components with Means Unequal, Standard Deviations Equal, and Proportions
Equal.

Decomposition of the original, total curve T in this case is a simple example (Figure 55)
and, in fact, is here represented by the sample of Table 9 and Figure 54 ( proportions assumed
equal). Component A may be determined using the point plotting formula A = (2 T) 100
where T is the upper abscissa cumulative percentile for the total (T) curve. For a given value
of T (e.g., 99.5%), the resulting plotting position of A (i.e., A = (2 x 99.5) 100 = 99%)


James H. Balsillie


Lecture Notes








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Cumulative %


Figure 54. Plot of component 1 and 2 differences from Table 7 versus
cumulative percent.


Phi
Grain
Size


Cumulative Percent


Figure 55. Case 1 original total distribution, T, and its constituent components A and B. See
text for discussion.


Lecture NoesJaesH.Basili


Lecture Notes


James H. Balsillie







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


or component A is located on the same horizontal line intersecting T = 99.5 on T. Note that
negative values and values exceeding 100% have meaning, since the domain of the total
curve T has been exceeded. Similarly, points for component B are identified by the point
plotting formula B = (2 T) 100. Constituent components (A and B) are plotted on Figure 55.
Because the Method of Differences is an approximation, recombination of components and
minor adjustments may be needed in order to locate the precise plotting position of the
components.

Case 2. Two Components with Means Unequal, Standard Deviations Unequal, and
Proportions Unequal.

This example is considerably more complex than case 1. The total distribution is
plotted in Figure 56. Furthermore, let component A comprise 75% of the original total sample
distribution, component B 25% of the distribution. The point plotting formula for the original
total distribution (T) and its relationship to component A (A) and component B (B) becomes
T = 0.25 A + 0.75 B or 4 T = A + 3B. It is critical that one first choose a component for
which there is a recognizable solution. This might require some trial-and-error computations.
Normally, however, the first component to be calculated is that which has the longest tails,
and the larger slope (i.e., larger standard deviation). As shall become increasingly apparent,
this assists in identifying the component which has the most percentiles for its computational


Phi
Grain
Size


Cumulative Percent


Figure 56. Case 2 original total distribution, T, and its constituent components A and B.
See text for discussion.


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


definition.

Analytical results for this decomposition analysis are given in Table 10. Note that for
the portion of the graph above, zone C of Figure 56, B percentiles are 100 and component A
can be readily calculated since A = 4 T 3 (100) = 4 T 300. Similarly, below zone C, B
percentiles are 0, and A = 4 T 3 (0) = 4 T. Now, component B can be readily calculated
in zone C according to the point plotting formula B = (4 T A)/3.

Table 10. Analytical results for determination of components A and B
of Figure 56.
P T
ST Comp A Comp B
S[Bottom [Top x- A = 4T-3B B = (4T A)/3
x-axis] axis]
-0.50 0.025 99.975 99.9 100
-0.25 0.075 99.925 99.7 100
0.00 0.225 99.775 99.1 A = 4T-3B 100
0.25 0.625 99.375 97.5 where B = 100, 100
0.50 1.50 98.5 94.0 then 100
0.75 2.875 97.125 88.5 A = 4T-300 100
1.00 5.25 94.75 79.0 100
1.25 8.58 91.42 65.68 100
1.50 14.50 85.50 50.0 96.3
1.75 36.63 63.37 36.0 0 < B < 100 72.49
2.00 75.63 24.37 22.0 Points read from 25.16
2.25 95.16 4.84 12.5 graph. 2.29
2.50 98.45 1.55 6.0 0.066
2.75 99.33 0.67 2.68 A = 4T-3B 0
3.00 99.75 0.25 1.0 where B = 0, 0
3.25 99.91 0.09 0.36 then 0
3.50 99.975 0.025 0.1 A = 4T 0


Again, because of the approximating nature of the methodology, recombination of components
and minor adjustments may be needed in order to more precisely plot positions of the
components. For more involved three component decomposition examples, see Tanner
(1959).

Note that numerically or physically determined components may not necessarily be
Gaussian. They may be truncated, or composed of multiple line segments and, hence, contain
additional components.

CARBONATES

Along both the east coast and lower Gulf coasts of Florida, the beaches are comprised
of significant amounts of calcium carbonate (CaC03) sediments, primarily shell hash. Such
deposits are characteristically variable, and highly so. That is, in one locality it might be 99%
quartz, and in another 99% calcium carbonate. When pursuing the collection of quartzose
samples, even for the informed perhaps the best one can do, is take a sample containing 20


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Phi
Grain
Size 1


99.99


50
Cumulative Percent


Figure 57. Beach sample from Sanibel Island, Florida, containing a
calcium carbonate shel fraction. Components were physically
determined using HCI. PoT designates the point of truncation. See text
for discussion.


to 30% CaCO3. Suppose that such a sample (50 to 100 grams) is taken on Sanibel Island
located along the lower Gulf Coast, such as one collected by Neale (1980). The sieved
results are plotted in Figure 57. Following sieving of the total sample (solid line in Figure 57),
we then digest the CaCO3 using HCI and re-sieve the mostly quartz insoluble residue. The
resulting distribution (83% of the total sample) is given by the dashed line of Figure 57. By
numerically subtracting the insoluble residue (mostly quartz) distribution from the originally
sieved distribution, the CaCO, distribution (17% of the total sample) is determined (dash-dot-
dash line of Figure 57). The shape of the originally sieved distribution should provide a clue
that the CaCO3 component is truncated. But, what of the two-segment quartz (insoluble)
distribution (dashed line)? In fact, the line segment labelled as "added" represents insolubles
appropriated by organisms and contained within the shell matrix, that were released due to
HCI digestion. Hence, these insoluble particles are not represented by the total curve, since
they were hidden, or filtered (see Tanner, 1964; Appendix X, p. 139).

Let us look at some other differences between quartz and calcium carbonate. In terms
of Mohs hardness scale, calcium carbonate is 4 orders of magnitude softer than quartz.
Hence, where quartz and carbonate mixtures occur, the quartz will accelerate abrasion of the
softer material. Just how fast this occurs is not known, but should be especially accelerated
during periods of higher energy, such as during storm impacts.

Mass densities of both quartz and calcium carbonate vary slightly, depending upon
impurities present. They are, however, quite similar in value.


Lecture Notes


James H. Balsillie









W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


In terms of chemical stability, calcium carbonate is 8 to 10 orders of magnitude
chemically less stable than quartz. Rainfall, runoff, and high tide waters will probably dissolve
CaCO3 in upper layers of the foreshore and beach, and precipitate at lower elevations in the
sediment column. How much lower in elevation? Not much. Beach rock that is well
developed in beaches of Florida, attests to the highly mobile mature of CaCO3, in terms of its
ability to be dissolved and re-precipitated. In southeast coastal Florida there are anthropic
materials cemented within beach rock, such as Coke bottle fragments and automobile parts.
Automobile parts certainly were not available in any quantity prior to about 1925. Such
cementation, therefore, requires less than 70 years. How much less is unknown.

Carbonate material has much more variability in shape than quartz. Mostly, CaCO, is
plate or rod shaped, while quartz particles are nearly equidimensional. In the company of one
another the plate-shaped particles significantly change the hydrodynamic response of the
quartz particles. Platy particles exhibit significant lateral movement when settling in water.
Consequently, the grain-size distribution is seriously impacted and becomes "warped" in some
way which cannot be analyzed.

Should we, therefore, forget about carbonates, and focus attention on the quartz
fraction only? Currently, we do not know with certainty what percent of the nearshore sand
pool is carbonate. At the very least, we need such measurements.


REFERENCES CITED AND ADDITIONAL
SEDIMENTOLOGIC READINGS

Apfel, E. T., 1938, Phase sampling of sediments: Journal of Sedimentary Petrology, v. 8, p.
67-78.

Arthur, J. D., Applegate, J., Melkote, S., and Scott, T. M., 1986, Heavy mineral
reconnaissance off the coast of the Apalachicola River Delta, Northwest Florida:
Florida Department of Natural Resources, Bureau of Geology, Report of Investigations
No. 95, 61 p.

Balsillie, J. H., 1985, Post-storm report: Hurricane Elena of 29 August to 2 September 1985:
Florida Department of Natural Resources, Beaches and Shores Post-Storm Report No.
85-2, 66 p.

Balsillie, J. H., in press, Seasonal variation in sandy beach shoreline position and beach width:
Florida Geological Survey, Open File Report, 39 p.

Bates, R. L., and Jackson, J. A., 1980, Glossary of Geology, American Geological Institute,
Falls Church, VA, 751 p.

Bergmann, P. C., 1982, Comparison of sieving, settling and microscope determination of sand
grain size: M.S. Thesis, Department of Geology, Florida State University, Tallahassee,
178 p.


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Demirpolat, S., and Tanner, W. F., 1987, Advanced grain size analysis and late Holocene sea
level history: Coastal Sediments '87, (N. C. Kraus, ed.), p. 1718-1731.

Demirpolat, S., Tanner, W. F., and Clark, D., 1986, Subtle mean sea level changes and sand
grain size data: [In] Suite Statistics and Sediment History, (W. F. Tanner, ed.),
Proceedings of the 7th Symposium on Coastal Sedimentology, Florida State University,
Tallahassee, FL.

De Vries, N., 1970, On the accuracy of bed-material sampling: Journal of Hydraulic Research,
v. 8, p. 523-534.

Doeglas, D. J., 1946, Interpretation of the results of mechanical analyses: Journal of
Sedimentary Petrology, v. 16, no. 1, p. 19-40.

Emmerling, M. D., and Tanner, W. F., 1974, Splitting error in replicating sand size analysis:
[ Abstract] Prog. Geological Society of America, v. 6, p. 352.

Fogiel, M., et al. 1978, The Statistics Problem Solver, Research and Education Association,
New York, N. Y., 1044 p.

Friedman, G. M., and Sanders, J. E., 1978, Principles of Sedimentology, John Wiley, New
York, 792 p.

Hobson, R. D., 1977, Review of design elements for beach-fill evaluation: U. S. Army Corps
of Engineers, Coastal Engineering Research Center, Washington, D. C., Technical Paper
No. 77-6, 51 p.

Hutton, J., 1795, Theory of the Earth, v. 2.

Jopling, A. V., 1964, Interpreting the concept of the sedimentation unit: Journal of
Sedimentary Petrology, v. 34., no. 1, p. 165-172.

Neale, J. M., 1980, A sedimentological study of the Gulf Coasts of Cayo-Costa and North
Captiva Islands, Florida: M. S. Thesis, Department of Geology, Florida State
University, Tallahassee, FL, 144 p.

Otto, G. H., 1938, The sedimentation unit and its use in field sampling: Journal of Geology,
v. 46, p. 569-582.

Rizk, F. F., 1985, Sedimentological studies at Alligator Spit, Franklin County, Florida: M. S.
Thesis, Department of Geology, Florida State University, Tallahassee, FL, 171 p.

Rizk, F. F., and Demirpolat, S., 1986, Pre-hurricane vs. post-hurricane beach sand:
Proceedings of the 7th Symposium on Coastal Sedimentology, (W. F. Tanner, ed.),
Department of Geology, Florida State University, Tallahassee, FL, p. 129-142.

Savage, R. P., 1958, Wave run-up on roughened and permeable slopes: Transactions of the
American Society of Civil Engineers, v. 124, paper no. 3003, p. 852-870.


Lecture Notes


James H. Balsillie






W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Socci, A., and Tanner, W. F., 1980, Little known but important papers on grain-size analysis:
Sedimentology, v. 27, p. 231-232.

Stapor, F. W., and Tanner, W. F., 1975, Hydrodynamic implications of beach, beach ridge and
dune grain size studies: Journal of Sedimentary Petrology, v. 45 p. 926-931.

Stapor, F. W., and Tanner, W. F., 1977, Late Holocene mean sea level data from St. Vincent
Island and the shape of the Late Holocene mean sea level curve: Coastal
Sedimentology, (W. F. Tanner, ed.), Department of Geology, Florida State University,
p. 35-67.

Sternberg, H., 1875, Untersuchungen Ober LAngen- und Quer-profil geschiebef0hrende FlOsse:
Zeitschrift Bauwesen, v. 25, p. 483-506.

Tanner, W. F., 1959a, Examples of departure from the Gaussian in geomorphic analysis:
American Journal of Science, v. 257, p. 458-460.

1959b, Sample components obtained by the method of differences: Journal of
Sedimentary Petrology, v. 29, p. 408-411.

_, 1959c, Possible Gaussian components of zig-zag curves: Bulletin of the
Geological Society of America, v. 70, p. 1813-1814.

,__ 1960a, Florida coastal classification: Transactions of the Gulf Coast Association
of Geological Societies, v. 10, p. 259-266.

1960b, Numerical comparison of geomorphic samples: Science, v. 131, p.
1525-1526.

1960c, Filtering in geological sampling: The American Statistician, v. 14, no. 5,
p. 12.

S1962, Components of the hypsometric curve of the Earth: Journal of Geophysical
Research, v. 67, p. 2841-2844.

1963, Detachment of Gaussian components from zig-zag curves: Journal of
Applied Meteorology, v. 2, p. 119-121.

1964, Modification of sediment size distributions: Journal of Sedimentary
Petrology, p. 34, p. 156-164.

1966, The surf "break": key to paleogeography: Sedimentology, v. 7, p. 203-
210.

1969, The particle size scale: Journal of Sedimentary Petrology, v. 39, p. 809-
811.


Lectue Noes Jmes H Ba/i/li


James H. Balsillie


Lecture Notes








W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


1971, Numerical estimates of ancient waves, water depth and fetch:
Sedimentology, v. 16, p. 71-88.

1978, Grain-size studies: [In] Encyclopedia of Sedimentology, (R. W. Fairbridge
and Joanne Bourgeois, eds.), Dowden, Hutchinson and Ross, p. 376-382.

,1982a, Sedimentological tools for identifying depositional environments: [In]
Geology of the Southeastern Coastal Plain, (D. D. Arden, B. F. Beck, and E. Morrow,
eds.), Georgia Geological Survey Information Circular 53, p. 114-117.

1982b, High marine terraces of Mio-Pliocene age, Florida Panhandle: [In] Miocene
of the Southeastern United States, (T. M. Scott and S. B. Upchurch, eds.), Florida
Department of Natural Resources, Bureau of Geology Special Publication 25, p. 200-
209.

1983a, Hydrodynamic origin of the Gaussian size distribution: Abstract with
Programs, Geological Society of America, v. 15, no. 2, p. 93.

1983b, Hydrodynamic origin of the Gaussian size distribution: [In] Near-Shore
Sedimentology, (W. F. Tanner, ed.), Proceedings of the 6th Symposium on Coastal
Sedimentology, Florida State University, Tallahassee, FL.

1986, Inherited and mixed traits in the grain size distribution: [In] Suite Statistics
and Sediment History, (W. F. Tanner, ed.), Proceedings of the 7th Symposium on
Coastal Sedimentology, Department of Geology, Florida State University, Tallahassee,
FL.

1988, Paleogeographic inferences from suite statistics: Late Pennsylvanian and
early Permian strata in central Oklahoma: Shale Shaker, v. 38, no. 4, p. 62-66.

1990a, Origin of barrier islands on sandy coasts: Transactions of the Gulf Coast
Association of Geological Societies: v. 40, p. 819-823.

1990b, The relationship between kurtosis and wave energy: [In] Modern Coastal
Sediments and Processes, (W. F. Tanner, ed.), Proceedings of the 9th Symposium on
Coastal Sedimentology, Department of Geology, Florida State University, Tallahassee,
FL, p.41-50.

1991a, Suite Statistics: the hydrodynamic evolution of the sediment pool: [In]
Principles, Methods and Application of Particle Size Analysis, (J. P. M. Syvitski, ed.),
Cambridge University Press, Cambridge, p. 225-236.

1991 b, Application of suite statistics to stratigraphy and sea-level changes: [In]
Principles, Methods and Application of Particle Size Analysis, (J. P. M. Syvitski, ed.),
Cambridge University Press, Cambridge, p. 283-292.

1992a, 3000 years of sea level change: Bulletin of the American Meteorological
Society, v. 83, p. 297-303.


Lecture Notes


James H. Balsillie







W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


1992b, Late Holocene sea-level changes from grain-size data: evidence from the
Gulf of Mexico: The Holocene, v. 2,p. 258-263.

1992c, Detailed Holocene sea level cuve, northern Denmark: Proceedings of the
International Coastal Congress Kiel '92, p. 748-757.

1993a, An 8000-year record of sea-level change from grain-size parameters: data
from beach ridges in Denmark: The Holocene, v. 3, p. 220-231.

1993b, Louisiana cheniers: clues to Mississippi delta history: [In] Deltas of the
World, (R. Kay and 0. Magoon, eds.), A.S.C.E., New York, p. 71-84.

1993c, Louisiana cheniers: settling from high water: Transactions of the Gulf
Coast Association of Geological Societies, v. 43, p. 391-397.

1994, The Darss: Coastal Research, v. 11, no. 3, p. 1-6.

and Campbell, K. M., 1986, Interpretation of grain size suite data from two small
lakes in Florida: [In] Suite Statistics and Sediment History, (W. F. Tanner, ed.),
Proceedings of the 7th Symposium on Coastal Sedimentology, Department of Geology,
Florida State University, Tallahassee, FL.

and Demirpolat, S., 1988, New beach ridge type: severely limited fetch, very
shallow water: Transactions of the Gulf Coast Association of Geological Societies, v.
38, p. 367-373.

Ul'st, V. G., 1957, Morphology and developmental history of the region of marine
accumulation at the head of Riga Bay, (in Russian), Akad. Nauk., Latvian SSR, Riga,
Latvia, 179 p.

Wentworth, C. K., 1922, A scale of grade and class terms for plastic sediments: Journal of
Geology, v. 30, p. 377-392.

Zenkovich, V. P., 1967, Processes of Coastal Development, Interscience Publishers (Wiley),
New York, 738 p.


Lecture Notes James H. Balsiiie


James H. Balsillie


Lecture Notes









W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


NOTES


Lecture- Notes JamesH. Balsilli


James H. Balsillie


Lecture Notes





W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Appendix I

Socci, A., and Tanner, W. F., 1980, Little known but important papers on
grain-size analysis: Sedimentology, v. 27, p. 231-232.

[Reprinted with permission]


Lecture Notes James H. Ba/si/lie


James H. Balsillie


Lecture Notes







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Srdimentology (1980) 27. 231-232




SHORT COMMUNICATION

Little known but important papers on grain-size analysis



ANTHONY SOCCI & W. F. TANNER
Geology Department, Florida Slate University, Tallahassee, Florida 32306, U.S.A.




ABSTRACT

Some important papers have apparently gone unnoticed by.most sedimentologists, as shown by their
absence from bibliographies of recent texts. These papers concern sample size, permissible number
of splits, sieving time, and sieve-vs-settling tube comparisons. These papers were published where
sedimentologists would not ordinarily see them, but should be required reading for students.


The recent appearance of two encyclopaedic works
on sedimentology (Friedman & Sanders, 1978; Fair-
bridge & Bourgeois, 1978) having unusuallycomplete
bibliographic references, provides an opportunity
to check the state of the art and to identify significant
gaps in the coverage provided. This is important
because these two books probably will serve as the
'core storage' for sedimentological knowledge for
some years to come.
We would like, therefore, to draw attention to
several key papers in sedimentology which we have
been unable to find referenced in Friedman &
Sanders (1978), Fairbridge & Bourgeois (1978),
Selley (1976), Pettijohn (1975), Pettijohn, Potter &
Siever (1972), Carver (1971), Blatt, Middleton
& Murray (1972), Folk (1974), Berthois (1975),
Griffiths (1967), and Tickell (1965).
For example, a classic paper by Mizutani (1963)
on sieving methodology was one of the compelling
reasons for insistence, some years ago, that scientific
work in the Florida State University laboratories be
carried out to new standards: quarter phi sieves,
30 min sieving time, and relatively small initial
sample (40-50 g, after no more than one split).
The most practical aspect of Mizutani's paper, in
0034-0746/80/0400-0231 S02.00
C 1980 International Association of Sedimentologists


our opinion, has to do with sieving time (although
he addressed a more important question than this).
De Vries (1970) considered the problem of sample
size. In a graph (p. 530) de Vries showed a plot of
representative grain size rs sample size, with index
lines for 'high accuracy', 'normal accuracy', and 'low
accuracy'. For example, for Ds, sand of 0-5 mm
diameter (84% of the sample is finer than 0-5 mm),
the high accuracy line indicates that the sample
size should be about 25 g. This important paper
likewise is not cited in any of the works mentioned
above.
Emmerling & Tanner (1974) showed that a suitably
small sample cannot be obtained by repeated
splitting, without introducing a devastating (com-
pounded) splitting error, and they recommended a
single split only. This suggests that the original
sample be not more than 60-100 g (or, in rare cases,
where two successive splits must be taken, regardless
of the error introduced, 120-200 g).
Coleman & Entsminger (1977), in a comparative
study of sieving, settling tube work, and grain
measurement under the microscope, showed that
there are important differences between sieve and
settling tube data, only one of which is that the
latter are not as accurate as the former (verification
under the microscope) as a measure of grain size.


Lectre Ntes ame I-I Balihi


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


A. Socci & W. F. Tunner


We would like to emphasize that our intention in
writing this note is not to criticize current texts, but
to draw attention to important papers, in publica-
tions not commonly read by sedimentologists. We
are aware of the almost impossible task of keeping
abreast of the ever-increasing volume of geologi-
cal information, even within one's own area of
specialization.

REFERENCES

BERTHOIS, L. (1975) rude Sidimentologiiue Des Roches
Meubes (Techniques et Mithodes). Doin Editeurs,
Paris. 278 pp.
BLArT, H., MIDDLSTON, G. & MURRAY, R. (1972)
Origin of Sedimentary Rocks. Prentice Hall, New
Jersey. 634 pp.
CARVER, R.E. (Ed.) (1971) Procedures in Sedimentary
Petrology. Wiley & Sons, New York. 653 pp.
COLEMAN, C. & ENTSMINGER, L. (1977) Sieving vs settling
tube: a comparison of hydrodynamic and granulo-
metric characteristics of beach and beach ridge sands.
In: Coasral Sedimentology (Ed. by W. F. Tanner), pp.
299-312. Geology Department, Florida State Univer-
sity. Tallahassee. Fl. 315 pp.


EMMERLING, M. & TANNER. W.F. (1974) Splitting error
in replicating sand size analyses. Ah.wr. Prog. geol.
Soc. Am. 6, 352.
FAIRBRIDGE, R.W. & BOURGEOIS, J. (1978) Encyclopedia
of Sedimentology. Dowden, Hutchinson and Ross,
Stroudsburg, Pa. 901 pp.
FOLK. R.L. (1974) Petrology of Sedimentary Rocks.
Hcmphill Publishing Co., Austin, Texas. 182 pp.
FRIEDMAN, G. & SANDERS, J.E. (1978) Principles of
Sedimentology. Wiley & Sons, New York. 792 pp.
GRIFrrIH, I.C. (1967) Scientific Methods in the Analysis
of Sediments. McGraw-Hill, New York. 508 pp.
MIZUTANI, S. (1963) A theoretical and experimental
consideration on the accuracy of sieving analysis.
J. Earth Sci. Nagoya. Japan. 11, 1-27.
PETTIOHN, F.J. (1975) Sedimentary Rocks. Harper and
Row, New York. 628 pp.
PrlruoHN, FJ.. PoTTER, P.E. & SIEvER, R. (1972)
Sand and Sandstone. Springer-Verlag, New York.
618 pp.
SELLEY, R.C. (1976) An Introduction to Sedimenrology.
Academic Press, New York. 408 pp.
TICKELL, F.G. (1965) The Techniques of Sedimentary
Mineralogy. Elsevier Publishing Co., New York.
220 pp.
DE VRIEs, N. (1970) On the accuracy of bed-material
sampling. J. Hydrand. Res. 8, 523-534.


(Manuscript received 10 August 1979; revision received 10 October 1979)


Lecture Notes James H. Balsillie


James H. Balsillie


Lecture Notes








W F Tame bEMr asrL da FS Cma, Falar. I 95


MOIES


Lecture Notes 74 James IL Bamili






IW. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Appendix II

Guidelines for Collecting Sand Samples


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Guidelines for Collecting Sand Samples

Items 1 through 14 of this list apply to sampling of beach ridge features. Items 7
through 14(depending upon the feature) apply to dunes, subaerial beaches, etc. Subaqueous
sampling requires specialized considerations.

1. Do not work at the map ends of beach ridges (map sense); stay reasonably close
to the middle (map sense). Hydrodynamic influences are too complicated at (or near) ends or
tips.

2. For multiple ridges, the numbering scheme should start with the oldest ridge
(Sample No. 1), and finish with the youngest. However, it is commonly advisable (for various
reasons) to start work with the youngest ridge; in this case, use Number 200 for the youngest
sample, then 199, then 198, etc. In this scheme, the oldest sample may turn out to be #153,
or something like that. This permits Little Ice Age ridges to be sampled, in case the profile
cannot be finished, or the number of ridges is small, or older ridges are problematical (the
younger ridges are generally easy to identify; they give a time interval between ridges, hence
tentative dates for the entire system).

3. Measure or pace, and record, distances between samples (ridges). Use this
distance when uncertain about the presence or absence of a subtle ridge.

4. Collect from the seaward face.

5. Select a site halfway (vertically) between crest and swale.

6. Avoid eolian hummocks, if there are any, by moving parallel with the crest,
maintaining the half-way position.

7. Dig to a depth of about 30-40 cm.

8. Use a spatula to collect a laminar sample, or nearly-laminar sample. If bedding is
not visible, then assume that it was parallel with the ridge face.

9. Measure the sample, in a calibrated measuring cup, as follows:

a. If one split MUST be made later: 90 100 grams.

b. For transport by air (no split): 45 50 grams.

Calibration of the measuring cup must be done in advance, using dry quartz sand.

10. Remove twigs, roots, leaves and other extraneous matter.

11. Place in plastic zip-loc bag (heavy duty); put sample number on high-adhesion
masking tape, on outside of the bag. Do not put paper inside bag; it tends to get wet. Do not
use ink or crayon on outside; it rubs off. Make sure the bag is locked tightly.


Lecture Notes


James H. Balsillie








W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


12. Clean cup thoroughly after collecting each sample. No single grain of sand, from
one sample, should be allowed to contaminate the grain-size distribution of the next sample.

13. Mark the beginning and end of the traverse on a topographic or other suitable map.
Place sample numbers, where appropriate, next to key features such as the junction of dirt
roads or trails.

14. Note the height of crest (above adjacent swales), front slope angle, map distance
between crests, and other pertinent information (such as extent of eolian decoration, if any).

If only one ridge is to be sampled, (e.g., there is only one ridge present, or one ridge
warrants detailed study), then multiple samples might be taken on the face of a cut (trench)
at right angles to the crest, in a horizontal line about half-way down from the crest. If no
trench can be dug, samples can be collected at regular intervals (such as 5 or 10 or 20 m),
on the seaward face, about half-way down from the crest, in a line parallel with the crest. In
any event, sample locations should be sketched (map sense).

Revised 28 April 1994 W. F. Tanner


Lectue Noes Jaes H BalIe


James H. Balsillie


Lecture Notes







W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


NOTES


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie







W. F. Tanner -- Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


Appendix III

Laboratory Analysis of Sand Samples


Lecture Notes James H. Ba/si/lie


James H. Balsillie


Lecture Notes








W. F.. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995




Laboratory Analysis of Sand Samples

In North America sieve nests are everywhere standardized and comprised of half-height
U. S. Standard sieves, 8 inches in diameter.

The initial sample should be 45-60 grams. If it is 80-120 grams, it can be split once.
A second split should not be made; samples larger than 120 grams are too large for useful
work, because they require more than one split and thus introduce a compound splitting error.

The initial sample should be very fine gravel, sand, and coarse silt (and perhaps a small
amount of clay), but nothing coarser, and nothing finer. It should be clean and free of plant
debris and /or shell fragments (of any size). Shell fragments can be removed with hydrochloric
acid; after treatment and washing, the residue should be 45-50 grams. Hydrogen peroxide
can be used to remove fine organic matter.

If some clay is present, it should be in dispersed form, but not in flocs, clumps, or
blocks. If it is not in dispersed form, then it should be treated with Calgon, or Varsol, and/or
ultra-sound. Normally, clay and/or very fine silt, up to about 15-20% of the total, can be
handled, more or less satisfactorily, in the sieving process. However, one gets more accurate
results by separating the clay-and-fine-silt fraction and then measuring it in the settling tube.
In this case, the sand fraction (down to 4.5 phi) can be analyzed by itself (clean sand). The
data on the silt-and-fine-clay must not be discarded.

The best procedure for measuring the sand grain size is sieving. Counting grains on
a microscope slide is extremely slow and tedious, and produces unknown operator error; it
is probable that it is not replicable. The settling tube displaces the mean significantly,
minimizes polymodality, reduces the numerical value of the standard deviation, and distorts
the higher moment measures, in many cases severely; this is because the settling tube adds
a particular hydrodynamic character (due to grain-to-grain interactions which modify greatly
the settling velocities of individual particles) which was not present in the original sample.

There are several other techniques for measuring grain size, but some of them do not
cover the necessary size range in acceptable fashion, and others have not been calibrated
properly yet.

Sieving should be done in 8-inch-diameter, half-height, steel-screen sieves having a
quarter-phi interval, and should use 30 minutes per sample on a mechanical shaker. Weighing
may be good enough to 0.001 gram, but if the balance is capable of doing so, 0.0001 is
better (for later rounding off). The weight prior to sieving should be compared with the total
of the size-fraction weights, to determine the magnitude of error in sieving; sieve loss is,
ideally, no more than 0.1 0.5 percent (about 10 to the negative 3).

The raw weights that are obtained in this fashion are suitable for advanced statistical
analysis, using the first six moment measures (GRAN-7 computer program). These parameters
can be evaluated for the entire sample suite, provided that it is homogeneous (using the
SUITES program). If the samples were taken along an historical line (e.g., from oldest to
youngest), individual parameters can be smoothed slightly (moving averages; window = 5,


Lecture Notes


James H. Balsillie







W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995


7 or 9), to produce a history of depositional conditions.

Cf. Socci and Tanner, 1980. In: "Sedimentology", v. 7, p. 231.

Revised March 1994


W. F. Tanner


Lecture Notes James H. Balsillie


Lecture Notes


James H. Balsillie







W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


NOTES


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Appendix IV

Example Calculation of Moments and Moment Measures
for Classified Data


Lectre NtesJame H.Balslli


James H. Balsillie


Lecture Notes








W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


Example Calculation of Moments and Moments Measures
for Classified Data
(After Fogiel, et al. 1978)

Mean
Frequency Mid-Point Mean f(X )2 f (X, )4
ClassR Deviation f, (X-2 f. (X1 X)3 f (X- X
f, (X X)
49-54 6 51.5 66.5 -15 6(225) =1350 -20250 303750
55-60 15 57.5 66.5 -9 15(81)=1215 -10935 98415
61-66 24 63.5 66.5 -3 24(9)=216 -648 1943
67-72 33 69.5 66.5 3 33(9)=297 891 2673
73-78 22 75.5 66.5 9 22(81)=1782 16038 144342
Totals 100 4860 -14904 551124


It is now possible to compute the moments and the moment measures, where n = I
fi. The first moment is the average or mean, m,, given by:


m fi X1 = 6(51.5) + 15(57.5) + 24(63.5) + 33(69.5) + 22(75.5) =66.5
n 100


which is also the first moment measure( which can have units).

The second moment, m2, is calculated according to:

f r,(X, X)2 4860
m2 = -- 49.09
n 1 99


which may have dimensions of units squared, and the second moment measure or standard
deviation (or sorting coefficient), a, is:

a == 1.09 = 7.006


with possible unit dimensions.

The third moment, m3, is determined as:

3 f, (X, ,)3 -14904 -150.55
m, = -150.55__ __
n- 1 99


and is always dimensionless. The third moment measure, termed the skewness, Sk, is also


Lecture Notes


James H. Balsillie







W. F. Tanner -- Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


dimensionless and is given by:

Sk m3 -150.55 -150.55 = -0.438
(m2)15 49.091.5 343.95


The fourth moment, m4, is produced by:

E f (X/ X)4 551124
S n 1 99 5566.91


and is dimensionless. The fourth moment measure, called the kurtosis, K, a dimensionless
parameter, is determined by:

K= m4 5566.91 5566.91 2.31
(mn)2 49.092 2409.83


Lecture Notes James H. Ba/si/lie


Lecture Notes


James H. Balsillie









W. F. Tanner Environ. Clastic Granulometry -- FGS Course, Feb-Mar, 1995


NOTES


Lectue Noes Jmes Basihi


James H. Balsillie


Lecture Notes




Full Text

PAGE 1

QE 99 .A341 no.40 William F. Tanner

PAGE 3

State of Florida Department of Environmental Protection Virginia B. Wetherell, Secretary Division of Administrative and Technical Services Mimi Drew, Director of Technical Services Walter Chief ...... .. . .. .......................... . . ..... ..... :: :Hl . : ..... =. ,:il:lw,:::::::'::::Jii::r ... No. ... : ,',( :.:::.: .. ::' '!,'' :iji' Tanner 1,11' =m;i1!llll11fflilli!lllllif oP. jllfH: .1lll!' ==== E .,,,,, ntal a m G 10 t :::: ==:: Rorida Geological Survey Talahassee, Rorida 1995 i

PAGE 4

ii

PAGE 5

Governor Lawton Chiles LETTER OF TRANSMITTAL Florida Geological Survey Tallahassee Florida Department of Environmental Protection Tallahassee, Florida 32301 Dear Governor Chiles: The Florida Geological Survey, Division of Administrative and Technical Services, Department of Environmental Protection, is publishing "William F Tanner on Environmental Clastic Granulometry" as its Special Publication 40. This document shall be of use to the State as a source of information related to sampling, analysis, and interpretation of the significantly large volumes of sedimentary lithologies of Florida Such work is a necessity and is important to consider when addressing environmental concerns and issues on the behalf of the welfare of the State of Florida. Respectfully yours, bJa \!:kAAWalter Schmidt, Ph.D., P.G. State Geologist and Chief Florida Geological Survey iii

PAGE 6

KEYWORDS: Beach, Depositional Environments, Eolian Grain Size, Granulometry, Fluvial, Kurtosis, Lacustrine, Littoral, Moment Measures, Probability Distribution, Settling, Sieving, Skewness, Suite Statistics, Wave Energy. Printed for the Florida Geological Survey Tallahassee, Florida 1995 ISSN 0085-0640 iv

PAGE 7

W. F. Tanner-Environ. Clastic Granu/ometryFGS Course, Feb-Mar, 1995 FOREWORD Among his many other geological pursuits, Dr. William F. Tanner has over 45 years of experience in sedimentologic studies and applications. He was chairman for the 1963 Society of Economic Paleontologists and Mineralogists (S. E. P. M.) interdisciplinary Inter-Society Grain Size Study Committee which established sedimentologic standards that remain the basis for sedimentologic work. His combined experience and expertise is of a calibre not commonly found at universities, Jet alone available for other instructional opportunites. W. F. Tanner has persisted through the years in amassing information on modern sedimentary environments, so that such information could be used in interpreting sedimentary rocks of the geologic column. Hence, not only can ancient and classical geological environments be addres sed, but so can modern sedimentary environments that have recently become of paramount importance concerning humankind's treatment of our planet . It will become apparent that W. F. Tanner has amassed a veritable arsenal of published works. Short of being a scholar of this published work, one might, however, be hard-pressed to discover the motivation, the rationale, and the logic behind his sedimentologic pursuits. A better, more revealing way in which to understand these things, to be able to place them into perspective, is to have the researcher, himself, teach a course on the subject. His offer to teach such a course at the Florida Geological Survey during the 1 995 Spring semester provided the opportunity, and motivated the compilation of this work. It is hoped that this document will, to some extent, capture and place into perspective William F. Tanner's approach to sedimentology and granulometry and its environmental ramifications. ACKNOWLEDGEMENTS James H. Balsillie March 1995 45MB Lecture attendees completing this February-March, 1995, course included: James H. Balsillie Paulette Bond Kenneth M. Campbell Henry Freedenberg Ronald W. Hoenstine Ted Kiper L. James Ladner Edward Lane Jacqueline M. Lloyd Frank Rupert Thomas M. Scott Steven Spencer Florida Geological Survey editorial staff that reviewed this volume were Jon Arthur, Kenneth M. Campbell, Joel Duncan, Rick Green, Jacqueline M. Lloyd, Frank Rupert, Walter Schmidt, and Thomas M. Scott. Their special attention, contributions leading to greater Lecture Notes v James H. Balsillie

PAGE 8

W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 clarity, and accelerated review are to be commended. During preparation of this document the generous counsel of Kenneth M Campbell was especially enlighten i ng. Compilation of this account was supported by funding from cooperative studies between the Florida Geological Survey (FGS) and the United States Geological Survey (agreement number 37-05-02-04-429) entitled the Florida Coastal Wetlands Study, and between the FGS and the Minerals Management Service (agreement number 37-05-02-04422) entitled the East-Central Coast of Florida Study. Copyrighted material appea r s in this work for which permission to publish was granted from several sources. Acknowlegements are extended to the journal of Sedimentology for the document : Socci, A., and Tanner, W F., 1980, Little known but important papers on grain-size analysis Sedi mentology v. 27, p. 231-232, to the journal TI'IIIISIIt:tions of the G_, Coast Assot:illtion of Geological Societies for the document: Tanner, W F 1990, Origin of barrier islands on sandy coasts : Transactions of the Gulf Coast Association of Geological Societies, v. 40, p. 90-94, and to the Jolll'lllll of Sedimenfllry PetrD/ogy (now the JIHIIIIIII of Sedimentllry Resean:h) for: Tanner W. F., 1964, Modification of sediment size distributions : Journal of Sedimentary Petrology, v. 34, no. 1, p. 156-164, and the abstract of: Doeglas, D. J., 1946, Interpretation of the results of mechanical analyses: Journal of Sedimentary Petrology, v. 16, no.2 1, p. 19-40. Certain ill u strations (figures 19, 20, 21, 22, 23, and 35 of this text) and two papers (in which the illustrations were originally published) appear in this document. The papers are : and: Tanner, W F., 1991 Suite statistics : the hydrodynamic evolution of the sediment pool: [In] Principles, Methods and Application of Particle Size Analysis, (J. P. M. Syv i tski, ed .), Cambridge University Press Cambridge, p. 225-236, Tanner, W. F 1991 Application of suite statistics to stratigraphy and sea-level changes: [In] Principles, Methods and Application of Particle Size Analysis, (J. P. M Syvitski, ed.), Cambridge University Press, Cambridge, p. 283-292. Lecture Notes vi James H Balsillie

PAGE 9

W. F. Tanner--Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 This published material was copyrighted by Cambridge Un i versity Press in 1991, and is here reprinted with the permission of Cambridge University Press. Lecture Notes vii James H. Balsil/ie

PAGE 10

W F. Tanner--Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 CONTENTS Page LETTER OF TRANSMITTAL . . . . . . . . . . . . . . . . . . . . . iii FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . v ACKNOWLEDGEMENTS ...... ....................................... v INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1 PARTICLE SIZE AND NOMENCLATURE ........ ... ........................ 3 ANAL VTICAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . 4 Laboratory Do's and Don'ts ...................................... 5 Sieving Time . . . . . . . . . . . . . . . . . . . . . . 5 Balance Acc,uracy ....................................... 5 Splitting ......................................... ..... 5 Sieve Sam pie Size . . . . . . . . . . . . . . . . . . . . 5 Sieve Interval . . . . . . . . . . . . . . . . . . . . . 5 Analytic Graphical Results ... ... ................................. 5 The Bar Graph . . . . . . . . . . . . . . . . . . . . . 5 The Cumulative Graph ..................................... 6 The Probability Plot . . . . . . . . . . . . . . . . . . . 6 Settling-Eolian-Littoral-Fluvial (SELF) Transpo-Depositional Environmental Identification .................... ....... 8 Line Segments versus Components, and Plot Decomposition ............... 9 The Key to Probability Distributions . . . . . . . . . . . . . . . . 1 0 Sieving Versus Settling . . . . . . . . . . . . . . . . . . . . 11 Moments and Moment Measures . . . . . . . . . . . . . . . . . 12 How Not to Plot -An Example . . . . . . . . . . . . . . . . . . 15 DETERMINING THE TRANSPO-DEPOSITIONAL ENVIRONMENTS . . . . . . . . 16 The Sediment Sample and Sampling Unit . . . . . . . . . . . . . . 16 Suite Pattern Sampling . . . . . . . . . . . . . . . . . . . . 16 The GRAN-7. Program . . . . . . . . . . . . . . . . . . . . 17 Example 1: Great Sand Dunes, central Colorado . . . . . . . . . 17 Example 2: St. Vincent Island, Florida ......................... 18 Example 3: The German Darss ........................... . 20 Example 4: Florida Panhandle Offshore Data .................... 22 Example 5: Florida Archeological Site ......................... 22 -------------------------------------------------------Lecture Notes ... V111 James H. Ba/sillie

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W. F. Tanner -Environ. Clastic Granu/ometry FGS Course, Feb-Mar, 1995 Example 6: Origin of Barrier Islands ........ ... .... . . ........ 23 Sample Suite Statistical Analysis ................... . ............. 24 Tail of Fines Plot . . . . . . . . . . . . . . . . . . . . 24 The Variability Diagram ................................... 25 Skewness Versus Kurtosis Plot .............................. 25 Diagrammatic Probability Plots . ............................ 25 The Segment Analysis Triangle .. .......... .................. 26 Approach to the Investigation .................................... 27 The Field Site ........................ ....... ........... 27 The Paleogeography ...................................... 28 Hydrodynamics . ............ .... ........... ....... ..... 28 The Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . 28 Kurtosis and Wave Energy Climates ........................... 29 Case 1. The Lower Peninsular East and West Coasts of Florida .. 29 Case 2. Denmark .................................. 29 Case 3. Captiva and Sanibel Islands, Lower GuH Coast of Florida . . . . . . . . . . . . . . . . . . 30 Case 4 Dog Island, eastern Panhandle Coast of Northwestern Florida . . . . . . . . . . . . . . . . . . 30 Case 5. Laguna Madre, Texas .... . ................... 31 Kurtosis versus Seasonal and Short-Term Hurricane Impacts ......... 31 Kurtosis and Long-Term Sea Level Changes ..................... 32 St. Vincent Island, Florida, Beach Ridge Plain . . . . . . . 33 St. Joseph Peninsula Storm Ridge . . . . . . . . . . . 34 Beach Ridge Formation Fair-Weather or Storm Deposits? ........... 34 Texas Barrier Island StudyConversation with W. Armstrong Price . . . . . . . . . . . . . . . . . . . 35 Transpo-Depositional Energy Levels and the Kurtosis; and an Explanation . . . . . . . . . . . . . . . . . . . . . 35 Importance of Variability of Moment Measures in the Sample Suite .......... 36 Application of Suite Statistics to Stratigraphy and Sea-Level Changes . . . . 36 Cape San Bias, Florida .................................... 36 Medano Creek, Colorado . . . . . . . . . . . . . . . . . 37 St. Vincent Island Beach Ridge Plain .......................... 38 The Relative Dispersion Plot . . . . . . . . . . . . . . . . 38 Lecture Notes ix James H Balsil/ie

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W. F Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 7995 The SUITES Program .......... ....... ......... ......... ... 39 Example 1. Great Sand Dunes Colorado .......... ............ 39 Example 2. Storm Ridge, St. Joseph Peninsula Florida ............. 39 Example 3 The Railroad Embankment, Gulf County, Florida .......... 44 The Storm Ridge versus the Railroad Embankment and the Z-Test ...... 45 Example 4. The St. Vincent Island Beach Ridge Plain ............. 46 Spatial Granulometric Analysis ...... .... .... .................... 51 Review .......... ......... ............... ................. 52 1 The Site . . . . . . . . . . . . . . . . . . . . . . 52 2 Paleogeography ......................... ............. 53 3. Kurtosis and Hydrodynamics ......... ...... ....... ...... 53 4 Sand Sources ...................... .... . ......... 53 5. Tracing of Transport Paths ............................... 53 6 Sea Level Rise . . . . . . . . . . . . . . . . . . . 54 7. Seasonal Changes and Storm / Hurricane Impact ................ 54 PLOT DECOMPOSITION: MIXING AND SELECTION ......................... 54 Sim pie Mixing . . . . . . . . . . . . . . . . . . . . . . . 55 Non-Zero Component .................................... 55 Case I . . . . . . . . . . . . . . . . . . . . . 55 Case II .......................................... 55 Zero Component . . . . . . . . . . . . . . . . . . . . 57 Selection . . . . . . . . . . . . . . . . . . . . . . . . . 57 Censorsh i p . . . . . . . . . . . . . . . . . . . . . . 57 Type I Censorship .................................. 57 Type II Censorhip . . . . . . . . . . . . . . . . . 57 Truncation . . . . . . . . . . . . . . . . . . . . . . 58 Filtering . . . . . . . . . . . . . . . . . . . . . . . 58 Summary ............................ ................ 59 Determination of Sample Components Using the Method of Differences ....... 59 Case 1. Two Components with Means Unequal, Standard Deviations Equal, and Proportions Equal . . . . . . . . . . . . . 60 Case 2. Two Components with Means Unequal, Standard Deviations Unequal, and Proportions Unequal ....................... 62 CARBONATES . . . . . . . . . . . . . . . . . . . . . . . . . . 63 REFERENCES CITED AND ADDITIONAL SEDIMENTOLOGIC READINGS . . . . . . 66 --------------------------------------------Lecture Notes X James H. Ba/sillie

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W F Tanner Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 APPENDICES Appendix I Little Known But Important Papers on Grain-Size Analysis ...... .... 71 Appendix II. Guidelines for Collecting Sand Samples ....................... . 75 Appendix Ill. Laboratory Analysis of. Sand Samples . . . . . . . . . . . . 79 Appendix IV. Example Calculation of Moments and Moment Measures for Classified Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Appendix V. The Darss . . . . . . . . . . . . . . . . . . . . . . 87 Appendix VI. Origin of Barrier Islands on Sandy Coasts . . . . . . . . . . . 95 Appendix VII. Suite Statistics: The Hydrodynamic Evolution of the Sediment Pool .. 101 Appendix VIII. Application of Suite Statistics to Stratigraphy and Sea-Level Changes . . . . . . . . . . . . . . . . . . . . . . . . . 115 Appendix IX. Sedimentologic Plotting Tools ................ ............. 127 Appendix X. Modification of Sediment Size Distributions . . . . . . . . . 133 Lecture Notes xi James H Bslsillie

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W F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar 1995 Lecture Notes xii James H. Balsi/lie

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W. F. Tanner-Environ. Clastic Granulometry-FGS Course, Feb-Mar, 1995 WIWAM F. TANNER on ENVIRONMENTAL CL4ST/C GRANULOMETRY Compiled by James H. Balsillie, P. G. No. 167 Coastal Engineering Geologist The Florida Geological Survey Chief Editor William F. Tanner, Ph.D Regents Professor Department of Geology The Florida State University INTRODUCTION Sedimentology encompasses the scientific study of both sedimentary rocks and unconsolidated sedimentary deposits. Sedimentology is defined by Bates and Jackson ( 1980) as the .. scientific study. of sedimentary rocks and of the processes by which they are formed .. and ... the description, classification, origin, and interpretation of sediments. They also define granu l ometry to be the ... measurement of grains, esp. of grain sizes. It should be apparent therefore, that granulometry is a pursuit that, while appearing to be more specialized, has significant impacts on the success of more generalized sedimentologic endeavors. Unconsolidated sedimentary particles range in size from boulders (e.g., glacially produced products) to colloids. This work deals with quartzose sediment sizes ranging from about -2.0 f/J (4 mm) to about 5.0 f/J (0.0313 mm), that is, those sediments whose bulk is comprised of sand-sized material. At the outset, it is important to understand that the majority, perhaps 90/o or more, of sand-sized siliciclastic sediments have been transported and deposited by water. In a recent paper on suite statistics (i.e., a collection of correctly obtained samples from a discrete sedimentologic body), W. F. Tanner ( 1991a) identified an historical paradigm and asked certain questions pertinent to the objectives of this account. Lecture Notes 1 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 For a century or so the purpose of making grain size measurements was to determine the diameter of a representative particle This is useful when one is studying reduction in grain size along a river (e.g., Sternberg, 1875) But it is a simplistic approach, and one is entitled to ask : Is the mean diameter the only information that we wish to get? Or does the simplicity of this first step make us think that we have now described the sand pool? When we measure grain size what do we really want to know? This does not refer to whether we measure the long axis or the short axis of a nonspherical particle, or whether we approximate the diameter by measuring a surrogate (such as a fall velocity). Rather, "Ye ask this question in order to get a glimpse of how far research has come in understanding transport agencies or conditions of deposition, and of the degree to which we might reasonably expect to improve our methods of environmental discrimination Does a set of parameters describing a size distribution for a sample set from a discrete sedimentary deposit allow us to compare the set with some other, that we might recognize a different transport agency or depositional environment? An answer or answers to this question constitutes an underlying objective of this However, the question also engenders complexity of the kind that would pique the interest of any researcher. Unfortunately, most of us (even if we were so motivated) are not afforded the luxury to pursue such matters. Rather we must be content to apply any answers to such a quest in a practical, a practicable, a pragmatic manner, which also constitutes an underlying objective of this work. In 1795,James Hutton p r oposed the Uniformitarian Principle, stating that .. thepresent is the key to the past. If this is so, then the corollary that the past is the key to present must also hold true. In addition, a second corollary must be true that the present is the key to the future. It might be submitted therefore, that i n this day and-age of environmental concern, we might well have a responsibility to place at least equal importance on the corollaries as on the principal. It would appear to be so critical, in fact, that at no time in the history of the discipline has, not just the investigation, but the application of "now geology .. or now earth science .. been more important. This document, while available for unlimited distribution, has not been designed to be a general information document tailored for the layman. It is a quite specific account, which requires some considerable familiarity with granulometry, sedimentology, and statistics associated with probability distribut i ons It is, therefore, designed for those who require specific information in the i r approach to environmental concerns i.e., it is a professional peer group educational/reference document. One might feel that there is an apparent lack of references to the work of others who have published countless papers on sedimentological matters. Please understand that this document is the result of a short course documenting contributions of one researcher. W. F. Tanner is adamant about giving credit where credit is due While recording of many references might not be apparent in the following account, they certainly are in his published works to which the reader is referred (e.g., see the appendices). Lecture Notes 2 James H. Balsillie

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. W. F..: Tanne.r -Environ . Clastic FGS Course, Feb-Mar, 1995 I \ SIZE AI/D NOMENCLATURE In sedimentologic endeavors particulate matter can cover a significant range in size. One scheme, for example encompasses a minimum of five orders in magnitude (Table 1 ) Note, also, that there is a consistent progression or square-root depending upon where the origin lies) in size and corresponding Table 1. Basic Paricle Size Nomeclature Distinctions nomenclature. Using another scale, that of Wentworth (1922), a similar although somewhat different nomenclature-size scale is espoused and commonly used (see Table 2). : :' Boulders 256mm Cobbles 64mm Pebbles 4mm Sand 1/16 mm Silt j_ 1'/256 : mm Clay . ; i.. . This course addresses s11nd-sized p11rtic/es, or in the case of the WentwoJth Scale s11nd-and gl'llnule-sized p1111ic/es. In addition, this co urse deal$ primarily with siliciclastics (i... e., : quartz particulate matter) For instance, heavy mineral-laden sediments (e.g., magnetite) behave differently than quartz to forcing elements, and granulometric interpretations will .. quite different. sediments also produce different results, not because of mass density differences but because of carbonate grain shape divergences. The latter, however, because of the preponderance of CaC03 sediments in south Florida will receive attention throughout course . . Numerical. :repr$s.entation of sediments is often given in millimeters (mm) There are, however, compelling reasons to the phi (pronounced conventipn ... Correct terminology is phi .. units, the phi s,:a/e, or phi meiiSf!te. Phi. units, denoted by Lecture Notes : 3 Table 2 Size Convensions .nc1 hrticle Nomenc:tmn ..... ........ w..twDdiiCiulicllliDw ... .. Boulder 256.00 -8.00 Cobble 64.00 -6.00 . 6 .60 .60 Pebble Gravel 4 .76 .26 4 .00 .00. 3 .36 .75 2.80 .60 Granule : 2 .38 .25 .2.00 .00 1.68 .0.75 Very 1 .41 .0.60 eo. ... 1.19 .0.26 S.nd 1.00 0.00 0.84 Coane 0 .71 0.60 S.ad 0.69 0 .76 0.60 1.00 0.42 1.26 Medium 0.36 1.60 Sud 8aad 0 .30 1.76 0.26 2 .00 0.21 2.26 Fine 0.177 2.60 Sand 0.16 2.76 0 .126 3.00 0 106 Very 0.088. 3.60 Fine .. 0.074 3.76 S.ad 0 .0625 4.00 O.Q626 4.25 0.0442 4.60 0.0372 4 .76 0 .0313 6.00 Sit 0.0263 6 .25 0.0221 6 .60 0.0039 8.00 . Clay 0 .0002 12.00 Colloid ., James H. Balsil/ie

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W. F Tanner--Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 the Gre ek symbols (lower case) or (upper case) are numerically defined by: cp = log2 d(mm} where d(mm) i s the part icle diameter in mm. Conversely, d(mm} = 2 -4> Computational equations for the above which can be easily (e. g ., Hobson 1977) programmed or evaluated using a hand-held calculator, are given by: cp = 1.442695 In d(mm} a nd d(mm} = /NV In ( 0.69315 cp) = e-0. 69315 4> This course uses and promotes universal use of the phi measure. adoption were forthcoming from the Reasons for its 1963 S E .P.M. Inter-Society Grain Size Study Committee They were published by Tanner (1969) and are listed in Table 3 ANALYTICAL CON SID ERA TIONS Sand-sized particulate matter is of such dimension that it responds in a timely manner to aero-and hydrodynamic forces (i.e., wind, waves, astronomical tides, currents, etc.). Conversely therefore, such sediments can reveal information about how they were transported and, hence, the paleogeography. See, for instance, Socci and Tanner ( 1980) and text reference to De Vries ( 1970) of ::A:>: ': , : : d,. w .. tX'.:' -.--:: .. -;., .... -;-.::::-:-:. There are, however, several considerations with which to contend First, field sampling and laboratory errors do occur. Second many samples, ... i.e sample suites, ... are required to verify transport and depositional interpretations and results (e.g., W. F. Lecture Notes Table 3. Reasons for Adoption of the Phi Scale (from Tanner 1969). (1) Evenly-spaced division points, facilitating plotting. (2) Geometric basis, allowing equally close inspection of all parts of the size spectrum. (3) Simplicity of subdivision of classes to any precision desired, with no awkward numbers. (4) Wide range of sizes, extending automatically to any extreme. (5) Widespread acceptance. (6) Coincidence of major dividing points with natural class boundaries (approximately) (7) Ease of use in probability analysis (8) Ease of use in computing statistical parameters (9) Amenability to more advanced analytical methods. (10) Fairly close approximation to most other scales, allowing easy adoption. (11) Phi-size screens are already available commercially. No other scale is even close to matching this list; most other scales do not have more than three or four of these advantages. 4 James H Balsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Tanner has analytical results for over 11,000samples from a multitude of transpo-depositional environments each comprised of many sample suites). Third, standardized laboratory and analytical procedures are crucial in order to realize accurate interpretations. Laboratory Do's and Don'ts Guidelines for the collection of sand samples are given in A:P.pendb(ll. Procedures for laboratory analysis of samples are given in The follc)w ing ; however, identify certain issues that deserve special, concerte .cfatte n tion : Sieving Tnne A minimum of 30-minutes is recommended for siliciclastic sediments (longer sieving time is a matter of diminishing returns); see the work of Mizutani as referenced in Socci and Tanner ( 1980). Balance Accuracy Weigh to 0.0001 grams, then round to the nearest 0.001 g Splitting Splitting is "bad news ... It is recognized that splitting might be a necessity under some circumstances. However, there should be no more than one split, and to "do without" is even better. See the work of Emmerling and Tanner (1974) referenced in Socci and Tanner (1980). Sieve Sample Size Introduce no more than 100 g to the -2.0 > or finer sieve. A larger mass or size will introduce overcrowding. An introductory sample size of 45 g is ideal, but can range from 40 to 50 g. For instance, for a sample containing 50/o quartz and 50/o carbonate material, a 100 g sample (maximum size allowable) needs to be sieved first. The C03 is then removed with HCI and the siliciclastic fraction resieved. Simple subtraction of the quartz distribution from the total distribution will yield the CaC03 distribution. Sieve Interval Without reservation, it IS recommended that 1 /4-phi s1eve intervals be used in granulometric work. Analytic Graphical Results The Bar Gn1ph The bar graph (Figure 1) is not a rigorous analytical tool; it is for the layman. It is not sufficient to utell the story" for analytical purposes. There is a better graphical method, Lecture Notes 5 James H. Ba/sil/ie

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W. F. Tanner-Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 however, that tells the story" with standardized clarity. The bar graph, however, c an be presented to facilitate a communicative link leading to the proper form of graphi c al presentation The Cumgllfive Graph This form of graphing (Figure 2) using various types of graph paper (e.g linear, log cycle, etc.) is too indefinite. Data and paper plotting ordinates may not be evenly spaced leading to possible multiple interpretations (e.g., fitted li nes A and 8) that can each have significantly high correlation coefficients. The ProbaWity Plot 3 875 i 3 625 i 3.375 .. 'E 2 875..g. 2 3 7 5 2 125 1 875 5: 1 625 1 3 7 5 1.125 0 875 .. 0 .625 0 2 4 6 8 10 12 1 4 16 1 8 2 0 2 2 24 Frequency% Figure 1 The bar graph. This form of plotting (Figure 3) uses arithmetic probability paper Such paper assures that points will be equally spaced Ensuing interpolation can then be accomplished with assurance Such assurance is not always possible using other types of graph paper Non10 0 p Finer ==:::parametric parameters such as the Figure 2. The cumulative graph. median (50th percentile value) can be located with a good deal of precision Arithmetic probability paper also allows for the procedure of decomposition to be discussed later. Moreover, statistical application and arithmetic probability paper constitutes a Coarse Ph i Fine 0 .1% 50% Figure 3. The arithmetic probability plot. 99.9% standardized approach for sedimentologic work. The line on the graph is a true Gaussian (after K F. Gauss) distribution because it plots as a straight line on probability paper It is more realistically the case, however, that the cumulative distribution for sandsized siliciclastic samples are comprised of multiple line segments (Figure 4). Esch segment, in fsct, commonly represents s different transpo-deposftionslprocessorsediment source RULE: a minimum of three (3) consecutive points are required to identify a segment Lecture Notes 6 James H Balsillie

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W. F Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Phi Fine 0 1% 50% 99.9% Rgure 4. The segmented arithmetic probabiity plot. Coarse Phi Fine 0.1% 50% Rgure 5. Effect of high energy transpo clepositonal processes. Coarse A Phi B 1 / 4 Phi Units 99.9% with assurance It is to be recognized that some transport processes, such as landslide debris and fluvial flooding, are so rapid that granulometric results are not afforded the time to become Gaussian However, mos t eolian and littoral processes provide sufficient time relative to sand-sized range response that analytical granulometric results are allowed to become Gaussian. Hence, transpo-depositional processes can be identified. High energy fluvial sediment data might appear as plotted in Figure 5 Note that the general trend of the slope of a straight line fitted to the erratic granulometric results is steep, indicating poorly sorted sediments. However, both eolian and littoral sediment data provide similar results ... they are very well sorted, i.e., along theyaxis the distributions encompass very few 1 /4-rp units, and line slopes are low. Note: parallel lines of Figure 6 indicate identical sorting, even though sample A has a coarser average size than sample B. In the example of Figure 7 sample 8 is better sorted than sample A, even though sample 8 has a coarser mean. Coarse Fine 0 1% 50% 99.9% B Rgure 6. Aner and coarser cistributions with identical sorting. Lecture Notes -Phi Fine 0 1% 50% 99.9% Figure 7. Coarser and finer distributions with clfferent sorting characteristics. 7 James H. Balsillie

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W F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Settling-Eolian-littorai-Rwia/ (SELF) Transpo-Depositional Environmentalldentificlltion Relative relationships of adjoining line segments require relative consideration when interpreting probability plot results which J H Balsillie has termed the WFT method of SELF detenninstion Consider the generalized plot of Figure 8 for possible combinations of interpretative results Interpretative descriptions are given in Table 4. High Energy Comer Coarse Phi D Possible Curve Combinations Fine Segments B C and D do not necessarily intersect. AEF AEG BEF BEG CEF CEG DEF DEG 50 % 99 9% Low Energy Comer Rgure 8. Basic ine segments on arithmetic probability paper. Table 4. Ruciments of WFT method of SELF determination for ine segments of Figure 8. Segment{S) Description of Interpretation I AEF The Gaussian distribution. Indicates that the operating transpo-depositional force element is wave activity ; point a, relative to segment E, is termed the sud-bi'Nk. This slope, which is gentle, represents beach sand ... it occurs no where else . it is definitive! The higher the B slope of segment 8, the higher the wave energy. Note that for sand-sized material, the surf-break normally appears for low-to moderate-energy wave climates. For high-energy waves, point a moves off the graph {to the left) and segment B disappears {i. e the wave energy is over powering even to the coarsest sand-sized sediment fraction available {Savage, 1958; Balsillie, in press)). D Indicates eolian processes; point a is termed, relative to segment E, the eolilln hump. Represents fluvial energy . has a steep slope, the greater the slope the higher the c energy expenditure. This segment is termed the llut!illl COliiSe fill, or may represent a pebbly beach. E Central portion of the distribution Is the low energy tail termed the settli11g fill and, if present, may indicate lowering G of energy for the total distribution or component distributions of the coarser sediments Lecture Notes 8 James H Balsillie

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W F Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Figures 6 and 7 have illustrated how one can identify finer and coarser distributions with different standard deviations (i.e., sorting). For future referen ce, what of skewness and kurtosis 7 F igure 9 illustrates how skewness appears on the arithmetic probability plot. Figures 1 Oa and 1 Ob illustrate the effect of kurtosis. These plots represent simple examples, ... more complicated results are certainly possible. It IS often advantageous to view concepts using a different approach Regarding moment measures, consider the following (refer to preceding figure s if necessary) First, the mean or average simply locates the central portion of the distri bution. Second, the standard deviation on arithmetic probability paper is the slope of the line representing the distribution Third, the skewness is 0 if the distribution is truly Gaussian (i.e., the often used normal or bell shaped curve terminology, terms which shourd be dropped from usage) and, therefore, as much of the distribution lies to the left of the 50th percentile as to the right. Fourth if the distribution plots as a straight line it is a true Gaussian distribution with a Kurtosis value of K = 3 .0. There is published work that identifies the Gaussian kurtosis as 0 or 1; these however, are but arbitrary definitions determined by subtracting 3 and 2, respectively, from the calculated 4th moment measure line Segments versus Components, and Plot Decomposition When dealing with plotted Coarse Ph i Fine 0.1% 50% 99. 9% Figure 9. Appearance of skewness on arithmetic probabi6ty paper. Coarse Phi Fine 0. 1 % 50% 99.9% Figure 10a. Appearance of kurtosis on arithmetic probabi6ty paper; plot is for a flat-topped (platykurtic) clisbibution. Coarse Ph i Fine 0.1% 50% 99.9% Figure 1 Ob. Appearance of kurtosis on arthimetic probabi6ty paper; plot represents a peaked (leptokurtic) cistribution. sedimentologic data on arithmetic probability paper one often sees multiple line segments (e. g., Figures 4 and 8). These segments represent, as we have learned different transpo depositional processes. They are not distributions in their own right. Lecture Notes 9 James H Balsillie

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W. F. Tanner-Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 There is a common belief espoused in the literature that one can lift out a line segment and examine it on its own to Coarse I -_ Component A ..... _____ ,.. _____ ___ determine low-or mid-level traction loads or suspended load Such advocates do not understand the aero-or hydrodynamics involved ----Phi Combined Curve ... ---.... ---Component 8 ------Where a probability plot has multiple line segments there are true component distributions or components that can be identified using the process of decomposition. For instance the combined distribution of Figure 11 {multi segmented curve) is comprised of two components (not three). Fine I 0.1% 50% 99.9% Rgure 11. Example of plot decomposition yielclng two samples with equal standard deviations and unequal mearis. The Key to Probability Distributions There is a property associated with the Gaussian {or any other) Distribution that is not widely known nor appreciated. However, it is so important that it deserves special identification here. To understand this property will lead to greater clarity as to how statistical distributions are to be viewed, treated, and understood. It is the tails of the distribution which dictate the shape of the central portion of the distribution. Most folks assume it is the central portion of the distribution which determines the behavior of the tails ... an assumption that is incorrect. This was first demonstrated to J. H. Balsillie in 1973 by W. R. James (a statistician and geologist, and student of W. C. Krumbein) Doeglas (1946), in an essentially unknown paper, understood this property ... see the underlined text in his abstract (Figure 12). Lecture Notes joouAL ott SlmDIEMT.UT PBnoLOGY, VoL. 16, No. 1, n. tC)-..40 FIGS. 1-30, TABLE l, APRIL, 1946 INTERPRETATION OF nfE RESULTS OF MECHANICAL ANALYSES1 D j DOEGLAS laboratorium N V. De Bataafache Petroleum Maatachappij Amsterdam ABSTRACT Mechanical analyses cl deposita of variou. sedimentary environments have been made by means of a new type of sedimentation balance for grain ai.zea from 500 to 5 ,. The results have been plotted on arithmetic probability paper Well-aorted sands give on this paper straight lines proving that they have a symmetrical size frequency distn"bution when an arithmetic grade acale is used The size frequency ditribution of the land and ilt grades of argt11aceou Sedimenu commonly is a of a aymmetric:al one. The arithmetic probabdity paper enables ua to study the phenomena c:auaed by the differentiation of the transported detritua. Three main types oC frequarcy distribution called R -, S-and T-types ocx:ur in sedimentary deposiu due to the sort.inJ ol the transporting medium. The characteristic features of a sedim siz e f uen distribution are found in the emea an not tn e centra a t e tstri ut1on. tats stt e ore o not ave sat1s act resu u. e aractens sc pe o e extremes of the distributions caused by the differentiatinr action are frequently blurred by later mixing of material due to variations in the capacity of the tranaportinr medium. Composite frequency cliltributiona, however, arc commonly recor nized if the mults are plotted on the probability paper. & far as analyses by means ol the aedhnentatJOD balance have been made sedimentary environments can be recognized by the predominance or alternation of certain frequency distributions . Agure 12. The Doeglas absbact (1eplinted with permission). 10 James H. Balsil/ie

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W F. Tanner --Environ. Clastic Granulometry -FGS Course, Feb-Mar, 7 995 Sieving Versus Settling Settling tubes have gained popularity because of their time saving capability and, hence, are most often referred to as Rapid Sediment Analyzers (RSA's). There are, however, serious problems associated with RSA's such as drag interference with side walls, and effects of sediment introduction into the fluid, etc. The most serious defect of RSA's, however, involves the production of von Karman vortex trails by the settling grains. Theodore von Karman was born in Hungary in 1881. He was trained as an engineer and became a U S. citizen in 1936. He was a noted aeronautical engineer and consultant to the U. S. Air Force during the late 1930's and the 1940's. He was recently honored with a U. S. postage stamp Up Figure 13. The von Kilmuin vortex tral phenomenon. For an automobile or boat wake the von Karman effect is two-dimensional. For a grain falling in water it i s three-dimensional. Each vortex .. kicks off .. at different times They are spaced at less than 120 degrees (say 1 06 to 108 degrees) which causes the entire system to spiral to the bottom (see Figure 13). These vortexes or vortices (latteral effects are 2 to 3 times the sediment grain diameter) affect other grains much in the same manner as the tailgating effect is used in auto racing. The net result is that larger grains entrain smaller trailing grains, increasing the fall velocity of the smaller grains; hence, the smaller grains appear to be larger than they actually are. At the same time, the smaller entrained grains slow the settling velocity of the larger gra i ns, making the latter appear smaller than they actually are. Bergman ( 1982) investigated the sieving versus settling problem by not only using sieve and settling tube results, but also microscope size determinations, and he verified the above results His findings are recounted in Figure 14. It is also important to note that sieves, at least in the U. S., are standardized. RSA's, however, can significantly vary in equipment type dimensions, fall velocity mathematics applied, etc. A most serious problem between RSA's, is that they are not calibrated from laboratory-to-laboratory. Hence, there is no standardized RSA. The bulk of the literature concerning the issue, supports sieving over settling devices. The U S. Army Corps of Engineers, regarding marine sediments and beach restoration design work, recognizes the problems with RSAs. Hobson (1977), in a Coastal Engineering Research Center document, lists some of the common problems as: (a) Failure of the fall velocity equations to account for the effects of varied particle shapes and densities, interference of falling particles with each other, Lecture Notes 11 James H. Balsillie

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W F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Abstract A comparison of the grain size data derived from sieving and settling techniques of sixty samples from modern sedimentary environments indicates that there exist important differences in the way grain size distributions are perceived by the two methods A third method of analysis, microscope grain size determination, supports the results of the sieve analysis, indicating that the settling tube has inherent properties which makes it Jess dependable for grain size studies. In comparisons of moment measures (sieving vs settling tube) significant differences were found. The settling tube perceives fine grain sizes coarser than they actually are, and coarse grain sizes finer that they actually are. A compression of the overall distribution of values results. This compression also occurs in individual samples, as indicated by studies of the probability plots. The settling tube fails to detect certain tails (in the distribution) that are indicated by the sieving results. This compression of samples is apparent in the standard deviation sieving vs. settling comparison. The settling tube consistently perceives the samples to be better sorted (lower standard deviation) than is indicated by the sieving results. Results of the skewness and kurtosis comparisons indicate the settling tube is not capable of detecting these small differences in the grain size distribution. The compression phenomenon caused by the settling tube is thought to have two possible sources. The first, a physical truncation of the distribution by sampling technique, is of varying signficance. The second, a hydrodynamic utruncation ", occurs in all samples but may be accentuated with certain changes in the distribution. Figure 14. Bergman's (1982) Masters Thesis Abstract on grain size determinations. and water turbulence; (b) drag interference between the cylinder walls and the settling particles; (c) the divergent difficulties of accurately timing the rapid fall of larger particles; and (d) various problems associated with introducing the sediment into the fluid. Hobson concluded that for practical beach engineering problems, sieve data are the most reliable and reproducible, especially among different laboratories He also reported that granulometric results from the two techniques (i.e., sieving and RSAs) are not to be mixed. Moments and Moment MeasuTeS Except for the first moment and the moment measure termed the average or mean, there is a difference between moments and moment measures. Specifically, moment measures are calculated from numerical consideration of moments. The first moment about zero (m1 ) is also the mean or average {p or M) calculated according to: where x is the class midpoint grain size, f is its frequency (weight percent), and n is the number of classes. Higher orders of moments are computed about the mean as a Lecture Notes 12 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 7 995 transcendental progress i on of the form: L l{x-m1)" m = =-----=P n 1 where p is an i nteger, and mP is the pth moment about the mean Moments required for the evaluation of moment measures are: E l{xm1)3 m3-n 1 and E l{xm1)4 m4-n 1 where m2 is the second moment, m3 is the third moment and m4 is the fourth moment. The second moment is actually the variance, and the standard deviation moment measure, becomes: The skewness moment measure, is calculated by: and the kurtosis moment measure, is calculated according to: An example of moment and moment measure calculations is given in -tidbdiW. . .. .. .. ...... . It is critically important to understand that higher moment measures progressively describe more about the behavior of the tails of the distribution as illustrated in the example Lecture Notes 13 James H. Balsil/ie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 of Figure 15. The figure illustrates that the higher moment measures are zero near the center of the distribution, whereas non zero values appear only as the tails of the distribution are approached. This is MOM-DEMO. Data source: Keyboard .. SampleTVER X-46. 02-06-1995 ( 1/4 sieves ) Example of calculation of moment measures: f(i) ProdMn MnDev ProdSD ProdSK ProdKu Prod6th Prod8th Prod10th (;;s) .625 .0021 .001 -1.46 .875 .0455 .039 -1.21 1.125 .2664 .299 -.96 1.375 1.6031 2.204 -.71 1.625 5.1485 8.366 -.46 1.875 13.4455 25.21 -.21 2.125-19.1243-40.639-.04-2.375 10.8556 25.782 .29 2.625 3.8318 10.058 .54 2. 875 4658 t'. 339 79 3.125 .0613 .191 1.04 3.375 .0168 .056 1.29 3.625 .0063 .022 1.54 3.875 .0033 .012 1.79 Sums: n.93g. 114.224 Mean is 2.084 114.224/54.93 [0.236 mm] .004 -.007 8.999999E-03 .02 .043 .092 .066 -.081 .097 .142 .207 .303 .245 -.235 .225 .207 .19 .175 .805 -.572 .405 .203 .102 051 1.084 -.498 .228 .048 .01 .002.587 -.123 .o2a---.oo1o o .032--.001==--0 0 0 0 919 267 071 0 1.121 .606 .328 096 .028-.ooa._ .291 23 .182 .114 .071 .044 .066 .069 .071 .078 .084 .091 028 .036 .046 .077 .129 .216 .014 .023 .035 .084 .2 .475 .01 .018 .033 .108 .349 1.12 5.272 -.266 1.761 1.184 1.413 2.577 Rgure 15. Higher moment measures describe the behavior of the tals of the distribution. For the higher moments, the even moment measures are more meaningful than the odd moment measures. Odd moment measures address asymmetry of the distribution, about which we know relatively little. A comprehensive list of the higher moments and corresponding moment measures (e.g., m5 is the 5th moment, and mm5 is the 5th moment measure; there are no descriptive names for mm5 and higher moment measures) are: Moment E f(x-m1 ) 6 l11s = =----n-1 Lecture Notes Corresponclng Measure 14 James H. Ba/sillie

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W F. Tanner --Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 .E f(xm1 ) 1 m, = =----n -1 How Not to Plot -An Example Figure 16 illustrates a "bad blunder ". F i rst just what is meant by the 11 third moment II i s uncertain. Second, the meaning of 11Zone of 2-way beach flow" is open to question. Third the plotted data are certainly not definitive in del i neating the two regions shown. By design or default, the figure certainly does not convince the student that statistics can work. One lesson is that we must be precise in our use and applicat i on of analytic numerical methodologies and data presentation A second l ess ion is that II single sample II data are commonly contradi ctory. c 0 ' Q) Q "0 Q) .0 :l 0 c as Q) -c: Q) E 0 "E .c 1! l I I I I I i I i i i I 0 lzon e flow on i ; I 1 5 ....... i -+-! 6____..!_s _an+: k s c+-f 1-+-'fv a y + ; ........ 1 +:--+1+II I I -I : I i I I I I I 0 5 11 I 01 I I' I i I. I ..J. 0 I I I I I I -0.5 I I 1 i I \ I I ! \ C 1 5 + ---!-+-; -l, I I I i I j i i i l I I \'"I I I i -2 0 0 0 0 1 0 2 0.3 0 4 0 5 0 6 0 7 0 8 0 9 1 1.1 1.2 1.3 1 4 1 5 Standard Deviation Agure 16. The Friedman and Sanders ( 1978) plot (replotted). Some 250 incividual sample results were originaly plotted; only those which cisagree with the arbibariy set civision (bold dashed ine) are replotted here. The area of uncertainty may contain multiple river sample results (unclear from the original figure). Lecture Notes 15 James H Balsillie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 DETERMINING TRANSPO-DEPOSfflONAL ENVIRONMENTS Rather than occupying careers as scientists purely for the sake of pursuing scientific discovery, most of us occupy positions where there is a limiting constraint of practicality or pragmatism. Let us apply this to the study of granulometry as it applies to sedimentology and environments of deposition. Should we be given a siliciclastic sediment sample of unknown or uncertain origin, can we ascertain its transpo-depositional environment? We can certainly address it. Although there is no certainty that we can -always provide a solution, in most cases we can. One of the basic issues concerns the hydrodynamics or aerodynamics associated with conditions of sediment transport and deposition. The Sediment Sample and Sampling Unit An underlying assumption with such sedimentologic studies is that the field sample we collect is a laminar sample. This is the sedimentation unit of Otto (1938, p. 575) defined as . that thickness of sediment which was deposited under esential/y constant physical conditions. Similarly, Apfel (1938, p. 67) defined a p!Jase as ... deposition during a single fluctuation in the competency of the transporting agent (the reader is also referred to the later work of Jopling, 1964). The sedimentation unit constitutes a narrowly defined event For instance, it is not deposited by a flood occurring over a period of 3 weeks, but it might be deposited by one energy pulse, with each pulse occurring over-and-over during the flood. It is not known what a sedimentation unit, lamina, or bedding plane is in terms of physical principles. But we can recognize them to some extent. Regardless of the unknowns, we should strive to collect sedimentation unit samples In indurated rocks, e.g., sandstones, ground water staining can cause features that appear to be laminae. Drilling can turbidate sediment, causing mixing and disruption of sedimentation units. In many cases, in the field one cannot see the laminae. At other times we can see or sense the laminar bedding in the field, but cannot define it. Where one cannot see the laminae, samples can be taken in a plane parallel to the existing surface if it is determined the surface is the active depositional bedding plane. At other times, a momentary glimpse of bedding planes (due to moisture content, evaporation and associated optics) might occur to aid in sample selection clues. Sampling a sedimentation unit can often be a matter of estimation. However, a multitude of samples termed the sample suite can aid in assuring sampling completeness. Suite Pattem Sampling A suite is a collection of samples that represents a deposit from one transporting agent under one set of conditions and, therefore, must have certain geometric relationships. For instance, it is not practical that 5 samples taken 100 km apart would represent a suite. Do five samples from one river bank or point bar, one beach, or one sand dune that are immediately adjacent to one another (i.e., touching) constitute a suite? By definition, the answer would be yes. However, the preceding two examples are the extremes. Suite samples must be far enough apart to show variation, and yet not spaced far enough apart to Lecture Notes 16 James H. Balsillie

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W. F. Tanner-Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 represent factors that are not waoted or not related. One can look for the transporting depositional agent involved and adjust the suite sampling procedure/schedule accordingly. The number and pattern of suite samples is not etched in stone For instance, road cuts are where you find them, they are not laid out in advance on a grid. Multi-level, hierarchical sampling schemes are not always possible or the best choice. One can also collect suite samples as a time series in the rock record .. vertical sequence, although in cross-bedded rocks it can be difficult. In .. more recent unconsolidated sediments comprising a fluvial point bar or beach ridge plain, the time sequence will be in the horizontal direction. The GRAN-7 Program While the computer programs W. F. Tanner has developed could be copyrighted as intellectual property, for various reasons he has not, and provides copies of software to all those making request for its use The GRAN-7 program is based on a program that James P. May wrote a number of years ago called GRANULO. GRAN-7 has been modified and extended in its analytical capability. Example 1 : Great Sand Dunes, central Colorado (Figure 17) On the first line KIRK identifies the graduate student (Kirkpatrick), the GSD signifies the locality for the Great Sand Dunes in centri> Colorado. The extension DT$ means that the sample number contains both numer i c (DT) and alpha ($)code. The first panel is the Table of Raw Data. The 5th and 6th columns are the decimal weight percentages or probabilities That is, multiply by 1 00 to obtain the values in per cent. These have been computed to 5 decimal places. The 2nd panel lists moment measures in phi units They are not graphic measures (which are no longer suitable for use) With the advent of the programmable calculator and Personal Computers, there is !lQ excuse to not use the method of moments and moment measures In fact, even 40 years ago when we did not have the computing power of today, graphic measures may have not been appropriate in many applications. The 2nd column lists moment measures excluding the pan fraction. The pan, however, may contain various sediments including clay sizes One may wish to process these using the settling tube. While there are various pan sizes listed, the literature suggests a standard pan size of 5 l/> for low percentages of the fine fractions (column 3). The 7f/> pan (column 6) can significantly weight the pan fraction. NOTE: the GRAN-7 program allows for saving this output so that it can be used in other ensuing software applications. The relative dispersion (or coefficient of variation) is oJM.. The smaller the value of the relative dispersion, the "tighter" the distribution. Also, tail of fines is the percent of the sample containing the 4f/> and finer fraction of the sample. If it is a relatively high percentage, then fluvial sediments are indicated. If it is relatively low, beach or dune sediments are indicated. Lecture Notes 17 James H. Ba/sillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Panel 4 is the frequency histogram; panel 5 is the cumulative probability plot with the eolian hump Note that the cumulative probability plot is much clearer in providing for identification of the eolian properties of the sample than the frequency plot. Example 2: St. Vincent Island, Florida (Figure 18) The sample is from St. Vincent Island, taken along the central profile. Note in panel 1 there is no pan fraction. The modal class listed in panel 2 is always the primary mode. At the 5 t/J pan, the standard deviation (panel 3) is 0.416 t/J. This value is not This is GRAN-7. The data source is kirk-gsd.dt$. 02-24-1995 Panel1 This is File: kirk-gsd.dt$. Sample: M-09. Table of raw data: MidPt(phi) .625 .875 1.::.25 1.375 1. 625 1.875 2.125 2.375 2.625 2.875 3.125 3.375 3.625 3.875 PAN MidPt(phi) Sieve(phi) .75 1 1. 25 1.5 1. 75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 Sieve(phi) Wt. (g.) .018 .397 4.059 15.989 16.016 19.894 16.369 14.007 8.514 2.766 1 .514 .351 .071 .013 .025 Wt. (g.) CumWt (g.) .018 .415 4.474 20.463 36.479 56.373 72.742 86.74901 95.26301 98.02901 99.54301 99.894 99.965 99.978 100.003 CumWt (g.) Wt (Dec.) .00017 .00396 .04058 .15988 .16015 .19893 .16368 .14006 .08513 .02765 .01513 .0035 .0007 .00012 .0002 Wt (Dec.) CUmulative weight, including pan (if any): 100.003 grams. Panel2 Cum.Wt(D} .00017 .00414 .04473 .20462 .36477 .56371 .72739 .86746 .9526 .98026 .9954 .9989 .99961 .99974 .9999 CUm.Wt(D) Results calculated by GRAN-7. File: kirk-gsd.dt$. Sample: M-09 Several versions are given below, with the pan fraction either omitted, or located at different places on the phi scale. A widely-used procedure (for moment measures} is to put it at 5 phi. The relative dispersion is standard deviation divided by the mean. The mean, std. dev., etc., are MOMENT (NOT graphic) measures. Median size: 1.91 phi. Modal class: 1.75 to 2 phi. Exclud.Pan Pan 5 Pan 5.5 Means: 1.948 1.949 1.949 Std.Dev.: .476 .478 .479 Skewness: .329 384 .418 JPMaySk: .164 .192 .209 Kurtosis: 2.674 3.031 3.351 Fifth Mom.: 2.793 5.334 8.244 Sixth Mom.: 12.37 28.751 53.089 Relative dispersion: .244 Dec.Wt. 4 phi & finer: .00032 .246 .246 Coarsest sieve (phi) : 5 phi, and at 5.5 phi: Pan @ 6 1.949 .48 .464 .232 3.841 13.294 101.485 .246 75 No. For pan fraction placed at SD/Ku: .1577037 .1429424 Mn/Ku: .6430221 .5816174 Pan weight (grams; decimal fraction; %) : 025 ; 0002 Pan 7 phi 1.949 .482 .594 .297 5.52 33.886 338.903 .248 of sieves: 14 .02 Figure 17. Example of granulometric output from GRAN-7 for sample M-09 from the Sand Dunes, central Colorado. Lecture Notes 18 James H. Balsil/ie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 Panel3 On the histogram, values > 69\ show as 69%. File: kirk-gsd.dt$. Sample; M-09 The column on the left shows screen sizes, not mid-points, in Phi. 0 10 20 30 40 so 60 t Phi + 1 + + + + 2 + + + + 3 ... + + -+ 4 + PN + 0 10 20 30 40 so 60 \ The column on the left shows screen sizes, not mid-points, in Phi. Panel4 1 2 3 4 PAN Next: Probability (decimal wt. vs Phi size). File: kirk-gsd.dt$. Sample: M-09 The column on the left shows screen sizes, not mid-points, in Phi. 0.1 1 2 5 10 20 30 so 70 80 90 95 98 99 99.9 \ 1 2 3 4 PAN O.l --Eolian Hump . . 1 2 s 10 20 30 so 70 80 90 95 98 99 99.9 % This is GRAN-7. Sieve interval: .25 File: kirk-gsd.dt$. Sample: M-09 Coarsest sieve: .75 phi. Pan contents (g., %) : .025 .0002 Figure 17. (cont.) particularly good for a mature beach sand. Mature beaches have o. values of from 0.30 to 0.50 (/); the lowest a. value WFT has seen is about 0.26. The cumulative plot of panel 4 shows the surf-break. The surf-break inflection point moves with time ... the plot, therefore, is a snapshot in the history of the evolution of the sample. With high enough wave energy or with sufficient time, the inflection point will move to the left and off the plot. Note, also, that there is a tail of fines Hence, the sample is one reflecting low wave energy. The surf-break occurs at about 4.5o/o with the settling curve comprised of less than 1 /o of the sample. Hence, we are looking at only about 5/o of the sample. By looking at a multitude of samples we can attempt to clarify our Lecture Notes 19 James H. Balsillie

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W F. Tanner -Environ. Clastic Granulometry --FGS Course Feb-Ma r, 1995 i n t e r pre t ations. Example 3 : T he Germa n Darss The Dar s s a German federa l nat ure pr ese rve i s located in Germ an y fro n t in g on the Balt i c sea jus t to the east o f the o l d East-West Ger m a n border. It is attract i ve t o study be ca u s e i t is not subjec t to open Atlantic Ocean waves. A ser ie s of 1 2 0 to 200 r i dges compri se t h e pla i n although it i s not poss i ble to coun t all the ridges b ec au s e wind work has be e n pervas i ve The f e ature has been inte r pret e d by many invest i gato r s ( 20) to represe n t This is GRAN-7 The data sourc e is stv-wei. d t $ 0 2 -24-1995 P anel1 This is GRAN-!7. Fiie: s tv-wei.dt$. Sample: .1.6. Tabl e of r aw d a ta: M i d P t ( phi) S ieve(phi) Wt. ( g.) CumWt ( g ) W t (Dec.) CUm.Wt(D ) 375 .5 021 .02 1 00041 0 0041 .625 .75 .146 .167 .00287 .00328 8 7 5 1 .348 .515 0 0685 0 1 0 1 3 1. :.25 1.25 1.00 3 1.518 .01974 .02988 1 .375 1.5 3.543 5.06 1 .06974 .09962 1.625 1. 75 8 .487 13.548 .16707 .26669 1.875 2 10.821 24.369 .21301 .47971 2 .125 2 .25 13.819 38.188 27203 .75174 2 .375 2 5 7.208 45.396 .14189 .89363 2 .625 2 .75 3.383 48.779 .06659 .96023 2 .875 3 1.579 5 0 .358 .03108 9 9131 3.125 3 .25 311 50.669 .00612 .99744 3 .375 3 5 .066 50.735 .00129 .99874 3.625 3 .75 .017 5 0 .752 .00033 .99907 3.875 4 .01.3 50.765 .00025 .99933 4.125 4 .25 .034 5 0 799 .00066 1 M idPt (phi) Sieve(phl) Wt. (g.) CUmWt (g.) Wt (Dec.) CUm. W t(D) Cumu lative weight, i n cluding pan (if any) : 50.799 grams. P anel 2 R esults calculated by GRAN-7 Pile: stv-wei.dt$. Sample: Centr.16 Several version s are given below, with the pan fraction e ither omitted, or located at different places o n the phi scale. A widely-used procedure (for moment measures) i s to put it at 5 p h i The relative dispersion is standard deviation divided by the mean. The mean, std. dev. etc., are MOMENT (NOT graphic) measures. Median size: 2 .01 phi. Modal class: 2 t o 2 .25 phi. Exclud.Pan Pan@ 5 Pan@ 5 5 Means: 2 .004 2 .004 2 .004 Std.Dev.: .416 .416 .416 Skewness: .08 .08 .08 JPMaySk: 04 0 4 04 Kurtosis: 3.806 3 .806 3.806 Fifth Mom. : 2 .208 2 .208 2 .208 Sixth Mom.: 33 3 3 33 R elative dispersion: .208 .208 .208 Pan (I 6 2 .004 .416 .08 04 3.806 2.208 3 3 .208 Pan @ 7 phi 2.004 .416 08 04 3.806 2 .208 33 .208 Dec.Wt. 4 phi & finer: .000 92 Coarsest sieve (phi): .s No of sieves: 16 For pan fraction placed at 5 phi, and at 5 5 phi: SD /Ku: .1093011 .1093011 Mn/Ku: .5265371 .5265371 N othing ir.. pan. Figure 18. Example of granulometric output from GRAN-7 for sample Centr. 16 from St. V1ncent Island Rorida. Lecture Notes 20 James H Balsillie

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W. F. Tanner --Environ. Clastic Granu/ometry FGS Course, Feb-Mar, 1995 Panel3 On the histogram, values > 69\ show as 69\. File: Sample; Centr.16 The column on the left shows screen sizes, not mid-points, i n Phi. 0 10 20 30 4 0 s o 60 \ Phi : + + 1 + + 2 3 -+ +. ... + + + + + + + 1 2 3 4 + 4 + PN + PAN 0 10 20 3 0 4 0 so 60 \ The c olumn on the left shows screen sizes, not mid-points, i n Phi. Panel4 Next: Probability (decimal wt. vs Phi size). File: stv-wei.dt$. Sample: Centr.16 The column on the left shows screen sizes not mid-points, in Phi. 0 1 1 2 s 10 20 30 so 70 80 90 9S 98 99 99.9 \ 1 ---Surf-Break 2 3 4 PAN . .. 0.1 1 2 s 10 20 30 so 70 80 90 95 98 99 99.9 t This is GRAN-7. Sieve interval: 25 File: stv-wei.dt$. Sample: Centr.16 Coarsest sieve: .S phi. Pan contents (g., \): 0 0 Rgure 18. (cont.) + + a dune field. Ul'st ( 1957) trenched the Darss ridges and found low-angle, fair-weather, beach type cross-bedding and concluded that they were beach ridges (i.e., wave deposited) with a top layer of eolian decoration. Zenkovich ( 1967), in his text ProcfJSSu of CoiiStl Development noted that Ul'st investigated the Darss ridges, but persisted to view them as dunes. [Aside: one should be very careful when using this textbook . it is written in such a manner that one can be easily misled.] Many of the dune proponents visually examined only the surface and of course, found eolian evidence. Harald Elsner, at W. F. Tanner's request, Lecture Notes 21 James H Bslsillie

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W. F. Tanner Environ Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 sampled the ridges where eolian reworking appeared minimal then trenched 30 to 50 em deep where the samples were taken. A total of 16 samples were sent toW. F Tanner for analysis, the results of which are described in detail in Of the 16 samples, 12 had the definitive surf-break Only one had the eolian hump. Not one sample plotted showed fluvial conditions, 5 samples plotted as swash, and 7 as settling. The features are, therefore, beach ridges and not dunes. Example 4: Florida Panhandle Offshore Data Arthur et al. { 1986) reported on offshore sediments along the northwestern panhandle Gulf Coast of Flor i da. Samples were taken from 1 to 15 km offshore. Can the surf-break be found in sediments found in fairly deep offshore coastal waters? There are two important considerations here: 1. How deep can storm waves affect bottom sediments? and 2. Has sea level rise during the last 15,000 to 20,000 years resulted in an onshore shore l ine transgression? The offshore sand sample data were analyzed and the surf-break inflect i on was found for most of the -samples {see Tanner, 1991 b Appendix VIII, p. 118). Example 5: Florida Archeological Site W. F. Tanner was asked to assess sediment from an archeological site on U. S. 90 just west of Marianna, FL, where there are several .. Indian moundsu. The State Archeologist wanted to know why they were composed of 98/o quartz sand, since such mounds are normally comprised of shell material The mounds were trenched. No bedding was found. Sample analysis showed the surf-break. The mounds probabily represent marine terrace deposits reworked by eolian processes. That is, some degree of eolian reworking may not always destroy the surf-break character of the sediments Such destruction of the indicator would require higher energy levels and/or time. Example 6: Origin of Barrier Islands Much of the work on the origin of barrier islands is in error (refer to Appendix VI entitled Origin of Barrier Islands on Sandy Coasts (Tanner, 1990a ; Appendix VI) Tanner (1990a; Appendix VI, p 96) presents a list and discussion of common origin hypotheses. Felix Rizk (Appendix VI, p. 97, 2nd column, 2nd paragraph down) trenched and took 10 or more samples from each of the two nuclei (i.e., initial vestiges of island formation). Means of the samples from the nuclei were 0.24 mm and 0.22 mm with a slight coarsening trend in one direction It is generally homogenized sand, all of which looks alike. Standard deviations (Appendix VI, p. 97, col. 2, paragraph 4) for the two areas were statistically the same. However, these numbers which have typical values for beach sand are a little larger than the adjacent, younger non-nuclei sediments. Hence the sorting of the younger non-nuclei sand has i mproved with time. We can draw the inference that this area has been reworked by waves. With assurance, neither nucleus was a dune, nor was it deposited by a river. Skewness values (Appendix VI, p. 97, col. 2, paragraph 5) are slightly negative. These values are typical of beach or river sand deposits, but rivers can be ruled out by the above. They are absolutely not dunes or deposits settling from water. Kurtosis values {Appendix VI, p. 97, col. 2, paragraph 6) are low to moderate, indicating low to moderate wave energy levels. Altogether, (Appendix VI, p 97, col 2, paragraphs 6 and 7) the nuclei were formed by the same agencies that formed everything else, that is by wave activity. Lecture Notes 22 James H. Balsil/ie

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W. F. Tanner --Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 This account is not advocating that barrier island formation, in isolated cases, cannot occur for some of the hypotheses listed, for example, drowning of dunes. However, the above example and data for other (e.g., St. Vincent Island (Appendix VI, p. 99, figure 1 ), and Johnson Shoal off of Cayo Costa (Appendix VI, p. 99, figure 2)) suggest that for the majority of cases, barrier island formation occurs because of small sea level changes of one or two meters and accompanying wave and swash activity. Sample Suite Statistical Analysis Please refer to entitled Suite Statistics: The Hydrodynamic Evolution of the Sediment Pool (W. F. Tanner, 1991 a, [In] Principles, methods, and application of particle size analysis. Cambridge University Press). Let us assume that we have 20 samples taken 10 m apart and representing some depositonal time frame, say, 10 years. Do not mix Cambrian with Devonian samples and expect to make sense of the results. For years in statistical pursuits large sampling statistics required the number of samples, n, to be 30 or more. That is not required in granulometric work. For instance, n = 1 5 or n = 8 may be quite enough. There is a way of checking the required value of n so that we do not have to be uncertain about it. A desirable number of sediment samples for a suite ts commonly from 15 to 20 samples. Also, what is a reasonable sampling distance? There is a no specified distance, except for the absurd. But, again, bear in mind that the field worker is a u prisoner of what is available ... one does the best that he or she can. Suite statistics, for our 20 samples above, might, for instance, yield 20 means, 20 standard deviations, 20 skewness values, 20 kurtosis values, 20 fifth moment measures, 20 sixth moment measures, and the tail of fines This encompasses 140 data points. If we use the same parameters in a suite analysis, 49 suite statistics will result, more if we recombine the original individual sample data. Therefore, there are many data with which to work. What we are interested in is a way to examine the behavior of sample suites relative to the individual samples. The plot of Figure 16 is an example of horrible scatter (see Tanner, 1991; Appendix VII, p. 1 04, second column for further discussion). There are procedures available to permit one to break a large number of samples into smaller groups. In addition, one can conduct repetitive recombinations of groups in order to inspect for improved grouping of one or more of the descriptive moment measures (e.g. mean, std. dev ... 6th moment measure, etc.). Please review from Appendix VII: last paragraph of page 1 02, Control factors -air versus water of page 103, Trapping phenomena beginning on the last paragraph, 1st column of page 1 03, Bivariate plots on page 1 04. Lecture Notes 23 James H. Balsil/ie

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W. F. Tanner Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 T of Fines Plot: [Appendix VII, p. 105, figure 16.1 ]. This is a plot of the suite means, p, and suite standard deviations, a, of the weight percents that are 4 f/> and finer (Figure 19). The Tail of Fines Plot is successful because it is dependent on the aeroand hydrodynamics. The suite mean separates a large, new sediment supply (i.e., river or closed basin sediments) from winnowing or sorting products (i.e., beach and dune sediments). The suite standard deviation separates BAFS (i. e mature beach and near-shore sediments) and large mass density differences (i.e., dune sediments) from settling and winnowed products. It is sensitive enough to distinguish between mature beach and mature dune sands, because the number of transport events for beaches is 1 05 or 1 06 times as large as it is for dunes during the annual period. )J 0001 0 .01 0 I T.F ...... ..... Figure 16.1. The lail-of-fmes diagram. The means and standard deviations of lhe weight percents on the 4; screen and finer are shown here. Four fairly distinct number fields appear, as labeled above, with relatively liUle overlap. Many suites plot neatly in a single field. In certain other cases the apparent ambiguity may be useful; for example, a point at a mean of 0 .01 and a standard deviation of 0.017 might indicate either dune or mature beach, and not formed in a closed basin. This diagram commonly gives a "river" position when in fact the river was the "last-previous" agency, but not the final one. The Vstillbility Dillgl'llm: [ Appendix VII, p. 105, figure 16.2]. Figure 19. Tail-of-Fines Plot. (From Tanner, 1991a). This plot is also based on suite statitics (Figure 20) where: oP = standard deviation of the individual sample means, and oa = standard deviation of the individual sample standard deviations. Why is the lower-left to upper-right band so broad? One might argue that there is lot that we do not know about this diagram. Richard Hummel of the Alabama State Survey has done some very good work with this plot, and suggests we are missing some transporting agencies. The diagonal Jines stop in the middle. Samples can, therefore, overlap and one may not know which agency is the primary transporting agent. Other plotting tools, therefore, would have to be consulted to clarify which is the transporting mechanism. Lecture Notes 24 Figure 16.2. The-variability diagram, showing the suite standard deviation of the sample means and of the sample standard deviations. Except for the extremes, the plotted position indicates two possible agencies (such as swash or dune). The decision between these two can be made, in most instances, by consulting other plots (such as Fig.16. 1). This diagram considers specifically the variability, with in lhe suiiC, from one sample to the others. Figure 20. The Varia.,_, Diagram. (From Tanner, 1991a). James H. Balsillie

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W F. Tanner --Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Skewness Vetsus Klllfosis Plot: (Appendix VII, p 106, figure 16.3]. F i gurt 16.3 Skewness vs kurtosis The suite means o f these two paramete:s arc used. POsitive skewness, as used bcre identifies a gcomcttic:ally d i stinctive fine tail ; if there is also a dist inctive coarse tail, it i s the smaller (weight percent ) of the two. The closed basin (settling) environment typi cal l y produces an obvious fine tail, much mor e so than beach or river sands. Eolian sands commonly have, instead of a well-developed fmc tail, a feature called the tolian luunp ( c f Fig. 16.5), which the skewness indica&es in the same way as it does a distinctive fine tail. Therefore the two tend to plot cogelher. Negative skewness identifies a distinctive coarse tail e i ther fluvial coarse aai l (large K) or surf break" (=kink in the probability plot; K in the range or 3-S or so) Many river and bc:ach sui tes appear in the same pan of &he diagram but are ordinarily easy to identify by using this fig ure f i rst and then the tail-of-fines diagram (Fig J6.1) Figure 21. Skewness vs. Kurtosis Plot. (From Tanner, 1991a). Suite averages for the skewness (Sk) and Kurtosis (K) are plotted in this diagram (Figure 21). R i ver ... . . Beach--Eolian & Settling ------Beach and river sands tend to be skewed to the coarse, i.e ., Sk < 0 1. Settling tail or closed basin sediments are skewed to the f i ne, i.e Sk > 0.1 Eoli an sands also occur for Sk > 0 1 as explained in text (Appendix VII, p 106, last paragraph, 1st column). There is no guarantee that thi s plot will produce definitive results. That is why a number of different plotting diagrams for process identification have been compiled Collective consideration of them together will more nearly allow one to ferret out the most plausible explanation. Using these plots one can tally the results for example see Table 5. While confusing results can certainly occur, i t is generally the case that the tally is never close, such as ident i fication of the beach transpo-depositional mechan i sm above. Table 5. Talying the granulomebic results. River Beach Settling Dune X X X X X X X X Pmbllbility Pita: [Appendix VII, p 108, figure 16.5]. These plots are for i ndividual samples (Figure 22). Note the eolian hump of sample 2. Question: the swash zone sand dries out and a relatively str ong wind removes the top layer Lecture Notes 25 James H. Balsillie

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W. F. Tanner -Environ Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 and transports it 4 m down the beach where it is deposited. At what split second in time did it quit being beach sand to become eolian material? That is, is there any place where one can identify a point in time between the two deposits wher e the sediment changed from beach to eolian sand? The answer should clearly be NO! There is no razor-sharp demarcating line or point ... it is gradational. Wind tunnel laboratory results confirm the process In fact, the results are normally clearer than one might expect, given that the philosophical concerns are not clear One has to realize that the previous transpo-depositional history of a sample is bound to characterize any sample and to show up i n these plotting tools Even so W. F. Tanner has been delighted with the success of these analytical diagrams w N c;; CUMWEIGHT PERCEN! 0.1 s 10 2-J 30 50 n ec ?:: o/.1 9':! 99 9 8 Figurt 16.5. Diagrammatic probability plots. (1) The Gaussian, rare among sands. (2) The distinctiv e eolian bump (E.H ) is common, but not universal, in dune sands. and so far bas not been observed in other sands thal did not bave any previous eolian bislory. (3) The surf break (S. B ) has been dcmonsrrated to C onn in the ;urf zone, as the sorting improves. (4) The fluvial coarse tail i s geometrically distinctive, but cannot be distinguished in every case from the surf break. (5) This curve has both a fluvial coarse tail and a fluvial fine ..UI; the cenual segment (C.S ) is 1he line between the two small squares. However, it is notlhe modal swarm (sec text). (6) The modal swarm (a grain size concept, nol a graphic one) obtained by subtraction from the original distribution; it shows the actual size distribution o f the cenU'3l segment (Jrapbic device) of line 5. L ines of these kinds help one visualize the effects summarized i n the bivariale plots. Rgure 22. Diagrammatic Plots. (From Tanner, 1991a). Aside: sampling of marine sediments is not easy It is h i ghly difficult to sample laminae. Grab samples from ship board are really not ideal. Rather, an experienced bottom diver is required. The Segment Anlllysis Tlillngle: [Appendix VII, p. 106, figure 16.4]. This is a very powerful tool. It cannot be plotted by computer program; data must be subjectively determined and then plotted (see Figure 23). Values are determ i ned from the probability plot (see F i gure 24) for each sample. There must first be identified a centrally located absolutely Gaussian, straight-line segment. Now, we want to identify the weight percentages for the coarse tail (CT) and fine tail (FT). The value to be plotted on the Segment Analysis Triangle S.Av.1 is calculated as: Lecture Notes 26 James H. Balsil/ i e

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 SEGMENT ANALYSIS, WT. % FJNE TAU .. .. !, . \ . coARS "-. - TAIL Figwe 16.4 The segment analys i s triangle. The procedure for septents and obtlilting the neccss:uy numbers is outlined in the text. The apex is ch:arocccrizcd by very smaU or negl i gible disLinc live tails ("no tails1. and the base (not shown) connects dislincth'C come wl (to the right) with distinc:livc fine 13il (to the left) four different environments are distinguished rensoiUibly clearly, except DJe:t of o'ICltlp; in lhis arc1. one e:t amincs llle probability plots for the eolian hump in order 10 sec which of lhe two is inckaled. Figure 23. The Segment Analysis Triangle. (From Tanner, 1991a). SAv.1 = B A where A and 8 are the respective weight percentages. Labels on the Segment Analysis Triangle include Sl for river silt and CL for river clay, or a closed basin such as an estuary, lake or lagoon, etc. Note that the river Sl and Cl and closed basin sediment field overlaps the dune sediment field. If the eolian hump does not show up in the probability plots of the samples, it is unlikely that the suite represents dune sediments Must be m absolutely Phi CT Fine 0.1 o/o A 8 99.9% SOo/o Figure 24. Detennination of values for A and B for evaluation of the Segment Analysis Triangle. Approach to the lnvestigllfion It should be obvious to the geologist with any experience that he or she needs all the help that he or she can get. There are often no easy answers in pursuing matters of a technical nature, particulary when we first are introduced to the field locatity that might be of interest There are, when undertaking such an investigation, some questions that we would like to address. The Field Site: The first endeavor is to try to identify just what we are dealing with. Examples might include: Lecture Notes B MB ED GLF Beach Mature Beach Eolian Dune (or ash, loess, etc. ) Glacial-Fluvial Deposit 27 James H. Balsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 s u Settling Basin Unknown The stratigraphic column, both the target and non-target stratigraphy, can often be useful to provide clues to the problem at hand. Classical geology dictates that the present is the key to the past. In many cases, the corollaries that the past is the key to the present and both the past and present are key to the future yields successful results. It is also important that any non-recognizable aspects of the stratigraphy are noted. The Paleogeography: The second pursuit is to make a statement or statements about the paleogeography of the site, if that is at all possible. For example if the deposit is identified as beach material it would be highly useful to discern in which direction lay the upland and in which direction lay the sea. Other similar determinations should be made depend i ng upon the paleoenvironment identified. Cross-plots, such as those of Figure 19 through 23, are useful tools to identify transpo depositional sediments such as those above, ... e.g., B, MB, ED, GLF, and S. Hydrodynamics: It is straighforward procedure to plot our data using a geological mapping format (e.g. grain size, heavy mineral content, etc.). Remember, however, thatwhen dealing with sand sized sediments, the central portion of the distribution tells us little about the sample. It is, rather, the tails of the distri'bution that provide us with useful information ... a lesson Doeglas taught some 50 years ago! By way of contrast, envision the scenario of the western flank of the Andes Mountains in which a talus slope near the upper base is comprised of 1 to 2 meter diameter boulders Farther to the west and down-slope on the river fan, sediment size diminishes greatly. The sediment size gradient, therefore, is highly significant. For our endeavors, however, such a gradient is not available, since we are working within the sand-sized range. If we take our clue from Doeglas and what we have learned about the tails of the sand-sized distribution and moment measures, we need to be looking at the 3rd moment measure or skewness, and the 4th moment measure or kurtosis. Specifically, as it relates to hydrodynamics, let us look at the kurtosis. The Kurtosis The bulk of the work on the relationship between hydrodynamics and kurtosis has been conducted on beaches, in particular, Florida beaches. Specifically, kurtosis and hydrodynamics can be related in terms of the energy levels associated with the hydrodynamics. Hydrodynamic force elements inducing a sedimentologic response include characteristic wave energy levels for coasts, long-term sea level rise, seasonal changes, and short-term storm tide and wave impact events. Lecture Notes 28 James H. Balsil/ie

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W. F. Tanner -Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 Kurtosis and Wave Energy Climates: Let us denote average wave energy in terms of wave height which, according to classical Airy or Small Amplitude wave theory, is given by: Guff of Mexico H 0.5 m K > 3.5 Atlantic Ocean H"' 1.0 m 3.0 < K < 3.5 in which E is the wave energy density per unit surface area, Pt is the fluid mass density, g is the acceleration of gravity, and H is the average wave height. Hence, simply put for diagrammatic uses, E ex H 2 Let us also denote the kurtosis as K. Consider the following five (5) example cases. Agure 25. Characteristic average wave heights and kurtosis values for the coasts of lower peninsular Roricla. Case 1. The Lower Peninsular East and West Coasts of Roricla. The prevailing wind direction fQr the lower peninsula of Florida is from the east. Noting that the Atlantic has a larger fetch (i.e., length over which the wind acts to generate gravity water waves) than the Gulf of Mexico, we would expect to find larger waves along Florida's east coast, lower waves along the lower Gulf Coast (Figure 25). In fact, the average wave height along the east coast is typically about 1 m. Along the lower Gulf Coast (Tampa to Naples) waves are generally 0.5 m or less. Kurotsis values for the east coast range from 3.0 (perfectly Gaussian) to 3.5, while along the lower Gulf K is greater than 3.5. Case 2. Denmark. The fetch is narrow for the Kattegat (Figure 26) separating Denmark and Sweden and characteristic wave heights are smaller than for the North Sea where the fetch is only slightly sheltered by the British Isles but not from northwest winds. The result is that Danish east coast sediments have a Lecture Notes North LMgerH SmalllrK !" \ \ I Sweden Figure 26. Charactetistic average wave heiglat and kurtosis conditions for opposing coasts of Denmark. 29 James H. Bslsillie

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W F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 7 995 N f _'\Island Highest Waves -.... C:;u;a 3.0 < K < 3.5 Island \ Wave height / diminishes from A NW to SE; K increases ___,_., Guff of \ Lowest Waves larger characteristic kurtosis value (lower wave energy) than the Danish west coast beach sediments (higher wave energy). Case 3. Captiva and Sanibel Islands, Lower Gulf Coast of Aorida. Cases 1 and 2 represent coastal reaches of regional extent Let us look at some specific cases representing more localized coastal reaches. Mexico K > 20.0 There are no quantified wave height data for the Captiva Sanibel Island coastal Agure 27. Wave energy -kurtosis behavior for the Captiva Sanibel Island coastal reach. reach. Wave refraction analyses, however, show that wave heights along the northern portion of the reach are largest. As the coastal curvature trends to the southeast and east, sheltering occurs and characteristic wave heights significanlty diminish (Figure 27). Corresponding response of the kurtosis is also significant (see Tanner (1992a, fig. 1) for quantitative details of the kurtosis data). It is to be noted that beach sediments along Sanibel and Captiva can be comprised totally of carbonate material. Care was taken, therefore, that the samples for this study were comprised of as much siliciclastic sand as was possible Case 4. Dog Island, eastem Panhandle Coast of Northwest Rorida. This example is for a reach located immediately adjacent to the classical zero energy Big Bend coast of Florida (Tanner, 1960a), located at the eastern end of the northwestern Panhandle Gulf Coast of Florida. Wave heights and energy are low. Results should, therefore, be quite sensitive regarding the interaction of wave forces and Lecture Notes 1 K 0 DO = drift divide HE = highest energy 1 km Figute 28. Correlation between kurtosis and wave energy in tenns of longshore transport energies for Dog Island, Roricla. (After Tanner, 1990b). 30 James H. Balsillie

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W. F. Tanner --Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 divergence or .. drift divide .. near the eastern central portion of the island (Figure 28). A combination refraction-longshore transport analysis confirms that lowest wave energy occurs at the drift divide (point DD). Highest energy levels occur at point HE. The refraction analysis attenuates shoaling waves, while the longshore transport equations are wave height driven. Forty-four lower beach sand samples were collected and analyzed (Tanner, 1990). Once again, kurtosis values are largest for the low wave energy portion of the island, and are smallest for the higher wave energy portion of the island. Case 5. Laguna Madre, Texas. The southern part of Laguna Madre is located near Boca Chica east of Brownsville, Texas. This part of the lagoon is separated from the Gulf of Mexico by a long, narrow, sandy peninsula. Two rnodern beach samples collected from the lagoon side had a kurtosis of 4.11, and 10. Adjacent and slightly older lagoon-side beach samples had kurtosis values of 4.2 or greater. Samples from beaches fronting on the Gulf of Mexico, however, had an average kurtosis of 3.39. The peninsula is a product of high-energy processes, as is indicated by the lower kurtosis. Kurtosis versus Seasonal and Short-Term Hurricane Impacts: While we should certainly desire more data on seasonal effects and extreme climatological impacts, there are not much data yet amassed Even so, the following should pique one's interest! Rizk ( 1985) studied beach 1.0sediments along Alligator Spit, located to the south of Tallahassee, FL and some few kilometers to the northeast of Dog Island. Again, overall wave O.S F--:---.N.o energy is not high for the reach. 0.6 Hurricanes In addition, the beaches of 0' K in Alligator Spit had not experienced 0.4 9 Years the effects of hurricane impact in .. ,....___.,.. 0.2 (3. 72)'-...,Summer ,' rl \ (3.61) (3.41 p ng\ I\ I (3.13) I I \ I l / \ _,/ -' \ I (3.39) -\ (3.25) / -\ I -9 years. Rizk found a correlation between kurtosis and wave energy levels, the latter being higher during the spring than the H. Elena H. Kate summer. Hence, kurtosis can distinguish seasonal effects. In addition, Figure 29 indicates that the standard deviation of the suite of samples, CJK, also correlates with extreme event energy conditions, being smaller in value during higher energy Aug Sep Late Nov 1985 1985 ----------Time ---Figure 29. Kurtosis data versus energy levels for seasonal effects and hunicane impacts for Spit, Roricla. Kurtosis values are in parentheses, "ec is the standard deviation of the kurtosis values of the sample suite kurtosis. (After Tanner, 1992a). conditions, ... larger during lower energy conditions. Two successive hurricanes impacted the area in 1985 (see Figure 29), and ensuing sedimentologic response was monitored by Rizk and Demirpolat (1986). During high energy Lecture Notes 31 James H Balsillie

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W. F. Tanner-Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 sedimentologic response was monitored by Rizk and Demirpolat (1986). During high energy conditions of Hurricane Elena kurtosis values were low compared to conditions weeks after the event. Note that shore-incident storms or hurricanes, not only produce exceptionally high waves, but also storm tides (which being a super-elevated water surface) allow for even h i gher waves (since waves are depth limited) closer to shore. Kurtosis values immediately after impact of Hurricane Kate and several weeks later are not different. Why this is so, is not clearly understood. Even so, standard deviations of the sample suites, oK, do show a correlation. Hence, oK is an additional tool that can provide valuable information. Kurtosis and Long-Term Sea Level Changes: Beach ridges are formed by small couplets of mean sea level rise and fall (1 0 to 30cm). In order to appreciate how beach ridge formation occurs, there must be some understanding of coastal, beach, nearshore, and offshore dynamics. First, in the topographic sense, slopes for nearshore and offshore profiles are very gentle Relief of any proportion at all does not occur until the shoreward portion of the nearshore, the beach, and the coast are encountered. Second, where shore-propagating waves begin to be attenuated due to drag effects with the bed is a function of the wave length. The deep water wave length, L0 in meters is given by L0 = 1 56 T2 where T is the wave period. The water depth where drag effects begin to occur is approximately given by L0 /2. Third, farther nearshore, waves are depth-limited. That is, waves will distort and break according to db = 1 .28 Hb where db is the water depth at breaking and Hb is the height of the breaking wave. Finally, where breaking is represented by final shore-breaking (i.e., the breaking waves cannot reform and again rebreak) swash runup mechanics are important in inducing final sedimentologic transport. Let us look at the case where there is a drop of several meters in sea level as illustrated in Figure 30a. For the pre-sea level drop case let us suppose that waves begin to experience bed drag at point A. There is, then, the distance a-A over which the waves will attenuate to eventually shore-break with a breaker height of Hba. However, when sea level drops these same deep water waves will begin to experience bed drag at point 8 which continues for the distance b-8, a distance that is much greater than distance a-A. That is, the longer the distance, the greater the attenuation of the wave height. Hence, where shore breaking, Hbb' occurs for the sea level drop scenario, Hbb will be smaller than Hba. Hence, breaker energy levels will be less, at least initially (i.e., a readjustment period of approximately 2 or 3 centuries might be appropriate for the Gulf of Mexico), when sea level drops. Lecture Notes Coast I Beach I NearShore --Pre-Sea Lwei Drop Profile Offshore Figure 30a. The .lttoral nd offshore profile and effect of se level drop on wave energy levels. 32 James H. Ba/sillie

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W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 7 995 Let us inspect the case for sea level r i se, illustrated in Figure 30b. Just the opposite occurs for sea level rise, compared to the sea level drop scenario. The distance a-A for the pre-rise sea level is longer than for the b-B distance following s ea level rise. Moreover, shore breaking wave heights Hbb will be larger than Hba. If we have learned our lessons from previous experience, it should be c l ear that kurtosis values for a sea level drop should be large and kurtosis values for a sea level rise should be small Coast lseacn I Near Shore --P r e-Sea Level Rise Prdle Off shore Agure 30b. The lttoraland offshore profile and effect of sea level rise on wave energy levels St. Vincent Island, Rorida, Beach Ridge Plain. St. Vincent Island a federal wildlife is located south of the town of Apalachicola along the eastern part of the northwestern panhandle coast of Florida. It is comprised of a sequence of beach ridge sets ranging in age from set A (oldest) to set K (youngest) as illustrated in Figure 31 Sets A, B, and D stand low. Three dates are available for the island : an archeological date of older than 3,000-3500 years B. P. (before present) is found on the northwest; a C14 date of 2110 130 years B P. near the east coast, and records of pond closure of approximately 200 years for the Sl Vincent Sound 0 \ KM 2 southern coast. Each beach ridge has been repetitively surveyed and sampled for granulometric analysis, by different investigators. Laminar samples for the seaward face of each ridge (one sample each) were taken at depths of from 30 to 40 em. The different C investigators did not know where the others had conducted work. Results were statistically identical for the 59 individual ridges along the profile. Agure 31. The St. Vancent lslllnd beach ridge plain. (After Stapor and Tanner, 1977). We should expect that when sea level drops, Lecture Notes 33 James H Balsillie

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W. F Tanner-Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 AlB I c I D I E F G I K Ridge Number O ldes t 10 20 50 Youngest 3 .00 3 25 3 .50 3000 2000 A roximate date (B .P.) Tim e -Figure 32. Plot of kurtosis versus time for secimentologic data from the St. Vmcellt Island Bech Plain. Letters d the top of the figure identify location of beach ridge sets of Figure 30. (After Tnner, 1992). for additional details). There are two (2) kurtosis values should i ncrease and when sea level rises kurtosis should decrease This is precisely what happens as illustrated by Figure 32. T i me spacing between points is approximately 50 years. Note that the beach ridge sets (sets are comprised of multiple beach ridges) each represent a different sea level stand and differ from one another in topographic height by about 1 or 2 meters. Also note that the ordinate is inverted to simulate 1 /K to directly correlate with hydrodynamic energy levels. Sea level changes range from 1 to 2 meters, and the plot includes 4 rises and 3 drops in sea level (see Tanner, 1992a, 1. Whether there are topographic data or not, one can (based on the kurtosis), identify when sea level rise occurred or when it fell. 2 Based on the kurtosis values, not a single value represents a storm. That is not to say that there are not laminae where K would represent storm activity, just that none were found. Certainly, there were storms in its 3 000-year history ... none have as yet been isolated. St. Joseph Peninsula Storm Ridge. However, Felix Rizk in work along St. Joseph Peninsula, not too far to the west of St. Vincent Island, found a storm produced ridge, amongst a beach ridge set, which is called the Storm Ridge. It's relief is about 4 meters 20 to 25m wide at the base. There are results for some sand samples from the ridge, which is composed of uniform bedding sloping at from 18 to 20 degrees downward in the seaward direction. Granulometry indicates storm depositional conditions. This is the ONLY storm ridge (not a lamina or a berm, but a complete ridge) in a beach ridge set that W. F. Tanner has found along the coastal northeastern Gulf of Mexico. What are the chances of a storm ridge being preserved here? Undoubtably it is much less than 1 o/o, and one might venture it is on the order of 0.01 /o. Beach Ridge Formation-Fair-Weather or Storm Deposits?: Of all the hundreds of beach ridges investigated, only one isolated beach ridge formed by a storm (preceding paragraph) has been identified by W. F. Tanner. However, in the popular textbook literature there is espoused the notion that each modern beach ridge we see today has been produced by a single storm event. In these same texts, however it is without exception, noted that storms erode beaches and coasts. These are diametrically opposed Lecture Notes 34 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 outcomes. Beach ridges are, with rare exceptions, fair-weather swash deposits. They are formed by small sea level rise followed by a small sea level drop occurring over a period of from 10 to 50 or so years. Run up from final shore-breaking waves plays an important role, where higher runup (larger breakers) forms the ridges and small runup (smaller breakers) forms the swales. Texas Barrier Island StudyConversation with W. Armstrong Price. A number of years ago, W. A Price had a summer contract to survey by plane table barrier islands and their lagoonal beaches between Brownsville and Corpus Christi, Texas. Two or so months into their work, Price and his survey crew noticed (having not been in that particular area for some time) a beach ridge on the lagoon side of a portion of the locale. This discovery brought a halt to field work while they re-checked their maps in order to determine if they had originally missed the feature. Confident in their work, it was decided the beach ridge was a new feature. Based on prevailing literature that each beach ridge is the product of a single storm, Price checked the records and found no such occurrence. How the beach ridge formed in a month or two is not known. However, it was not storm-produced. Transpo-Depositional Energy Levels and the Kurtosis; and an Explanation: From the preceding examples we can draw some general conclusions In general, kurtosis and transpo-depositional energy levels can be related. A diagrammatic representation is suggested by Figure 33, for which the energy, E, is related to the kurtosis, K, according to: where for waves E ex H2 where H is the wave height. Tanner and Campbell (1986) found K values ranging from 3.7 to 13 for beaches of some Florida lakes which represent a combination of low wave energy and settling mechanics A consistent algebraic expression 100 ,...-----------------. t SO. \ II. Increased Settling I \ \ -----20 \ Combined K 10 J Processes \_\,/ .,, s r wave Energy-., KValues 3 ------------------111. Mixing .. Zero High Figure 33. Generalzed relationship between energy levels and kurtosis. relating K and energy levels, in particular, wave energy for sand-sized and finer sediments, has not been discovered. What, then, is the explanation for the inverse relationship between kurtosis and energy levels? Let us use the littoral zone as an example, one characteristically experiencing, say, low to moderate wave energy levels. Suppose that normal wave conditions are operating wherein shore-propagating waves break once at the shoreline. It is well known that sediments Lecture Notes 35 James H Balsillie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 just shoreward of the breaker position (e. g ., plunge point and foreshore slope) are the coarsest sediments found along the beach and offshore profile. This occurs because finer sediments are sorted out, and transported alongshore and offshore. The result is that the sedimentologic distribution is compressed, leading to a peaked or leptokurtic kurtosis (K > 3.0). Suppose that a storm makes impact. Now, energy conditions are greatly increased due to both an increase in the water level (storm tide) and larger incident waves. In fact, because of fully aroused seas, waves are breaking across the entire littoral zone which is significantly wider than under normal conditions, affecting not only the nearshore, but also the beach. The result is a significantly wide high energy expenditure zone where sediment mixing occurs That is, more sediment is added to the tails of the distribution, resulting in a reduction of the kurtosis relative to normal conditions, and reaching a value of K 3.0. Importance of Variability of Moment Measures in the Sample Suite Refer to the Friedman-Sanders plot (Figure 16). The apparent reason of this figure is to convince the reader that such comparison does not work as an analytical tool. Let us assume their samples were correctly taken, etc. In addition, let us look, for the moment, at the hydrodynamic differences between beaches and rivers. Uprush and backwash on beaches are characterized by a thin layer or .. sheet'' of water 1 to 5 em thick. Hydrodynamically, this condition should be represented by very small Reynolds numbers ( !Jl) and very large Froude numbers ( fJ ). River channels, on the other hand, with much greater depths and unidirectional flow conditions should have large !Jl 'sand very small 65' 's. These differences are great enough that the beach and river points of Figure 16 should not overlap. Why the overlap? There is a basic principal that requires observance: the hydrodynamic infonnation we obtain from granulometry is the result of the variability from sample-to-sample within the sample suite. If the same level of energy of a force element (e.g., waves) is the same day-after-day-after-day, the variability between sand samples representing daily samples should be very small. However, this is almost never the case. Rather, there is not only turbulence but multi-story turbulence; that is, turbulence on quite different scales due to different energy levels and features. Hence, it is desirable that there should be some degree of variablity between parameters such as the mean or kurtosis, etc., for samples comprising the sample suite. Therefore, Friedman and Sanders should have used averages of sample suite parameters. Application of Suite Statistics to Stratigraphy and Sea-Level Changes Refer to IP.P.iil@f.iti.J.l entitled Application of Suite Statistics to Stratigraphy and Sea Level Changes 1991, Chapter 20, [In] Principals, Methods, and Application of Particle Size Analysis. Cambridge University Press). Discussion of the rationale for Chapter 20 (i.e., Appendix VIII this work) is given by Chapter 16 (i e ., Appendix VII, this work). Cape San Bias, Aorida [Appendix VIII, p. 116, 3rd paragraph). The beach sands of Cape San Bias provide simple and straightforward granulometric Lecture Notes 36 James H. Balsil/ie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 interpretations (see the reference). Let us look at a more complicated case. Medano Creek, Colorado [Appendix VIII, p. 116, last paragraph]. This locality was selected for study to avoid the charge of looking only at simple or easy examples. It is not an easy example. Medano, pronounced MED (as in ED) aNO, is Spanish for "sandy placeu. Medano Creek, located in central Colorado, flows through Great Sand Dunes National Monument in a southerly direction along the eastern side of the sand dunes (Figure 34). The dunes have a relief of some hundreds of feet. To the east of the creek lies an area of crystalline rocks. The creek bed, which is very flat because it is composed of quartz sand with no binding fines (i.e., silts or clays), is about 20 meters wide with water depths of only about 2 em. Prevailing winds from west to east provide one source of sediments to the creek. The other is the creek itself. Sand samples (23, which is a large Prevailing Wind E \ MOdanoCreek Rgure 34. Conceptualzed cross-section of the Great S.nd Dunes and Meclano Cntek (drawing not to scale). number of samples, rarely are this many needed) from the Great Sand Dunes, using plotting techniques of Figure 19 through 23, confirm eolian transport and deposition. Note also, using the diagrammatic probability plot (Figure 22), only 1/4 to 1/2 of the plots need to show the eolian hump to confirm eolian processes. The creek samples show a faint but sharply developed fluvial coarse tail. If the creek sands were lithified and sampled in section, the environmental intrepretation would probably be dune, but some minor fluvial influence should be evident ... remember, this is a very shallow creek not a river of consequential dimensions Hence, we should be looking for subtleties. One might consider these to be coastal dunes. However, homogeneity of parameters for the suite of samples is greater than one would find in coastal environments, and they should be recognized as non-coastal eolian sediments. Greater homogeniety for eolian transport should occur because of the greater mass density differential between air and quartz, than it is between water and quartz. Even so, swash zone sediments do also show remarkable homogeneity due to the number of uprush and backwash events that occur. Note also the Tail-of-Fines Diagram (Appendix VIII, p. 117, figure 20. 1) and The Variablity Diagram (Appendix VIII, p. 117, figure 20.2). Do these plotting techniqes (i.e., Figures 19 through 23) plot with 1 00/o assurance? Note that the river, R, suite results misplot on figure 20.2 (Appendix VIII, p. 117). So, they do not always plot with total success. Individual plotting tools appear to have maximum success rates of from 80/o to 90/o. However, taken all together, the diagrams have a success rate of from 90 to 95%. The Suite Skewness Versus Suite Kurtosis Plot (Appendix VIII, p. 120, figure 20.3) Lecture Notes 37 James H. Balsil/ie

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W. F. Tanner --Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 does not allow one to distinguish fluvial from beach sands, but does allow one to distinguish between eolian and hydrodynamic influences. St. Vincent Island Beach Ridge Plain Figure 20.4 of Appendix VIII, page 121, is an example from computer program LINEAR for sediment samples from beach ridges 1 through 37 (the older ridges) for St. Vincent Island. The plot comprised of $ represents a 3-point floating average for 1 /K. The program identifies, based on a mean/kurtosis quotient of 0.68, where sea level should be low by the 11LOW? .. designat i on which can be confirmed from topographic data for beach ridge set elevations. Other parameters which also correlate with changes of sea level stands are the quotients mean/kurtosis and standard deviation/kurtosis, and differences of the standard deviations. Beach ridge set sedimentologic means and set means of the standard deviation also provide information. These are discussed on page 120, 2nd column of Appendix VIII. The Relative Dispersion Plot The Sediment Analysis Triangle is again discussed on page 121 of Appendix VIII. An additional interpretative aid is provided by the Relative Dispersion Plot (Appendix VIII, p. 122, figure 20. 6) shown here as Figure 35. The relative dispersion, R. D. (also known variously as the coefficient of variation), is given by: Standard Deviation = a = a R.D. = --------Mean M J.L If the standard deviation is large because the mean is large, one does not want to interpret the result in terms of the scatter. The relative dispersion eliminates this effect. Two parameters are calculated for use in the Relative Dispersion Plot. The relative dispersion of the means, p*, is given by: 0 1 02 / IS Figure 20 .6. Rel.alive dispersions of means lUld smndard deviations, showing settling (S), river (R), beach. and dune areas. There is a small overlap a1 two places. See Figure 20.1 for key. Figure 35. ne Relative Dispersion Plot. (From Tnner, 1991b). in which oP is the standard deviation of the means of the suite samples, and Jlp is the mean of sample averages comprising the suite. The relative dispersion of the standard deviations, o*, is evaluated by: where otl is the average standard deviation of the sample standard deviations comprising the suite, and ptl is the mean value of the Lecture Notes 38 James H. Balsillie

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W F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 standard deviations of the suite samples. Note from Figure 35 that there are some small regions that overlap. Even so, the Relative Dispersion Plot provides an additional and useful analytical tool. Again, these plotting tools ... Figures 19 through 23 and Figure 35 and computer tools such as GRAN-7 ... when the results are tallied, have never resulted in a tie between transpo-depositional agencies. A predominant mechanism has always surfaced to identify the last mode of the depositional environment. Copies of these working plotting tools (and a few others which have merit) are provided in The SUffES Progam The SUITES com. puter program, written by W. F Tanner, provides the means for computing suites statistics and for assessing the results. The program requires stored output generated by the GRAN-7 computer program. Following are examples Example 1. Great Sand Dunes, Colorado. Figure 36 represents SUITES output for the Great Sand Dunes just to the west of Medano Creek, Colorado. There are 21 samples Notice from panel 1 that the samples are so .. clean .. that there is no tail-of-fines. Inspect the 2nd panel entitled suite homogeneity. Plotted values are much less than 0.5 o. This is marvelously good homogeneity. Good homogeneity would occur near 0.5 o. Even for excellent or good homogeneity outliers are possible. Consistently poor homogeneity, or heterogeneity, e.g., from high energy rivers, glacial fluvial deposits, etc.), would exceed 0.5 o. In panel 3, the vertical columns contain the basic parameters that we are summarizing in the SUITES program. The horizontal lines are suite means, standard deviations, kurtosis, etc. of the basic data. The last (4th) panel provides an environmental It states the procedures used and assesses 6 commonly encountered sedimentologic depositional environments, i.e., dune, mature beach (MB), river (Riv), settling from relatively still water (Sett), tidal flats (TFiat), and glacio-fluvial (GLF). A capital X signifies assured environmental identification of the transpo-depositional environment, a lower case x indicates less assured identification. The highly diagnostic eolian hump is identified from the probability plot and interactively noted in the data entry portion of the SUITES program. The overwhelming evidence identifies that the deposit is, indeed, eolian. Example 2. Storm Ridge, St. Joseph Peninsula, Aorida. Felix Rizk found the St. Joseph Peninsula Storm Ridge locality. W. F. Tanner sampled the deposit. This storm deposited ridge described previously (p. 34) is located along the central port i on of St. Joseph Peninsula (see Figure 41 for an approximate location). Suite results are given by Figure 37. Rizk took his samples in a vertical direction (14 or 15 samples), which meant that they represented the difference between the upper and lower portions of the swash resulting from final shore-breaking storm wave activity. W. F Tanner, however, re-sampled (21 samples) the ridge in a horizontal direction to look at the middle or central portion of swash/runup force element activity. The results provided more continuity. Panel 2 indicates very good homogeneity, internal to which there is variability and, therefore, a good suite of samples. [NOTE: the computer file .5P5 indicates that the original data source generated from GRAN-7 contained 5 parameters with the pan fraction Lecture Notes 39 James H. Balsillie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 This is SUITES. Data source:. kirk-gsd.7p5. No. of Samples: 21 02-24-1995 This program produces suite, or group, statistics for a suite, or set, of samples, presumably all representing the same depositional environment. Tabulation of data: Sample T-01 T-02 T-03 T-04 '!'-05 T-06 T-07 M-08 M-09 M-10 M-11 M-12 M-13 M-14 B-15 B-16 B-17 B-18 B-19 B-20 B-21 Sample Mean 2.18 2 .161 2.214 2.14 2.167 2.218 2 .208 1. 929 1 949 1. 872 1. 938 1. 966 2 .032 2 .039 1 .856 1.825 1. 835 1.88 1.877 1. 94 1.967 Mean Std.Dev. 477 .518 .486 .434 .514 .511 .494 .5210001 .478 .499 .504 .451 .445 .486 .425 .431 .378 .466 .477 .409 .434 Panel1 Skewness .5 .337 .632. .39 .636 .528 .537 1.092 .384 .592 .501 .541 .283 .446 .677 .638 .766 .277 489 .397 .168 Kurtosis 4.321 3 .128 4.527 4.936 4.644 4.413 7.138 3.031 3.051 3.107 3.556 3.047 3.208 4.043 3.498 3.573 2.728 2. 904 2.894 2.967 Std.Dev. Skewness Kurtosis Panel2 5thM.M. 10.369 3.139 11.631 14.224 12.728 10.513 10.842 32.523 5.334 6.356 5.79 7.2 2.583 6.01 6.289 5.567 6.642 2 .204 3.611 2 .9 1.453 5thM.M. 6thM.M. 62.935 19.1 67.575 106.378 71.723 60.682 65.12 189.064 28.751 28.967 27.861 39.116 16.771 32.501 33.716 21.791 24.372 11.996 14.221 14.759 14.104 6thM.M. Suite homogeneity, in terms of departures of sample means and standard deviations from the suite mean values (of means & std.devs.) T.of F. .00257 .00104 .00257 .00109 .00305 .00264 .00226 .00451 .00032 .00043 .00038 .00031 .00001 .00041 0 0 0 0 0 0 0 T.of F. as an evaluation of uniformity. Crosses represent numbers on far right. Mean and Std. Dev. of Means: 2.009 .135 and of Std.Devs.: .468 .038 Std.Dv. .521 .518 .513 .51 .504 .499 .493 .486 .486 .477 .476 .476 .465 .451 .44.(. .433 Dep.of Std.D. .053 -.5 0. +.5 Dep. of Mean 433 .43 .425 .409 .377 .OS .046 .042 .036 .031 .025 .018 .018 .009 .009 .009 -.003 -.017 -.024 -.035 -.035 .038 .043 -.059 .091 + + + + + + + + + + + + + + + + + + + + -.082 .15 .157 .208 -.072 .138 .197 .203 .028 .062 -.134 .171 -.13 044 .023 -.044 .13 -.186 -.154 -.071 .175 Std.Dv. Dep.of Std.D. -.5 0. +.5 Dep. of Mean Evaluation of homogeneity. Crosses represent numbers on far right. Outliers, if any, should be obvious. Data Source: kirk-gsd.7p5 If any point needs to be removed from the suite, the program should be run again with a reduced number of samples. Rgure 36. Eumple of SUITES output for the Great Sand Dunes, central Colorado. Lecture Notes 40 James H. Balsillie

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W. F. Tanner Env i ron. Clastic Granu/ometry FGS Course Feb-Mar, 1995 This is S UITES. Results: Panel3 The sequence o results, for each parameter such as the m ean, six moment measures, then percent on the 4 -phi-sieve-and-finer. That is, the first line refer s to the mean of the means, mean of the standard deviations, mean of the skewnesses, etc. Source of data kirk-gsd.7p5. N = 21 Samples, 1 to 2: Means Std. Dev Skewn Kurtos. 5th. M M 6th.M.M. Mean of the: 2 009 468 514 3 76 7.995 4 5.309 Stnd. Dev.: 135 .038 19 3 1.005 6 547 40.347 Skewness: .316 -.541 908 1. 74 2.404 2.202 Kurtosis: 1.585 2 452 4.688 6.388 9.579 8 048 Fifth Mom. : .879 -3.4 0 8 10.218 20.345 35 047 27 65 1 Sixth Mom.: 2.883 9 72 1 35 484 68 628 131.71 98.046 18.495 Rel.Disp.: 067 082 .376 267 .8J.8 .89 Invrtd.R. D : 14 838 2.657 3.74 1 221 1 .122 Std.Dev / Ku. = .124 Kurt. /Mean -= 1.871 T .of F. Mns & Std.Devs as Percent: .1 ; 13 Mn & StdDev of Mn/Ku & of SD/Ku: .534 108 .124 .028 The Relative Dispersion (or Coefficient of Variation) is the Standard Deviation divided by the Mean. Panel4 The primary use of the next display is to minimize weight of certai n interpretations (e.g., no X's). Of those that are left, a single line with 2 X's mus t not be taken t o demonstrate either one alone; FIRST, identify SINGLE-X lines a n d their site m eanings. NOTE that t h e Tail-of-Fines tends to identify the last-previous agency. T .Fines 001 0013 1.155 3 .195 ?.165 1.2 68 788 For best results, plot numerical data by hand on p roper bivariat e charts. MB=Mature Bch; SettsSettling (Closed Basin); TflatTidal Flat; GLFGlacio-Fluv. Parameter (below ) Environment: Dune MB Riv Sett TFlat GLF Procedure s giving 1 or 2 answers : . . . . . . ..... Mean of the Skewness: Variability diagram: Procedures g enerally giving one answer: RelOisMn v s RelOisStdOev: Mean of the Tails-of-Fines: StdDev of Tail-of-Fines: Tail-of-Fines diagram: Inverte d RelDisp ( S k vs K; Min u sefulness): Eo lian hum p (defin itive!): X X X X X X X X X X This is S UITES. D ata source: kir k -gsd.7p5. N 21 1 t o 21 02-24 1 995 The End Figure 36. (cont ) Lecture Not es 41 James H Ba/sillie

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W. F Tanner Environ Clastic Granulometry FGS Course, Feb-Mar, 1995 This is SUITES. Data source: stormrdg.sps. No. of Samples: 21 02-27-1995 program produces suite, or group, statistics for a suite, or set, of samples, presumably a l l representing the same depositional environment. Pan e l1 Tabulation of data: Sample Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M. T.of F. SJ89-20 2.012 .338 .061 3.399 1 1 .00029 SJ89-21 2.039 .317 .143 3.744 1 1 .00031 SJ89-22. 1.973 .347 -.01 3.797 1 1 .00036 SJ89-23 1. 88 .29 .124 3 .974 1 1 .0002 SJ89-24 1.932 .302 .085 3.745 1 1 .00021 SJ89-25 2.114 .256 .192 4.359 1 .00024 -SJ89-26 2.043 .338 .057 3.033 !. 1 .00019 SJ89-27 2.247 .286 .063 3.533 1 1 .000!7 SJ89-28 2.085 .274 -.038 3 .837 1 l .00014 SJ89-29 1 .914 .34 -.187 3.264 1 l .00012 SJ89-30 2.253 .289 -.087 3.507 1 l .00019 SJ89-3l 2.239 .269 039 3.771 1 l .00017 SJ89-32 2.158 .261 .162 4.015 1 1 .00027 SJ89-33 2.068 .337 -.081 3.308 1 1 .00028 SJ89-34 2.036 .342 .113 2.765 1 1 .00016 SJ89-35 1.951 .354 -.033 3 .066 1 1 .00017 SJ89-36 1. 88 .327 .127 3.147 1 1 .00012 SJ89-37 2.105 .293 .051 3.727 1 1 .0003 SJ89-38 2.067 .346 -.1 3.341 1 1 .00015 SJ89-39 2.08 .345 -.195 3.263 1 1 .00013 SJ89-40 2.109 .332 -.014 3.358 1 1 .0002 Sample Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M. T.of F. Panel2 Suite homogeneity, in terms of departures of sample means a n d standard deviations f r om the suite mean values (of means & std.devs.) as an evaluation of uniformity. Crosses represent numbers on far right. Mean and Std. Dev. of Means: Std.Dv. .354 .347 .345 .344 .342 .34 .337 .337 .337 .331 .326 .317 .301 .293 .289 .289 .286 .273 .268 .261 .256 Std.Dv. Dep.of Std.D. .041 .034 .032 .032 .029 .027 .025 .025 .024 .018 .013 .004 -.012 -.02 -.024 -.024 -.027 -.04 -.044 -.052 -.057 Dep.of Std.D. -.5 -.5 2.056 + + + .108 + + + 0 + + + + + + + + + + .0. + + + + and of Std.Devs.: .313 +.5 +.5 .031 Dep. of Mean -.106 -.083 .009 .023 -.02 -.143 -.044 -.015 012 .052 -.176 -.018 -.124 .048 -.176 .196 .189 .028 .182 .101 .057 Dep. of Mean Evaluation of homogeneity. Crosses represent numbers on far right. Outliers, if any, should be obvious. Data Source: stormrdg.SpS If any point needs t o be removed from the suite, the program should be run again with a reduced number of samples. Figure 37. Example of SUITES output for the Storm Ridge deposit of St. Joseph Peninsula, Roricla. Lect ure Notes 42 Jame s H Bals illi e

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 This is SUITES. Results: Panel3 The sequence of results, for each parameter such as :he mean, is: six moment measures, then percent on the 4-phi-sieve-and-finer. That is, the first line refers to the mean of the means, mean of the standard mean of the skewnesses, etc. Source of data stormrdg.5p5. N= 21 Samples, 1 to Means Std.Dev. Skewn. Kurtos. 5th.M.M. 6th.M.M. Mean of the: 2.056 .313 .022 3.521 0 0 Stnd. Dev.: .108 .031 .106 .374 0 0 Skewness: .166 -.431 -.45 .132 0 0 Kurtosis: 2.335 1.702 2.344 2.62 0 0 Fifth Mom.: .984 -l. 646 -2.393 1.047 0 0 Sixth Mom.: 6.327 3.934 7.511 10.114 0 0 Rel.Disp.: .052 .1 4.751 .106 0 0 Invrt
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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 beach and nearshore profiles for 3 hurricanes and 2 storms that, on the average, 16o/o of the area impacted by the extreme events resulted in accretion. The standard deviation for these data was only 0 059o/o! It is also interesting that the volume of sand accreted during the storms was 27/o of the eroded volume (i.e., TYPE I erosion where accretion was not even considered). This is a rather large volume considering that but 16/o of the impacted area(s) experienced accretion. Furthermore, there is no singular area within the 1st quadrant where accretion occurs; rather, it appears to be random. Example 3. The Railroad Embankment, Gulf County, Florida. The Railroad Embankment is located in Gulf County just to the east of Cape San Bias (see Figure 41 for an approximate location locale RREMB). It is a ridge with 4 or 5 meters of relief, and is comprised of parallel to sub-parallel, lowangle, cross-bedding planes sloping 6 to 8 degrees down in the seaward direction It, again, shows good homogeneity (Figure 38) This is SUITES. Data source: rr-emb$.5p5. No. of Samples: 11 03-01-1995 This program produces suite, or group, statistics for a suite, or set, of samples, presumably all representing the same depositional environment. Panel1 Tabulation of.data: Sample Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M. RR-1 2.782 .32 211 3.882 1 1 RR2 2 583 .389 -.176 3.177 1 1 RR-3 2.158 .473 .113 2.416 1 1 RR4 2.703 .333 -.163 3 .117 1 1 RR9 2.463 .375 -.093 3.523 1 1 RR-13 2.545 .325 -.128 3.461 1 1 RR-19 2.422 .382 -.018 3.196 1 1 RR-20 2 583 .353 -.128 3.24 1 1 RR-7n 2.195 434 -.204 3.1 l l RR-6n 2.262 .398 -.201 3 .414 1 1 RR-3n 2.44 .341 .172 3 .52 1 1 Sample Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M Panel2 Suite homogeneity, in terms of departures of sample means and standard deviations from the suite mean (of & std.devs.) T.of F 0 .0001 .0001 0 .0001 .0001 .00001 0 0001 .0001 .000 1 T.of F as an evaluation of uniformity. Crosses represent numbers on far right. Mean and Std. Dev. of Means : 2.466 .191 and of Std.Devs.: .374 .045 Std.Dv. .472 .433 .398 .388 .381 .375 .352 .34 333 .324 .319 Std. Dv. Dep.of Std.D. .098 .059 .023 .014 .007 0 -.022 -.034 -.042 -.05 -.055 Dep .of Std. D. -.5 + + -.5 0. + + + 0 + + + + + + 5 +.5 Dep of Mean -.309 273 204 .115 046 -.005 .115 028 .236 .078 .314 Dep. of Mean Evaluation of homogeneity. Crosses represent numbers on far right. OUtliers, if any, should be obvious. Data Source: rr-emb$.5p5 If any point needs to be removed from the suite, the program should be run again with a reduced number of samples. figure 38. Example of SUITES output for the Ralroad Embankment. Lecture Notes 44 James H. Balsillie

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W F. Tanner --En v iron. Clastic G r anulometry FGS Course Feb-Mar 1995 This is SUITES Results: Panel3 The sequence of results, for each parameter such as the mear. is: six moment measures, then percent on the 4-phi-sieve-and-finer. That is, the first line refers mean of the means, mean of the standard Aeviations, mean of the skewnesses, etc. Source of data rremb$.Sp5 11 Samples, 1 to 11 Mean s Std.Dev. Skewn. Kurtos. Sth.M.M 6th.M.M Mean of the: 2.466 374 -.126 3.276 0 0 Stnd . Dev.: 191 .045 .092 35 0 0 Skewness: -.134 .731 1.481 -.82 0 0 K urtosis: 2.02 2.654 4 295 4 16 0 0 Fifth Mom. : -.277 4.131 10. 234 -6.667 0 0 Sixt h Mom.: 4 657 10.105 26.508 22 244 0 0 Rel.Disp.: .077 121 -.74 .107 0 0 Invrtd.R.D.: 12.901 8 235 1.353 9.338 0 0 StdDev/Ku. = .114 Kurt./Mean 1.328 T.of F Mns & StdDevs as Percent: 0 i 0 Mn & StdDev of Mn/Ku & of SD/Ku: .752 .071 .114 .029 The Relative Dispersion (or Coefficient of Variation) is the Standard Deviation divided by the Mean P a n el The primary use of the next display is to minimize the w eight of certain interpretations ( e g., no X 's). Of those that are left, a single line with 2 X's must not be takeh to demonstrate either one alone; FIRST, identi.fy SINGLE-X lines and their site meanings. NOTE that the Tail-of-Fines tends to identify the last-previous agency. T .Fines 0 0 -.577 1.343 -1.372 2.175 .727 1.37-
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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 and slopes), indicate that they are different. Is there any other way that would indicate a difference? Yes, probability applications can be employed. Results from a Z-Test are listed in Table 6. The Z-Test determines the degree of difference between averages, in this case suite means for the first 4 moment measures. The number of samples for the Storm Ridge (STORMRDG.5P5) was 21, with 11 samples comprising the suite representing the Railroad Embankment (RR-EMB$ 5P5) Input data are listed under the heading .. summary of means and standard deviations". The column with the header az VALUE .. lists the Z value results; the larger the Z value the greater the statistical difference between averages tested. Exceedence probability and significance of the ZTest results are shown by the Z and P rows near the bottom of the table. Moment measures foro, p, and the tail-of-fines (T of F) are significantly different to the Jess than 0.00005 confidence level, K is significantly different to less than the 0.05 confidence level. Hence, the two deposits are not the same. Table 6. Z-Test for the Storm Ridge (STORMRDG.5P5) and Railroad Embankmen t (RR-EMB$.5P5) deposits of GuH County, Florida. This is Z-IESI Data sources: STORMRDG.5P5. RR-EMB$ .5P5 : 21 11 Summary of means and.standard deviations: and SD, Variable 1 : Variabl e 2: o Variable 3: Sk Variabl e 4: K Variable S:TofF 4.E97459E-05 2.056429 .1085852 .3134762 3.138014E-02 .0224762 .1067845 3 .521572 .3742375 2 .080952-04 6.751506E-05 File Mn and SD, R R -ENB$.5P5. 2 .466909 .1912094 .3748182 4.551521E-02 -.1255455 9 .283353E-02 3.27691 .3508905 6.454546E-05 If these are sedimentological data, the variables MAY BE the mean, standard devi a tion, skewness and kurtosis. The values above are means & standard d eviations of the variables for each datafile. Z VALUE Std Err Degr.Freedom Firs t Variable: Second Variable: tl Thir d Variable: Sk Fourth \'ariable: K F ifth Va riable: T. of F. 6 .585459 3 .999623 4.064234 1.830617 7.024088 6.233l31E-02 1.533693E-02 3 .642056E-02 1 3365 2.043679R-05 30 30 30 30 30 If the deerees of freedom > 25-to-30, then large-sample procedures are appropriate. K P is of exceeding Z b y c hance: z: 1.645 2.054 2.170 2.3' 26 2.576 3.090 3.290 3.? 19 P: 0.05 0.02 0.015 0.010 0.005 0.001 0.0005 0 .0001 T of F 3.891 4 .265 \ l 0 .00005 0.00001 This i s Z-TEST Sources: STORMRDG.5P5, RR-BMBS.5P5 02-15-1995. Tbe End Example 4. The St. Vincent Island Beach Ridge Plain. It would be remiss if we did not show SUITES results for the classic St. Vincent Island Beach Ridge Plain. Results for all 59 individual r i dges for the plain are given by Figure 39. Again, the homogeneity (panel 2) is very good Panel 4 overwhelmingly ind i cates that the Lecture Notes 46 James H. Balsillie

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W F Tanner --Environ. Clastic Granulometry FGS Course Feb Mar, 1995 This is SUITES. Data source: stvin-ak.4p5. No. of Samples: 59 03-01-1995 This program produces suite, or group, statistics for a suite, or set, of samples, presumably all representing the same depositional environment. Panel1 Tabulation of data: Sample Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M. T.of F. AB1 2.31 8 .378 -. 072 3.928 1 0 AB2 2.362 .38 -.135 3.578 1 1 0 AB3 2.274 .387 -.133 3. 728 1 1 0 AB4 2.346 .379 -.109 3.158 1 1 0 AB5 2.23 .468 -.141 3.459 1 1 0 AB6 2.381 .37 .093 3.658 1 1 0 AB7 2.392 .407 -.133 3.403 l 1 0 C1 2.445 .38 -.137 3.355 1 1 0 C2 .427 -.266 3.266 1 1 0 C3 2.338 .43 -.153 2.861 1 l 0 C4 2.434 .433 -.165 3 .019 1 1 0 C5 2.315 .415 -.052 3.048 1 1 0 C6 2.303 .379 .01 3.455 1 1 0 C7 2.297 .411 -.011 3.33 1 1 0 Dl 2.34 .38 .03 3.92 1 1 0 02 2.29 .43 .04 3.54 1 1 0 03 2.21 .42 -.09 3.4 1 1 1 0 04 2.14 .42 1 3.84 1 1 0 DS 2.43 .34 -.08 3.82 1 -0 06 2.3: .4 .11 2.9 1 1 0 E1 2.42 .37 -.22 3.45 1 1 0 E2 2.2 .47 .24 2.99 1 1 0 E 3 2.42 .35 .21 2.39 1 1 0 E4 2.37 .36 .13 3.2 1 1 0 ES 2 .43 .4 -.32 3.74 1 1 0 E6 2 .45 .36 2 3.26 1 1 0 E7 2.52 .36 -.16 3.12 1 l 0 E8 2.24 .43 .02 2.8 1 1 0 E9 2.47 .37 .08 2.92 1 1 0 E10 2 .53 .37 .14 3 .14 1 1 0 Ell 2 .47 .39 -.11 2.9 1 1 0 El2 2.35 :39 .09 2.96 l l 0 El3 2 .46 .37 -.15 3.15 l l 0 El4 2.57 .37 -.16 3.33 l l 0 Fl 2.19 .45 -.18 2.93 l l 0 F2 2.23 .36 -.15 3 .71 l 1 0 F3 2 .19 .38 -.17 3 .52 l l 0 F4 2.39 .36 -.14 3.24 1 1 0 F5 2.43 .36 -.12 3.1 l l 0 F6 2.45 .42 -.32 3.75 l l 0 F7 2.56 .37 -.22 3.06 l 1 0 F8 2.32 .37 -.11 3.33 1 1 0 F9 2.28 .33 .11 3.4 1 l 0 FlO 2.1 .44 -.09 3.01 1 1 0 Fll 2 .21 .5. -.11 2.86 1 1 0 Gl 2.28 .39 .01 3.14 1 1 0 G2 2.22 .45 .01 2.8 5 1 1 0 G3 2.14 .38 .08 3.46 l 1 0 G4 2.05 .41 .03 3.57 l 1 0 GS 2.1 2 4 -.03 3.75 l l 0 G6 2 .24 .35 .02 3.47 1 1 0 K1 2.21 .37 -.01 3.7 8 1 1 0 K2 2.52 .38 .01 3 .01 1 1 0 K3 2.31 .39 -.03 2.96 1 1 0 K4 2.34 .41 -.09 3.2 1 1 0 K5 2.4 .34 -.04 3.39 1 1 0 K6 2.43 .38 -.07 2 .95 1 1 0 K7 2.43 .38 -. 04 2.84 1 1 0 K8 2.14 .43 .07 2.89 1 1 0 Sample Mean S td.Dev. Skewness Kurtosis SthM.M 6thM.M T.of F. Agure 39. Example of SUITES output for the St v-.cent Island Beach Ridge Plain. Lecture Notes 47 James H Bs l sillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Panel2 Suite homogeneity, in terms of departures of sample means and standard deviations from the suite mean values (of means & std.devs.) as an evaluation of Crosses represent numbers on far right. Mean and Std. Dev. of Means : 2.334 .122 and of Std.Devs.: .393 .034 Std.Dv. .5 .469 .467 .449 .449 .439 .432 .43 .43 .43 .43 .426 .U9 .419 .419 .414 .411 .409 .409 .407 .4 .4 .4 .389 .389 .389 .389 .386 .379 .379 .379 .379 .379 .379 .379 .379 .379 .379 .377 .37 .37 .37 .37 .37 .37 .37 37 37 .36 .36 36 .36 .36 36 .349 .349 .34 .34 .33 Std.Dv. Dep.of Std.D. .106 .076 .074 .056 .056 .046 .039 .037 .037 .037 .037 .033 .026 .026 .026 .021 .018 .016 .016 .013 .006 .006 .006 -.004 -.004 -.004 -. 004 -.007 -.014 -.014 -.014 -. 014 -.014 -.014 -.014 -. 014 -.014 -.014 -.016 -.024 -.024 -.024 -.024 -.024 -.024 -.024 -.024 -.024 -.033 -.033 -.033 -.033 -.033 -.033 -.044 -.044 -. 054 -.054 -.063 Dep.of Std.D. -.5 + + + + + + -.5 + + + + + + + + + + .0. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0. + + + +.5 + + + + + + 5 Dep. of Mean -.125 -.136 -.105 -.116 -.145 -.235 .098 -.195 -. 046 .003 -.095 .137 .115 -.195 -.125 -.02 -. 038 -.285 .004 .057 .094 .216 -.026 .014 -.055 .135 -.026 -.062 .094 094 -.145 .185 .027 .109 -.195 .004 .01 -.033 -.018 .234 -.125 .125 .194 -.015 .224 .1.35 .085 .046 .185 .115 .035 .094 .054 -.105 .085 -.095 .064 .094 -.055 Dep. of Mean Evaluation of homogeneity. Crosses represent numbers on far right. Outliers, if any, should be obvious. Data Source: stvin-ak.4p5 If any point needs to be removed from the suite, the program should be run again with a reduced number of samples. Figure 39. (cont.) Lecture Notes 48 James H. Balsillie

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W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 This is SU:TES. Results: Panel3 The sequence of results, for each parameter such as the mean, is: six moment measures, then percent on the 4-phi-sieve-and-finer. That is, the first line refers to the mean of the means, mean of the standard deviations, mean of the skewnesses, etc. Source of data stvin-ak.4p5. N 59 Samples, 1 to 59 Means Std.Dev. Skewn. Kurtos. Sth.M. M 6th.M.M. T.Fines Mean of the: 2.334 .393 -.104 3 274 0 0 Stnd. Dev. : .122 .034 .084 .336 0 0 Skewness: -.195 .775 -.258 .06 0 0 Kurtosis: 2.318 3.383 3.222 2.409 0 0 Fifth Mom.: -1.116 6 332 -2.368 -.692 0 0 Sixth Mom.: 7.499 20.873 15. 594 9.385 0 0 Rel.Disp.: .052 .087 -.817 .102 0 0 Invrtd.R.D.: 19.111 11. 374 -1.225 9.718 0 0 StdDev / Ku. = .12 Kurt./Mean = 1.402 T.of F. Mns & StdDevs as Percent: 0 ; 0 Mn & StdDev of Mn/Ku & of SD/Ku : .712 0 .12 0 The Relative Dispersion {or Coefficient of Variation) is the Standard Deviation divided by the Mean Panel4 The primary use of the next display is to minimize the weight of certain interpretations (e.g., no X's). Of those that are left, a single line with 2 X's must not be taken to demonstrate either one alone; FIRST, identify SINGLE-X lines and their site meanings. NOTE that the Tail-of-Fines tends to iden.tify the last-previous agency. 0 0 0 0 0 0 0 0 For best results, plot numerical data by hand on proper bivariate charts. MB=Mature Bch; (Closed Basin); Tflat=Tidal Flat; GLF=Glacio-Fluv. Parameter (below) Environment: Dune MB Riv Sett TFlat GLF Procedures giving 1 or 2 answers: . . ....... Mean of the Skewness: Variability diagram: Procedures generally giving one answer: RelDisMn vs RelDisStdDev: Mean of the Tails-of-Fines: StdDev. of Tail-of-Fines: Tail-of-Fines diagram: Inverted RelDisp (Sk vs K; Min usefulness: St. Vincent Island, FL beach ridges. X X X X X X X X X This is SUITES. Data source: stvin-ak.4p5. N 59 1 to 59 03-01-1995 The End Rgure 39. (cont.) suite of samples represents a mature beach deposit. The majority of probability plots did show the surf-break, although it was not interactively so noted in the SUITES program. The relationship between 1/K and relatively small sea level changes (1-2m) for all St. Vincent Island beach ridges is illustrated by Figure 40. Sets are identified depending upon whether sea level was low or high and, therefore, sets were correspondingly low or high Lecture Notes 49 James H. Balsillie

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W. F. Tanner-Environ. Clastic GranulometryFGS Course,_ Feb-Mar, 1995 This is MOVAVG. N: 62 Width of window: 5 Orand Mn, so; Ord +I-.sso: .307 .032 . 323 .291 The number in the Qolumn is located at the center of the Data source: STVIN.4AL Variable No. 4 out of 4 Inverted. OrMn-SD/2; GrMn ; GrMn+S0/2: I Sua(I} Mn(l) 3 1.408066 .281 4 1.426856 .285 5 1.441229 .288 6 1.471051 .294 7 1.46058 .292 8 1.521007 .304 9 1.578869 .315 10 1.613095 .322 1l 1.604468 .32 12 1.598584 .319 13 1.504157 3 14 1.455408 .291 15 1.420579 .284 16 1.39156 .278 17 1 .35304 .27 18 1.442765 .288 19 1 .450134 .29 20 1. 491328' 298 21 1.649321 .329 22 1. 700041 34 23 1.622593 .324 24 1 .639486 .327 25 1.625551 .325 26 1.564284 .312 27 1.59425 .318 28 1 .645341 .329 29 1.68342 .336 30 1.700745 .34 31 1.661063 .332 32 1 .618897 .323 33 1.641723 .328 34 1 566437 313 35 1.51269 .302 36 1.503872 .3 37 1 .526152 .305 38 1.451522 .29 39 1.508778 .301 40 1.524987 .304 41 1. 510463 302 42 1.520108 .304 43 1.603092 .32 44 1.594766 .318 45 1.645343 .329 46 !.640242 .328 47 1.588129 .Sl7 48 1.505145 .301 49 1.474868 .294 50 1.383048 .276 51 1 .368003 .2?3 L 0 w L .. .. S2 !.376909 .276 53 1.374792 .274 0 w ,' 54 :.418834 .283 55 1.497604 .299 56 1.5!6132 .307 57 1. 542099 308 58 1.616532 .323 59 1.636419 .321 60 1.644602 .328 I Sum ( I ) l'ln
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W. F Tanner-Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 Spatial Granulometdc Analysis Probability applications can also be employed to identify geographic distribution of sediments Pairs of sample suites can be statistically compared using the Z Test as discussed in the previous section. For example, in Figure 41, fourteen suites of samples have been so analyzed. Analysis of one of the pairs has already been presented in Table 4 for the Storm Ridge versus the Railroad Embankment (RREMB) in which it has been demonstrated that they are two types of deposits They have not been deposited by the same transpo depositional processes. Another interesting pair is found on St. Vincent Island where the classic beach ridges and ridge sets of Figu r es 31 and 32 are quite different from a set of G) Dog Island St. George Island Little St. George Island Cape St. George Shoal St. Vincent Island Cape San Bias /ttl" Numbers are Averages for SUite Statistics In Following Order : I' tl Sk K GULF OF MEXICO RREMB 2.467 0 .375 .0. 126 3.m N (!) St. Joseph Peninsula @ Apalachicola Bay ....... \ I @I 2.35 OAO .0. 002 2.02 3 .15 0.63 0 .13 3 67 tl Sk K 1.14 0 03 Coarsest Finest Best Worst Most oft Most +w Highest Lowest 1 .66 -o.33 0.03 5A1 1.59 0.31 0.081 Dog Island RREE Dog Island ar.nneman Little St. George Brenneman N.E. St. George lsi Brenneman 1.59 2M7. 0.30 1.014 .OA2 0.115 6.11 Figure 41. Z-test results for phi of suite par11meters for mean grain size (p), standard deviation (,, skewness (Sk), and kurtosis (K) for westem panhancle Rorida Gulf coast seclments. Paired site means were tested using the Z-test; bold clashed lnes represent sbdisticaly significant clfference between mean values to the standard 0.01 confidence level (actualy to the 0.0001 level). Offshore islands have been shifted to the south (narrow verticallne and arrows) to lstings of data. Lecture Notes 51 James H. Balsillie

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W F. Tanner-Environ Clastic GranulometryFGS Course, Feb-Mar, 1995 smaller ridges (labelled small ridges in Figure 41) found along the southeastern tip of the island. Table 7 shows that suite averages for both a and K are significantly different to less than the 0.005 confidence level. This should be enough evidence to suggest that these ridge sets are different. Sediments from these small ridges are not different from sediment from Little St. George Island Hence, the small ridges have been deposited by essentially the same depositional agencies that formed Little St. George Island which, in turn, represents a different depositional regime than eastern St. George Island. The bold dashed lines delineate where areas are different. Z-Test probabilities that these sediment deposits are the same are negligible. Table 7. ZTest for St. Vincent Island Beach Ridge Plain (STVIN .4EK) and the southeastern small ridges of St. Vincent Island (CLARK.5P5), Florida. This is Z-TBST Data sources: CLARK.5P5. N = 39 13 Summar y of means and standard deviations: File Mn and SD, STVIN.4EK Variable 1: 2.335384 2: o .388718 Variable 3: Sk -.1130769 Variable 4: K 3.19282 1386392 3". 6386371!-02 8.397658E .3166097 File Mn and SD, CLARK.5PS. 2.300923 7.652164E-02 .4141539 -6.907693B-02 1802351 3 936308 6842861 If these are sedimentological data, the variables MAY BE the meanJ standard deviation, skewness and kurtosis. The values tiven above are means standard deviations of the variables f o r eaeh datafile. Z Value Std Err First Variable: 1.122053 .0307127 50 Second Variable: (J 2.747476 9.257903E-03 50 Third Variable: Sk 8499909 5 .176S28E-02 50 Fourth Variable: K .19644-17 50 If the degrees of freedom > then lar1e-sampre procedures are appropriate. (J P ie the probability of exceeding Z chance: Z: 1.645 2.054 2.170 2 326 2.576 3,090 . 3.290 P: 0.05 0.02 0.015 0.010 0.005 0.001 0.0005 This is Z-TBST Sources: STVIN.4BX, CLARK.5P5 Ok Review K 3.719 3.891 4.265 0.0001 0.00005 0.00001 10-24-1989. The End. Employing the granulometric methods that have been presented, we can accomplish at least 7 tasks. These are: 1. The Site: Although, from time-to-time, it has been requested, one cannot (based on granulometry alone), identify the location where a sample was taken, that is, the beach name, river name, or latitude-longitude. Lecture Notes 52 James H. Ba/sillie

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W. F. Tanner--Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 2. Paleogeography : Granulometric suite statistics and the inherent v ariability within is correlativ e with paleogeographic evidence. For instance, Tanner ( 1 988), demonstrated the correlation for ancient lithified late Pennsylvanian early Permian sedimentary rocks of central Oklahoma (Figure 42). 3. Kurtosis and Hydrodynamics: OPEN SEA N on-cross -bedded al t ernating s h ales sands & limest o nes : > 100 marine i nvert eb ra t e species y H c r oss -bedd ed sa nd s up t o Obble s, seve r al species o f f resh wat er gas tropods micro-fo ssils, fossil tree bran ches & t runks an d organic matter, beac h g ranulometry LAGOON Fineg raine d sedi ment s appr ox 12 no nmarine spec ies. 4 ra r e t rilobite species settling g ranulo m etry N If we can identify a mature beach, then the kurtosis will tell us about the wave energy levels at the time the beach was formed. Figure 42. Paleogeography and granulometry for a late Pennsylvanian early Permian coastal complex in central Oklahoma. The seciment source for the complex was the Arbuckle Mountains lying southeast of the study area. 4. Sand Sources: The sand source, in terms of its depositional environment, can be determined, a nd we can distinguish one sediment pool from another. For example, see Figure 41 for the Apalac hi c ola area and the Z-Test. 5. Tracing of Transport Paths: The coast of Brazil in the vicinity of Rio de Janeiro is characterized by hills of deeply weathered Mesozoic igneous rocks with pocket beaches lying between (see Figure 43). The question has been asked as to the direction of longshore sediment transport. At the outset one would expect to find coarser sediment at the updrift end of a longshore transport cell becoming finer in the downdrift direction. The subject pocket beaches however, have finer sediments at the central portion of the beaches, and coarser sediments at the ends of the beaches. Granulometri c evidence suggests Lecture Notes c = Coane HdlrNntS F = Fme sedamenls DMPy WN!hwed M .-ozao c ( e g ol N type o1 IN!ure ) ATLANTIC OCEAN Figure 43. Granulometry and seciment transport paths. 53 James H. Ba/sillie

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W. F. Tanner --Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 that little, if any, sand is escaping from beach-to-beach in the longshore direction. 6. Sea Level Rise: Kurtosis correlates inversely with even small changes in sea level (rise and fall). This applies to long-term sea level changes, as well as to extreme event impacts (i.e., hurricanes and storms). 7. Seasonal Changes and Storm/Hurricane Impact: In the northern hemisphere, astronomical tidal levels are slightly depressed during the winter months relative to summer months. In addition, wave energy levels are normally higher during the winter months Storm and hurricane impacts result in both high storm tides and wave energy levels Again, there appears to be an inverse correlation between energy levels for these two examples and the kurtosis, as illustrated by Figure 29. The term "appears" is used because there are not much data available to quantify the relationship, and the reader is encouraged to pursue the collection of such information. PLOT DECOMPOSITION: MIXING AND SELECTION On probability paper, quartzose sediment distributions commonly plot as zig-zag lines. Even so, the hypothesis that the basic distribution is Gaussian (i.e., mean = mode = median or 50th percentile) and will, therefore, plot as a straight line remains valid. It is departure from the Gaussian that provides additional characterization of the sediments. Each segment on probability paper is important to consider because it is indicative of a process or processes leading to its appearance. That such identification can be made relating force and response elements using probability paper is not commonly understood. Again, a segment and a component are not the same, although it has been so stated in the literature; a segment must be recalculated to 1 00/o to be a component. Multi-segmented, zig-zag, or multi-component sand distributions have been discussed by a multitude of investigators. However, in a series of papers, Tanner ( 1 964; p. 134) found that zig-zag modifications of the straight line plot include mixing arl"cfsfiiecHon which, in turn, can be subdivided as follows: Mixing: Selection: +Non-zero component +Zero component +Censorship +Truncation +Filtering In reality, when we obtain a sand sample it is usually already a mixture of components. In order to determine the components, the distribution must undergo the process of decomposition. It is easier, however, to understand decomposition using the reverse process, e g., the simple mixing of known component distributions and then determining the resulting total distribution. Lecture Notes 54 James H. Balsil/ie

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W. F Tanner-Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 Many sedimentologists / soil scientists do not utilize probability paper in the man n e r presented i n this work. They most often use it in a manner that suppresses the very details that we wish to observe It is W. F. Tanner's opi nion that they have not seriously nor carefully thought the issue thr ough. Simple Mixing In order to discuss mixing it helps to specify some conditions such as proport i ons of mixtures (P), means (p), and standard deviations (o). Non-Zero Component: Case 1 Let us in spect the case for two component mixing where the proportions a r e equal, the means differ, and the standard deviations are ident i cal i. e ., P, = p 2 p, =I= P 2 [i.e., p, > P2l F i n e 0.1 o/o 50% 99. 9 % Figure 44. Case 1 example of two-component Plotted components and the resulting simple mixing. mixed distribution are illustrated by Figure 44. The resultant d i stribution is by adding for each size class and dividing by two. An example for Figure 44 is given by Table 8. If proportions change then the combination of curves plotted in F i gure 44, will slide either to the right or to the left. Case 2. Let us make a change in the component characteristics where: P, = p2 p, =I= 1'2 [i.e ., p < P2l o =I= o2 [ i .e., o < a2 ] Component 1 might represent a beach sand, and component 2 a river sand (although it is not Lecture Notes Table 8. Example calculation of component mixing illusbated in Figure 44. Component 1 Component 2 Combined Curve Cumulative Cumulative Cumulative Percent Percent Percent 0 0 1 0 0.05 0 .25 1.0 0 0 5 0 5 6 0 0 3 0 0 .75 21. 0 0 10. 5 1 .00 50.0 0 25. 0 1 .25 78.0 0 39. 0 1 .50 94. 0 0 47.0 1 .75 99.0 0.1 49.55 2 .00 99. 9 1 0 50.45 2 .25 100.0 6 0 53. 0 2.50 100.0 21. 0 60. 5 2 .75 100. 0 50. 0 75. 0 3 .00 100. 0 78. 0 89. 0 3.25 100. 0 94. 0 97. 0 3 .50 100. 0 99. 0 99. 5 3 .75 100. 0 99. 9 99.95 55 James H. Balsillie

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W. F. Tanner -Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 normally possible to have a Gaussian distribution for a fluvial sediment) Would it be possible in nature to have two components of fluvial sediments? The answer is certainly yes; for instance, where two streams meet and one of them has a higher gradient and/or flows across a different lithology than the other, the sediment loads might very well be different. Component 1, however, would more nearly be representative of a beach sand. Note for cases 1 and 2, that 2 components result in a distribution comprised of 3 segments. There is one instance where 2 components cannot be distinguished from one another ... that occurs where p, = p2 and o, = o2 or multiples of such components, regardless of the proportions involved. Now then, if one component is quartz and the other is something different, say olivine, that is a different matter (i.e., chemistry must be considered); or if one is quartz and the other is composed of calcium carbonate shell fragments, then grain shape will affect the outcome. In general, however, the above discourse constitutes the basic preliminary rules for the treatment of simple mixing. Coarse Phi Component 1 Fine 0 .1% 50% 99.9% Figure 45. Case 2 example of two-dimensional simple mixing. Phi Fine 0.1% .... .... 50% .... .... .... ..... .... 99.9% Figure 46. Two component simple mixing with cisjointed component cistributions. Let us inspect the case where the components to be mixed are disjointed samples. That is, for the sake of discussion, component 1 is a Gaussian sample of particles ranging in size from baseballs to ping-pong balls, and component 2 is a Gaussian sample ranging in size from marbles to beads. coarse Simple mixing results in a distribution illustrated in Figure 46. The vertical segment of the resulting distribution is a zero sediment segment (the gap) and contains no sediment particles. An example of simple mixing with 3 components is illustrated in Figure 47. For natural sands, 2 to 4 component mixing is common. Lecture Notes Phi Fine 0.1% ' Com ent2 Component3 50% 99.9% Figure 47. An example of simple threeaeomponent mixing. 56 James H. Balsillie

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W. F. Tanner -Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 Zero Component: Sed i ments cannot have a zero component, since as a response element the sediment is either available or it is not present. However, it is important to realize that there are natural distributions that can have a zero component, such as ocean waves which constitute a force element that induces sedimentologic response For instance, 5 0 0 1% 50% 99. 9% along the lower Gulf Coast of Florida Figure 48. An example of a distribution with a seas are calm for about 30/o of the zero component, in this ocean waves. annual period In fact, for beach sands, wave heights somewhere in the range of from 3 to 5 em no longer have the competence to transport significant, if any, quantities of sand, and may be considered to be a part of the zero wave energy component An example is illustrated by Figure 48. Selection Simple mixing is not the only way of combining components, or of distorting the distribution. Three additional methods, described as ustatistical selectionu, are censorship, truncation, and filtering. Selection examples can be explained by laboratory procedures or by natural processes. Censorship: Censoring involves the suppression of all the data of one variety within a certain range of values. The missing data normally occurs in the tails of the distribution, but can occur in the central portion. There are two types of censorship. Type I Censorship: This occurs Coarse Ph i Fine 0.1% I Censored Point d I 50% 99.9% where the number of suppressed phi size Figure 49. Eumple of Type 1 censorship classes is known. An example is illustrated by figure 49, where one data point (i.e one sieve) is missing. However, we know the total sample weight (which we measured prior to sieving}, and the percentages for the other data points Hence, we should be able to recover the entire characteristics of the distribution Type II Censorship: This occurs where the number of suppressed measurements is known, but the numerical values to be assigned to the individual items (e.g., diameters for the screens lost) are not known. For instance, the finest sieve used in the 1/4-phi interval sieve nest was 3 .5. Hence, data for the 3. 75 tfJ and finer sieves are missing However, the pan Lecture Notes 57 James H Bslsillie

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W .. F .. Tanner-Environ .. Clastic GranulometryFGS Course, Feb-Mar, 1995 collects the total not retained by the missing sieve fractions Again, the total weight of the sample is known and the bulk of the weight data for the missing fractions is available. Censorship is the mildest form of selection. In some cases, more than 50o/o of a sample can be missing without impeding successful analysis. In fact, many published sediment curves show simple censorship. Censorship is seldom serious because it does not generally alter the appearance of the probability curve. Truncation: Truncation occurs where there is a total loss of information for a number of adjacent missing 1 /4-phi classes, or for a number of missing items (i.e., n number of sand grains within a 1/4-ph i size class) Generally this occurs in one or both of the tails of the distribution. The result is more serious than censorship For instance, i f we did not have the total weight of the sample before sieving and, for some reason, the pan fraction were lost, then the total weight of the sample represents only those sieves in which sediment was retained. Truncated probability curves are difficult to handle and may require trial and-error tessellation in order to find the original distribution (see Tanner, 1964; Appendix X, p 139) However, one should at least be able to readily identify when truncation has occurred. It is Coarse Phi Fine 0.1% 50% Figure 50. Example of single truncation. Coarse --Original ---Truncated Phi Fine 0.1% 50% characterized by typically smooth, gentle Figure 51. Example of double truncation. curves on probability paper; no inflection 99.9% 99.9% points occur unless some other modifications have also taken place. The truncated tail has better sorting because it plots as a flattened line compared to the rest of the curve Either tail can be truncated to result in single truncation (see Figure 50), or both tails can simultaneously be truncated (see Figure 51 ) Altering : Filtering is more problematic than either censorship or truncation. It is not relegated to a continuous segment (i. e., several sieves or size classes in numerical order), but the removal of, say, some sediment (varying amounts) from each of any numbe r of random sieves or size classes, for which we have no quantitative information Viewed in some ways, filtering is negative mixing, i e., component 1 plus component 2 for mixing, component 1 minus component 2 for filtering. One might assume that the filter is Gaussian and that a negative component added to the filtered distribution will result in the original straight-line probability Lecture Notes 58 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 distribution. An example is illustrated in Figure 52, where the standard deviations of the filter and the original sample are identical. An example where the standard deviations of the filter and original distribution are unequal IS illustrated by Figure 53. There are no guidelines to correct for filtering in order to determine the original distribution. It is prudent to assume that filtering has not occurred unless there is no other explanation. Summary Employing Occam' s Razor the simplest procedure is probably the best procedure. A practicable endeavor might be to ignore the effects of censorship (since it does not generally alter the shape of the probability curve), to reject an hypothesis of filtering unless other evidence compels one to do so, and to distinguish through inspection of the probability curve any difference between truncation and simple mixing. The latter should not be difficult, inasmuch as the two processes normally produce qui te different and d i stinguishable results. Once interpretive decisions have been made, the task of resolving the components can be undertaken ... including the identification Coa r se P hi F i n e 0. 1 % 50% 9 9. 9 % Figure 52. Example of fitering where the titer mean is coarser than the original cisbibution and standard deviations are equal. Coarse Ph i F i ne 0.1% -. .f!lter ,-, ........................ ...... ... a ...... :reO' ...... ... 50% ... .. 99.9% Figure 53. Example of fitering where the titer man is coarser than the original distribution and standard clftiations are unequal. of points and agencies of truncation, if any. Detenninllfion of Sample Components Using the Method of Diffetences The preceding section dealing with plot decomposition has demonstrated the process using, for example, s imple mixing of components. In reality, however, we usually have a complete sieved sample with identificable line segments that we m i g h t w i s h to decompose into its constituent components. In order to do so, we can employ the Method of Differences (Tanner, 1959), which constitutes an approximation to the method of derivatives. The method i s one that applies to the decomposition of any probability d istri b u t ion, not j us t one dea ling with sed iments. Such work could have important implications, assisting i n identify i ng force and response element re lationships that might not otheriwse be possible to i dentify As an example, let us select an original sedimentologi c distribut ion that i s compri sed Lecture Notes 59 James H Balsillie

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W. F. Tanner-Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 Table 9. Cumulative and frequency per centages, and first and second cifferences. 1 2 3 4 5 Caanul-freq. 1st 2nd ative % % Diffs Dlffs 0 0 3 0 3 [0 125] [0. 95] -1.0 0.25 1.6 1 3 +1. 3 [0.375] [3.4] -2.3 0 5 5.2 3.6 +1.9 [0.625] [9 1] -4.2 0.75 13 0 7.8 0 [0.875] [19. 0] -4. 2 1.00 25. 0 12. 0 -7. 2 [1.125] [30. 5] +3. 0 1 .25 36. 0 9 0 +2. 0 [1.375] [40.0] +1. 0 1.50 44.0 8 0 -1 0 [1. 625] [47.0] +2. 0 1 .75 50. 0 6.0 +1. 0 [1 .875] [52.5] +1. 0 2.00 55. 0 5 0 +5. 0 [2.125] [59.5] -4. 0 2.25 64.0 9 0 -2.0 [2.375] [69.5] -2.0 2 .50 75. 0 11 0 .0 [2.625] [81 .0] 1 0 2 .75 87. 0 12. 0 -5.0 [2.875] [91 .0] +4. 0 3 .00 95. 0 8.0 -o. 7 [3 125] [96. 65] +4. 7 3.25 98. 3 3 3 +2. 8 [3 .375] [99.0] +1.9 3 .50 99.7 1 4 +0.78 [3.625] [99.8] +1.15 3 .75 99.95 0 .25 NOTE: Numbers in [ ] are interpolated values for plotting purposes. of two Gaussian components (Table 9). Initially from the cumulative probability distribution percentages (Table 9, column 2), the inner differences or frequency percentages are determined (column 3). First differences are determined from the frequency percentages and are listed in column 4 Second differences are determined from column 4 and listed in column 5. Results of Table 9 are then plotted as in Figure 54. Important points identifying the character of the distribution and its components occur where first differences (solid line) equal zero. That is: Where first differences equal zero and second differences are negative, approximate means appear. Where first differences are zero and second differences are positive, approximate proportions appear. Hence, Figure 54 confirms that the total or original distribution is compr i sed of 2 means, and 2 proportions or components. Proportions are 54o/o for the first component and 46/o for the second. However, because of the approximating nature of this method (e.g., we are using 1/4-phi intervals) we can assume that the proportions are 1 : 1 The degree of complexity involved in decomposing distributions depends on whether means, standard deviations, and proportions are equal or not. Let us look at two cases. Case 1 Two Components with Means Unequal, Standard Deviations Equal, and Proportions Equal. Decomposition of the original, total curveT in this case is a simple example (Figure 55) and, in fact, is here represented by the sample of Table 9 and Figure 54 (proportions assumed equal). Component A may be determined using the point plotting formula A = (2 T) 100 where T is the upper abscissa cumulative percentile for the total (T) curve. For a given value ofT (e.g., 99.5/o), the resulting plotting position of A (i.e., A = (2 x 99. 5) 100 = 99o/o) Lecture Notes 60 James H. Balsil/ie

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W F Tanner Environ. Clastic Granulometry -FGS Course F eb -Mar 1995 6 5.5 5 4.5 4 3 5 2 1.5 1 0.5 Ill -O. g Ql -1 g -1.5 Ql -2 (i> -2.5 :e -3 i5 -3.5 -4 -4.5 -6 -6J -7.5 -8 I I I : I I I i I I I I I 1.. I lJI,..,,...,..., T T -I I ''"'"'"'' 1 / I I I I I \ I I r-..... I \ I I I I T I I J I \ 0 I I I{ I 1 1\. \ . I I I .. I I / ....... I 1 / 11 I I I \ 7 I I 1\. _L \ rr \ I 'I I \ : 1 7 \ \. I .I I 1\ \ I I I I 1\ \ I '1\__..-r I X I I I I I I \ .... ,_.. I T \. I \ I I I \ / I I I I I I \ v i I .. :ll. ,-,.eu. \ \ / I I 1 I ;::Jl VIII;:) I \ V ; i I I I I 'X I 1 \ I -.:1 I I I I I ,.., J. N U I I I I LIIIU Ulllt:> : J I I I \'/ I I I I I l I I I I I I I t:" A O I I I I ltiCOJ I ._ I 'I' r---.-o-I ... I I I I I I I I J 0 5 1 0 1 5 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1 00 Cumulative % Figure 54. Plot of component 1 an d 2 differences from T abl e 7 versus cumulative percent Lecture Notes 61 Jame s H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 or component A is located on the same horizontal line intersecting T = 99.5 on T. Note that negative values and values exceeding 1 OOo/o have meaning, since t he domain of the total curve T has been exceeded. Simi larly, po ints for component B are identified by the p oint plotting formula B = (2 T)100. Constituent components (A and B) are plotted on Figure 55. Because t he Method of Differences is an approximation, recombination of components and minor adjustments may be needed in order to locate the precise plotting position of the components. Case 2. Two Components with Means Unequal, Standard Deviations Unequal and Proportions Unequal. This example is considerably more complex than case 1. The total distribution is plotted in Figure 56. Furthermore let component A comprise 75o/o of the original total sample distribution, component B 25/o of the d istribution. The point plotting formula for the original total distribution (T) and its re lationship to component A (A) and component B (B) becomes T = 0.25 A + 0. 75 B or 4 T = A + 3B. It is critical that one first choose a component for which there is a recognizable solution. This might require some trial-and-error computations. Normally, however, the first component to be calculated is that which has the longest tails, and the larger slope (i.e., larger standard deviation) As shall become increasingly apparent, this assists in identifying the component whic h has the most percentiles for its computational Phi Grain Size "'" ........ -0 -r-. r-t-0 5 . ,.. ... .. .... 1 0 .; : .. -.!--:+ 1.5 2 0 2 5 3.0 3 5 -. -+ .. 1-i-f H 1-' t. . . :c.. r Ul t.MUU U 1 l .,.. .. Sl f f.h. f+ i-0 1...:.:. 1.0 JO .. Sl Cumulative < 10 1 0 ::J t i 0 rr .. fl II !-'. :; T I J. &a 10 Ill Percent I 0$ 0 2 C I 0 0 5 e'l T-"7 .-: 7 t-+-rrt'!! o ....:. t-0 ' I i 1 1- I ' :: t:f:.;;:---1-'1' . .l ... .. --t.: ::;: .. + j.;.;' I I I I .. o1 :f-:7;. .. . '""'t .,. .. 0 -. ... ----. .: ---= ; 1-' --.::: ltJ; '-i .. _....___ .. -+::r: 1 . ;.+t:-:-;. I -. li j .. .. . . .. .... " Figure 56. Case 2 original total cistribution, T, and its constituent conponents A and B. See text for ciscussion. Lecture Notes 62 James H. Balsillie

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W. F. Tanner-Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 definition. Analytical results for this decomposition analysis are given in Table 10. Note that for the portion of the graph above, zone C of Figure 56, 8 percentiles are 100 and component A can be readily calculated since A = 4 T -3 ( 1 00) = 4 T 300. Similarly, below zone C, 8 percentiles are 0, and A = 4 T-3 (0) = 4 T. Now, component 8 can be readily calculated in zone C according to the point plotting formula 8 = (4 T-A)/3. Table 10. Analytical results for determination of components A and B of Figure 56. p T CompA CompB til [Bottom [Top x-A= 4T 38 B= (4T A)/3 x-axis] axis] -0.50 0.025 99.975 99. 9 100 -0.25 0 .075 99.925 99. 7 100 0 .00 0 .225 99.775 99.1 A= 4T-38 100 0 .25 0 .625 99.375 97.5 where 8 = 100, 100 0 .50 1.50 98. 5 94. 0 then 100 0.75 2.875 97.125 88.5 A= 4T300 100 1.00 5.25 94.75 79.0 100 1.25 8 .58 91.42 65.68 100 1.50 14.50 85.50 50.0 96. 3 1.75 36.63 63.37 36.0 0 < 8 < 100 72.49 2 .00 75.63 24.37 22. 0 Points read from 25.16 2.25 95.16 4 .84 12. 5 graph 2.29 2.50 98.45 1.55 6.0 0.066 2 .75 99.33 0.67 2.68 A= 4T-38 0 3.00 99.75 0 .25 1 0 where 8 = 0, 0 3 .25 99.91 0 .09 0.36 then 0 3 .50 99.975 0.025 0 1 A= 4T 0 Again, because of the approximating nature of the methodology, recombination of components and minor adjustments may be needed in order to more precisely plot positions of the components For more involved three component decomposition examples, see Tanner (1959). Note that numerically or physically determined components may not necessarily be Gaussian. They may be truncated, or composed of multiple line segments and, hence, contain additional components. CARBONATES Along both the east coast and lower Gulf coasts of Florida, the beaches are comprised of significant amounts of calcium carbonate (CaC03 ) sediments primarily shell hash Such deposits are charcteristically variable, and highly so. That is, in one locality it might be 99o/o quartz, and in another 99o/o calcium carbonate. When pursuing the collection of quartzose samples, even for the informed perhaps the best one can do, is take a sample contain i ng 20 Lecture Notes 63 James H. Balsil/ie

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W. F. Tanner Environ. Clastic Granu/ometry -FGS Course; Feb-Mar, 1995 1 0 Phi Grain Size 1 2 0.01 50 99.99 Cumulative Percent Rgure 57. Beach sample from Sanibel Island, Rorida, containing a calcium carbonate shel fraction. Components were physicaly detennined using Ha. PoT designates the point of truncation. See text for ciscussion. to 30/o CaC03 Suppose that such a sample (50 to 100 grams) is taken on Sanibel Island located along the lower Gulf Coast, such as one collected by Neale (1980). The sieved results are p l otted in Figure 57. Following sieving of the total sample (solid line in Figure 57), we then digest the CaC03 using HCI and re-sieve the mostly quartz insoluble residue. The result i ng distribution (83/o of the total sample) is given by the dashed line of Figure 57. By numerically subtracting the insoluble residue (mostly quartz) distribution from the originally sieved distribution, the CaC03 distribution (17/o of the total sample) is determined (dash-dot dash line of Figure 57) The shape of the originally sieved distribution should provide a clue that the CaC03 component is truncated. But, what of the two-segment quartz (insoluble) distribution (dashed line)? In fact, the line segment labelled as .. added a represents insolubles appropriated by organisms and contained within the shell matrix, that were released due to HCI digest i on. Hence, these insoluble particles are not represented by the total curve, since they were hidden, or filtered (see Tanner, 1964; Appendix X, p 139). Let us look at some other differences between quartz and calcium carbonate In terms of Mohs hardness scale, calcium carbonate is 4 orders of magnitude softer than quartz. Hence, where quartz and carbonate mixtures occur, the quartz will accelerate abrasion of the softer mater i al. Just how fast this occurs i s not known but should be especially accelerated during periods of higher energy, such as during storm impacts. Mass densities of both quartz and calcium carbonate vary slightly, depending upon impurities present. They are however, quite similar in value. Lecture Notes 64 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 In terms of chemical stability, calcium carbonate is 8 to 10 orders of magnitude chemically less stable than quartz. Rainfall, runoff, and high tide waters will probably dissolve CaC03 in upper layers of the foreshore and beach, and precipitate at lower elevations in the sediment column. How much lower in elevation? Not much. Beach rock that is well developed in beaches of Florida, attests to the highly mobile mature of CaC03 in terms of its ability to be dissolved and re-precipitated. In southeast coastal Florida there are anthropic materials cemented within beach rock, such as Coke bottle fragments and automobile parts. Automobile parts certainly were not available in any quantity prior to about 1925. Such cementation, therefore, requires less than 70 years. How much less is unknown. Carbonate material has much more variability in shape than quartz. Mostly, CaC03 is plate or rod shaped, while quartz particles are nearly equidimensional. In the company of one another the plate-shaped particles significantly change the hydrodynamic response of the quartz particles. Platy particles exhibit significant lateral movement when settling in water. Consequently, the grain-size distribution is seriously impacted and becomes uwarpedu in some way which cannot be analyzed. Should we, therefore, forget about carbonates, and focus attention on the quartz fraction only? Currently, we do not know with certainty what percent of the nearshore sand pool is carbonate. At the very least, we need such measurements. REFERENCES CITED AND ADDfflONAL sEDIMENTOLOGIC READINGS Apfel, E. T., 1938, Phase sampling of sediments: Journal of Sedimentary Petrology, v. 8, p. 67-78. Arthur, J. D., Applegate, J., Melkote, S., and Scott, T. M., 1986, Heavy mineral reconnaissance off the coast of the Apalachicola River Delta, Northwest Florida: Florida Department of Natural Resources, Bureau of Geology, Report of Investigations No 95, 61 p. Balsillie, J. H., 1985, Post-storm report: Hurricane Elena of 29 August to 2 September 1985: Florida Department of Natural Resources, Beaches and Shores Post-Storm Report No. 85-2, 66 p. Balsillie, J. H., in press, Seasonal variation in sandy beach shoreline position and beach width: Florida Geological Survey, Open File Report, 39 p. Bates, R. L., and Jackson, J. A., 1980, Glossary of Geology, American Geological Institute, Falls Church, VA, 751 p. Bergmann, P. C., 1982, Comparison of sieving, settling and microscope determination of sand grain size: M.S. Thesis, Department of Geology, Florida State University, Tallahassee, 178 p. Lecture Notes 65 James H. Balsillie

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W. F. Tanner-Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 Demirpolat, S., and Tanner, W. F 1987, Advanced grain size analysis and late Holocene sea level history : Coastal Sediments '87, (N. C Kraus ed.), p. 1718-1731 Demirpolat, S., Tanner, W. F., and Clark, D., 1986, Subtle mean sea level changes and sand grain size data: [In] Suite Statistics and Sediment History, (W. F Tanner, ed ) Proceedings of the 7th Symposium on Coastal Sedimentology, Florida State University, Tallahassee, FL. De Vries, N 1970, On the accuracy of bed-material sampling: Journal of Hydraulic Research, v 8 p. 523-534. Doeglas D J. 1946, Interpretation of the results of mechanical analyses: Journal of Sedimentary Petrology, v. 16, no 1, p. 19-40. Emmerling, M. D and Tal)ner, W F., 1974, Splitting error in replicating sand size analysis: [ Abstract] Prog. Geological Society of America, v. 6, p. 352. Fogiel, M., et al. 1978, The Statistics Problem Solver, Research and Education Association, New York, N. Y. 1044 p Friedman, G M and Sanders J. E., 1978, Principles of Sedimentology, John Wiley, New York, 792 p. Hobson, R. D., 1977, Review of design elements for beach-fill evaluation: U. S. Army Corps of Engineers, Coastal Engineering Research Center, Washington, D. C., Technical Paper No. 77-6, 51 p. Hutton, J., 1795, Theory of the Earth v 2. Jopling A V., 1964, Interpreting the concept of the sedimentation unit: Journal of Sedimentary Petrology, v. 34. no. 1 p. 165-172. Neale, J. M 1980, A sedimentological study of the Gulf Coasts of Cayo-Costa and North Captiva Islands, F l orida: M. S Thesis, Department of Geology, Florida State University, Tallahassee, FL, 144 p. Otto, G. H 1938, The sedimentation unit and its use in field sampling: Journal of Geology, v. 46, p. 569-582. Rizk, F. F., 1985, Sedimentological studies at Alligator Spit, Franklin County, Florida : M. S Thesis, Department of Geology, Florida State University, Tallahassee, FL, 171 p Rizk, F. F and Demirpolat, S., 1986, Pre-hurricane vs. post-hurricane beach sand : Proceedings of the 7th Symposium on Coastal Sedimentology, (W. F. Tanner, ed.), Department of Geology, Florida State University, Tallahassee, FL, p. 129-142. Savage, R. P., 1958, Wave run-up on roughened and permeable slopes : Transactions of the American Society of Civil Engineers, v 124, paper no. 3003, p 852-870. Lecture Notes 66 James H. Ba/sil/ie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Socci, A., and Tanner, W. F., 1980, Little known but important papers on grain-size analysis: Sedimentology, v 27, p. 231-232. Stapor, F. W., and Tanner, W. F., 1975, Hydrodynamic implications of beach, beach ridge and dune grain size studies: Journal of Sedimentary Petrology, v. 45 p. 926-931 Stapor, F. W., and Tanner, W. F., 1977, Late Holocene mean sea level data from St. Vincent Island and the shape of the Late Holocene mean sea level curve: Coastal Sedimentology, (W. F. Tanner, ed.), Department of Geology, Florida State University, p. 35-67. Sternberg, H., 1875, Untersuchungen uber Langenund Quer-profil geschiebefuhrende Flusse: Zeitschrift Bauwesen, v. 25, p. 483-506. Tanner, W. F., 1959a, Examples of departure from the Gaussian in geomorphic analysis: American Journal of Science, v. 257, p. 458-460. ----' 1959b, Sample components obtained by the method of differences: Journal of Sedimentary Petrology, v. 29, p. 408-411. ----' 1959c, Possible Gaussian components of zig-zag curves: Bulletin of the Geological Society of America, v. 70, p 1813-1814. 1960a, Florida coastal classification: Transactions of the Gulf Coast Association ----of Geological Societies, v. 10, p. 259-266. ____ 1960b, Numerical comparison of geomorphic samples: Science, v. 131, p. 1525-1526. ____ 1960c, Filtering in geological sampling: The American Statistician, v. 14, no. 5, p. 12. 1962, Components of the hypsometric curve of the Earth: Journal of Geophysical ---Research, v. 67, p. 2841-2844. 1963, Detachment of Gaussian components from zig-zag curves: Journal of ----Applied Meteorology, v. 2, p. 119-121. 1964, Modification of sediment size distributions: Journal of Sedimentary ____ Petrology, p. 34, p. 156-164. ____ ., 1966, The surf break .. : key to paleogeography: Sedimentology, v. 7, p. 203-210. ____ ,, 1969, The particle size scale: Journal of Sedimentary Petrology, v. 39, p. 809811. Lecture Notes 67 James H. Bslsillie

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W. F. Tanner Environ. Clastic Granulometry -: FGS Course, Feb-Mar, 1995 ____ 1971, Numerical estimates of ancient waves, water depth and fetch: Sedimentology, v. 16, p. 71-88. ----' 1978, Grain-size studies: [In] Encyclopedia of Sedimentology, (R. W. Fairbridge and Joanne Bourgeois, eds.), Dowden, Hutchinson and Ross, p 376-382. ____ 1982a, Sedimentological tools for identifying depositional environments: [In] Geology of the Southeastern Coastal Plain, (D. D. Arden, B. F. Beck, and E. Morrow, eds.), Georgia Geological Survey Information Circular 53, p. 114-117. ____ 1982b, High marine terraces of Mio-Piiocene age, Florida Panhandle: [In] Miocene of the Southeastern United States, (T. M. Scott and S. B. Upchurch, eds.), Florida Department of Natural Resources, Bureau of Geology Special Publication 25, p. 200-209. ____ 1983a, Hydrodynamic origin of 'the Gaussian size distribution: Abstract with Programs, Geological Society of America, v. 15, no. 2, p. 93. 1983b, Hydrodynamic origin of the Gaussian size distribution: [In] Near-Shore ----Sedimentology, (W. F. Tanner, ed.), Proceedings of the 6th Symposium on Coastal Sedimentology, Florida State University, Tallahassee, FL. ----' 1986, Inherited and mixed traits in the grain size distribution: [In] Suite Statistics and Sediment History, (W. F. Tanner, ed.), Proceedings of the 7th Symposium on Coastal Sedimentology, Department of Geology, Florida State University, Tallahassee, FL. 1988, Paleogeographic inferences from suite statistics: Late Pennsylvanian and ----early Permian strata in central Oklahoma: Shale Shaker, v. 38, no. 4, p. 62-66. _______ 1990a, Origin of barrier islands on sandy coasts : Transactions of the Gulf Coast Association of Geological Societies: v. 40, p. 819-823. 1990b, The relationship between kurtosis and wave energy: [In] Modern Coastal Sediments and Processes, (W. F. Tanner, ed.), Proceedings of the 9th Symposium on Coastal Sedimentology, Department of Geology, Florida State University, Tallahassee, FL, p.41-50. ____ 1991 a, Suite Statistics: the hydrodynamic evolution of the sediment pool: (In] Principles, Methods and Application of Particle Size Analysis, (J. P M. Syvitski, ed.), Cambridge University Press, Cambridge, p. 225-236. ____ ., 1991 b, Application of suite statistics to stratigraphy and sea-level changes: [In] Principles, Methods and Application of Particle Size Analysis, (J. P. M. Syvitski, ed.), Cambridge University Press, Cambridge, p. 283-292. 1992a, 3000 years of sea level change: Bulletin of the American Meteorological Society, v. 83, p. 297-303. Lecture Notes 68 James H Ba/sillie

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W. F Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 1992b, Late Holocene sea-level changes from grain-size data: ev i dence from the Gulf of Mexico: The Holocene, v 2 p 258-263. ____ 1992c, Detailed Hol ocene sea level cuve, northern Denmark : Proceed i ngs of the Internat i onal Coastal Congress Kiel '92, p 748-757. ____ 1993a,An 8000-yearrecord of seal evel change from grain-size parameters: data from beach ridges in Denmark: The Holocene v. 3, p 220-231. ____ 1993b, Louisiana cheniers: clues to Mississippi delta history : [In] Deltas of the World (R. Kay and 0. Magoon eds.), A S.C.E., New York p. 71-84. 1993c, Louisiana chen i ers: settling from high water: Transact i o n s of the Gulf ------Coast Association of Geological Soc i eties v 43, p. 391 -397. ____ , 1994, The Darss: Coastal Resear ch, v. 11, no. 3, p. 1-6. ---' and Campbell K M. 1986, Interpretation of gra i n size su i te data from two small lakes in Florida: [In] Suite Statistics and Sediment History, (W F Tanner ed ) Proceedings of the 7th Symposium on Coastal Sedimentology Department of Geology Florida State University, Tallahassee FL. ____ ,, and Demirpolat S., 1988, New beach ridge type: severely limited fetch, very shallow water: Transactions of the Gulf Coast Association of Geological Societies, v. 38, p. 367-373. Ul'st, V. G., 1957, Morphology and developmental history of the region of marine accumulation at the head of Riga Bay, ( i n Russian), Akad. Nauk ., Latvian SSR, R i ga, Latvia, 179 p. Wentworth, C. K 1922, A scale of grade and class terms for clastic sediments : Journal of Geology, v. 30, p 377-392. Zenkovich V P., 1967, Processes of Coastal Development, lnterscience Publishers (Wiley), New York, 738 p. Lecture Notes 69 James H. Balsil/ie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Appendix I Socci, A., and Tanner, W. F., 1980, Little known but important papers on grain-size analysis: Sedimentology, v. 27, p. 231-232. [Reprinted with pennission] Lecture Notes 71 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Scdimmto/ugy ( 19!!0) 27. 231-232 SHORT COMMUNICATION Little known but important papers on grain-size analysis ANTHONY SOCCI & W F TANNER Geology Deportment, Florida State University, To/Jaho.SSu, Florida 32306, U.S.A. ABSTRACT Some imponant papers have apparently gone unnoticed by most sedimentologists as shown by their absence from bibliographies of recent texts These papers concern sample size, permissible number of splits, sieving time, and sieve-vs-scttJing tube comparisons These papers -.-ere pubiished where sedimcntologists would not ordinarily see them, but should be required reading for students. The recent appearance of rwo encyclopaedic works on sedimentology (Friedman & Sanders, 1978; Fair bridge & Bourgeois, 1978) having unusually complete bibliographic references provides an opponunity to check the state of the an end to identify significant gaps in the coverage provided This is imponant beause these two books probably will serve as the 'core storage' for sedimentological knowledge for some years to come. We would like, therefore, to draw attention to several key papers in sedimentology which we have been unable to find referenced in Friedman .& Sanders (1978), Fairbridge & Bourgeois (1978). Selley (1976), Pettijohn (1975), Pettijohn Potter & Siever {)972), Carver (1971), Blatt, Middleton & Murray (1972), Folk (1974), Bcrthois (1975), Griffiths (1967) and Tieken (1965). For example, a classic paper by Mizutani (1963) on sieving methodology was one or the compeUing for insistence, some years ago, that scientific in the Aorida State University laboratories be carried out to new standards: quarter phi sieves, 30 min sieving time. and relatively small initial sample (40-.50 g, after no more than one split). The most practical asPect of Mizutani's paper, in 0034..()746/80/0400.()231 S02.00 <0 1980 International Association of Scdi mentologists Lecture Notes 72 our opinion; has to do with sieving t ime (although he addressed a more imponant question than this}. De Vries (1970) considered the problem of sample size. In a graph (p. 530) de Vries showed a plot of representative grain size a.s sample size, with index Jines for 'high accuracy', 'normal accuracy, and 'low accuracyt. For example. for D,. sand of 0 5 mm diameter (84% of the sample is finer than 0 mm), the high accuracy line indicates that the sample size should be about 25 g. This important paper likewise is not cited in any of the works mentioned above Emmerling& Tanner (1974) showed that a suitably small sample cannot be obtained by repeated splitting, without introducing a devastating (com pounded) splitting error, and they recommended a single split only. This suagests that the original sample be not more than 60-100 g (or, in rare cases, where two succ:cssive splits must be caken, regardless of the error introduced, 120-200 g). Coleman & Entsminger (1977) in a comparative study. of sieving. settling t ube work and grain measurement under the microsoope, showed that there are imponant differences between sieve and settling tube data, only one of which is that the latter are not as accurate as the former (verification under the microscope) as a measure of grain size. James H. Balsillie

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W. F. Tanner-Environ. Clastic Granulometry-FGS Course, Feb-Mar, 1995 A. Socci & W. F. T unmr We would like 10 emphasize thai our inte n rion in writing this is not to criticize current texts, but to draw attenlion to important papers, in publica lions not commonly read by sedimentologisrs We are aware of the almost impossible cask of keeping a breast of &he ever-increasing volume of geologi cal information. even within one's own area of specialization. REFERENCES 8RTHOJS, ).. (1975) lrurk SidimoJiologiqw Roches tl MithOtks). Doin tditeurs. Paris 278 pp BLATT, H., MIODUTON. G. &. MURRAY, R (1972) Oritin of StdimtnJorJ ROC'ks. Prentice Hall. New Jeney 634 pp CARVfR, R .E. (Ed.) (1971) in Stdimtntory Pttrology Wiley&. Sons. New York. 653 pp COLEMAN, C .&. ENTSMINGER, l. (1977) Sievin& vs senling tube : a comparison of hydrodynam ic and granuloc:baraaeristics of beach and bcac:h rid1c sands In : Coastal SHiimtnto/ogy (Ed. by W F Tanner) pp. 299-312. Geology Depanmcnt, Florida State Univer sity, Tallahassee, Fl 315 pp. M & TAJioO,.Eit. W.F (1974) Splitting errur i n replicat ing sand s ize Ah.fJr Prug. gt>al. Sue Am 6 352 FAIItBRIOG, R W & BOURGEOI S J ( 1978) of Dowden, Hu tc hinson and Ross. Stroudsburg. Pa 901 pp. FOLK R .l. (1974) o/ Roc ks. Hemphill Publishing Co . Austin. Texas 182 pp. FRIEDMAN G & SANDERS J.E. (1978) Principlt s of Wiley&. Sons, New York. 792 pp GRIFFITHS, I .C. (1967) Scitn t ific in Analys i s of Stdimtnts Mc:Graw Hill. New York 508 pp MIZUTANI S (1963) A theoretical and experimental consideration on the accuracy of sieving analys i s J Eanh Sci Nogoya, Japan Jl, 1-27 PTTIJOHN, F J (1975) Stdinwnrory Rks. Harper and Row, New York. 628 pp. PTTJJOHN, FJ .Pono. P.E It SIEVER, R (1972) Sattd tllld Sprinecr -Ver)ag, New York 618 pp Su.uv, R C (1976) An Introduction to Sedimtnrolag )'. Academic: Press. New York 408 pp. TJCKEU., F G (1965) Tht of Stdimtntary Mineralog y Esevier Publish in g Co New York 220pp DE VlltES. N ( 1970) On the accuracy o f bed-material samplinJ, J Hydrmrl. ks. 8, 523-534 ( M anusn'ipt reuir1td I 0 A ugusr J 979; rnisit"' rtctiwd I 0 Octo/Nr 1979) Lecture Notes 73 James H. Ba/sillie

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II IIDIES Lecture Notes .JJamnes H lkllsiiffe

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W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 Appendix II Guidelines for Collecting Sand Samples Lecture Notes 75 James H. Ba/sillie

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W. F Tanner-Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 Guidelines for Collecting Sand Samples Items 1 through 14 of this list apply to sampling of beach ridge features. Items 7 through 14 (depending upon the feature) apply to dunes, subaerial beaches, etc. Subaqueous sampling requires specialized considerations. 1. Do not work at the map ends of beach ridges (map sense); stay reasonably close to the middle (map sense) Hydrodynamic influences are too complicated at (or near) ends or tips. 2. For multiple ridges, the numbering scheme should start with the oldest ridge (Sample No 1 ), and finish with the youngest. However, it is commonly advisable (for various reasons) to start work with the youngest ridge; in this case, use Number 200 for the youngest sample, then 199, then 198, etc. In this scheme, the oldest sample may turn out to be #153, or something like that. This permits Little Ice Age ridges to be sampled, in case the profile cannot be finished, or the number of ridges is small, or older ridges are problematical (the younger ridges are generally easy to identify; they give a time interval between ridges, hence tentative dates for the entire system). 3. Measure or pace, and record, distances between samples (ridges). Use this distance when uncertain at>out the presence or absence of a subtle ridge. 4. Collect from the seaward face. 5. Select a site halfway (vertically) between crest and swale. 6. Avoid eolian hummocks, if there are any, by moving parallel with the crest, maintaining the half-way position. 7. Dig to a depth of about 30-40 em. 8. Use a spatula to collect a laminar sample, or nearly-laminar sample. If bedding is not visible, then assume that it was parallel with the ridge face. 9. Measure the sample, in a calibrated measuring cup, as follows: a. If one split MUST be made later: 90-100 grams. b. For transport by air (no split): 4550 grams. Calibration of the measuring cup must be done in advance, using dry quartz sand. 10. Remove twigs, roots, leaves and other extraneous matter. 11 Place in plastic zip-loc bag (heavy duty); put sample number on high-adhesion masking tape, on outside of the bag. Do not put paper inside bag; it tends to get wet. Do not use ink or crayon on outside; it rubs off. Make sure the bag is locked tightly. Lecture Notes 76 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulo.metry FGS Course, Feb-Mar, 1995 12. Clean cup thoroughly after collecting each sample. No single grain of sand, from one sample, should be allowed to contaminate the grain-size distribution of the next sample. 13. Mark the beginning and end of the traverse on a topographic or other suitable map Place sample numbers, where appropriate next to key features such as the junction of dirt roads or trails 14. Note the height of crest (above adjacent swales), front slope angle, map distance between crests, and other pertinent information (such as extent of eolian decoration, if any). If only one ridge is to be sampled, (e.g., there is only one ridge present, or one ridge warrants detailed study), then multiple samples might be taken on the face of a cut (trench) at right angles to the crest, in a horizontal line about half-way down from the crest. If no trench can be dug, samples can be collected at regular intervals (such as 5 or 10 or 20 m), on the seaward face about half-way down from the crest, in a line parallel with the crest. In any event, sample locations should be sketched (map sense). Revised 28 April 1994 W. F. Tanner Lecture Notes 77 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 Appendix Ill Laboratory Analysis of Sand Samples Lecture Notes 79 James H. Balsillie

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W. F . Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Laboratory Analysis of Sand Samples In North America sieve nests are everywhere standardized and comprised of half-height U. S. Standard sieves, 8 inches in diameter. The initial sample should be 45-60 grams. If it is 80-120 grams, it can be split once. A second split should not be made; samples larger than 120 grams are too large for useful work, because they require more than one split and thus introduce a compound splitting error. The initial sample should be very fine gravel, sand, and coarse silt (and perhaps a small amount of clay), but nothing coarser, and nothing finer. It should be clean and free of plant debris and /or shell fragments (of any size). Shell fragments can be removed with hydrochloric acid; after treatment and washing, the residue should be 45-50 grams. Hydrogen peroxide can be used to remove fine organic matter. If some clay is present, it should be in dispersed form, but not in floes, clumps, or blocks. If it is not in dispersed form, then it should be treated with Calgon, or Varsol, and/or ultra-sound. Normally, clay and/or very fine silt, up to about 15-20/o of the total, can be handled, more or less satisfJJctorily, in the sieving process. However, one gets more accurate results by separating the clay-and-fine-silt fraction and then measuring it in the settling tube. In this case, the sand fraction (down to 4.5 phi) can be analyzed by itself (clean sand). The data on the silt-and-fine-clay must not be discarded. The best procedure for measuring the sand grain size is sieving. Counting grains on a microscope slide is extremely slow and tedious, and produces unknown operator error; it is probable that it is not replicable. The settling tube displaces the mean significantly, minimizes polymodality, reduces the numerical value of the standard deviation, and distorts the higher moment measures, in many cases severely; this is because the settling tube adds a particular hydrodynamic character (due to grain-to-grain interactions which modify greatly the settling velocities of individual particles) which was not present in the original sample. There are several other techniques for measuring grain size, but some of them do not cover the necessary size range in acceptable fashion, and others have not been calibrated properly yet. Sieving should be done in 8-inch-diameter, half-height, steel-screen sieves having a quarter-phi interval, and should use 30 minutes per sample on a mechanical shaker. Weighing may be good enough to 0.001 gram, but if the balance is capable of doing so, 0.0001 is better (for later rounding off). The weight prior to sieving should be compared with the total of the size-fraction weights, to determine the magnitude of error in sieving; sieve loss is, ideally, no more than 0.1 0.5 percent (about 10 to the negative 3). The raw weights that are obtained in this fashion are suitable for advanced statistical analysis, using the first six moment measures (GRAN-7 computer program). These parameters can be evaluated for the entire sample suite, provided that it is homogeneous (using the SUITES program). If the samples were taken along an historical line (e.g., from oldest to youngest), individual parameters can be smoothed slightly (moving averages; window = 5, Lecture Notes 80 James H. Balsillie

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W F. Tanner-Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 7 or 9), to produce a history of depositional conditions. Cf Socci and Tanner, 1980. In: Sed i mentology ", v 7, p. 231 Revised March 1 994 W F. Tanner Lecture Notes 81 James H Balsil/ie

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W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 AppendixN Example Calculation of Moments and Moment Measures for Classified Data Lecture Notes 83 James H. Bslsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Example Calculation of Moments and Moments Measures for Classified Data (Aher Fogie/, eta/. 1978) Mean Frequency Mid-Point Mean Clas s Deviation f, (X;X}2 f, (X;. X}3 f1 (X, -X}'' f, x, x (X1 -X} 49-54 6 51 5 66. 5 -15 6(225) = 1350 -20250 303750 55-60 15 57. 5 66. 5 9 15(81)=1215 -10935 98415 61-66 24 63.5 66. 5 3 24(9)=216 -648 1943 67-72 33 69.5 66. 5 3 33(9)=297 891 2673 73-78 22 75. 5 66. 5 9 22(81 )=1782 16038 144342 Totals 100 4860 -14904 551124 It is now possible to compute the moments and the moment measures where n = I f i The first moment is the average or mean, m, given by: 6(51.5) + 15(57.5) + 24(63.5) + 33(69.5) + 22(75.5) 100 which is also the first moment measure( which can have units). The second moment, m2 is calculated according to: = 4860 = 49.09 99 = 66.5 which may have dimensions of units squared and the second moment measure or standard deviation (or sorting coefficient) o, is : a = {iii; = v'49.09 = 7.006 with possible unit dimensions. The third moment, m3 is determined as: 3 m3 = L X) = 14904 = 150.55 n -1 99 and is always dimensionless The third moment measure, termed the skewness, Sk is also Lecture Notes 84 James H. Balsil/ie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 dimensionless and is given by: 150.55 49.091 5 = 150.55 = -o.438 343.95 The fourth moment, m4 is produced by: L X)4 m = 4 n -1 551124 = = 5566.91 99 and is dimensionless The fourth moment measure, called the kurtosis, K, a parameter, determined by: K = m4 = 5566.91 = 5566.91 = 2 31 49.092 2409.83 Lecture Notes 85 James H Bslsil/ie

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W. F. Tanner--Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 Appendix V Tanner, W. F., 1994, The Darss: Coastal Research, v. 11, no. 3, p. 3-6. Lecture Notes 87 James H. Balsil/ie

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W. F. Tanner --Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 Coastal Research VoL 11 No. 3 October 1994 ISSN-0271-5376 The Darss William F. Tanner, Geology Dept., F.S.U., Tallahassee, Fla. 32306-3026 U S.A. Abstract Beach on the Oarss (Baltic coast, Germany} are in good part masked by eolian sand, but nevertheless show clear evidence that they were formed under low-to-moderate-energy swash on a !air-weather beach. This is indicated by granulometry of 16 samples from trenches; suite analysis methodology makes the distinction easily. Probability plots show many examples of the "surf break," but not the "eolian hump,'' and each of these is fully diagnostic. Therefore the ridges have only minor eolian content, primarily in the form of a wind-worked cover. Many workers, without trenching, identified the ridges as dunes, because of surface geometry. Ul'st (1957) reported low-angle fair-weather beach-type cross-bedding, -but his work has been ignored or rejected. Even though the origin is clear, t.he number of ridges is very difficult. to ascertain, because of the eolian veneer. Introduction This brief preliminary report treats the ridge system on the Darss, on the Baltic coast northeast of Restock, and northwest of Stralsund, Germany. This system has been described by various authors as made up of beach ridges, dunes, dune ridges, or foJ,"edunes (ct. Kolp 1982). Most authors have chosen "dunes." Johnson (1919 p ; 427) in a photo caption called them "forested dune ridges" (linear dunes). Schiitze (1939) followed earlier writers, who had assumed that they are dunes. Fukarek (1961) quoted Hurtig (1954, 1957) to the effect that the ridges were built of sand from offshore sand-banks; this is not a definitive statement about immediate origin. Zenkovich (1967 p. 295, 609-612) labelled them as dunes; although he cited Ul'st (1957) showing beach-type cross-bedding, he rejected that idea, and chose an eolian origin. Lobeck (1939 p. 356) identified them, correclly, as dune-covered beach ridges. Although Ul'sl (1957) labelled the alignments on the Darss as "dunes" (because they look like dunes; brief caption, p. 161), he also commented in more detail that they are beach with a covering of eolian sand (p. 160}. Eolian deposits on top of swash-built beach ridges are common in many places, and the wind-blown sand tends to accumulate on the ridge crests, but irregular eolian topography is not a clue to ridge origin. Elsner (personal comm 1993) inspected the area and described the ----------------------------------Coastal Research has been published since 1962. Send cor.respondence to Dr.W.F. Tanner, Geology Department, Florida State Univ. Tallahassee, Fla. 32306-3026, U.S.A. (telephone 904-644-3208, fax 904-644-4214). Subscription price: $6 per year in the U.S.A., $7 per year elsewhere. Copyright 1994 Lecture Notes 88 James H. Balsil/ie

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W. F. Tanner-Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 Page 2, October 1994 Coastal Research eolian influence as pervasive. He collected 16 sa:ild samples, using standardized field procedure (requiring trenching). Those samples have been analyzed, using "suite statistics" methods (Tanner 1991-a, 1991-b). As is true in other places, wind work was not as effective as had been thought. The fact that pre-dune samples were obtained is due to the practice of avoiding obvious eolian features, and taking no surface sand, but digging to. a depth of some 30-50 em for each sample. That is done because much so-called dune deposition in beach ridge systems is in fact only a veneer of eolian sand on top. Furthermore, modest reworking by wind commonly does not change beach grain size distributions to eolian ones. It takes a good deal of transport to erase all the granulometric characteristics of the mature beach, and to impart the characteristics of wind work. Granulometry Data from six Darss sand samples (No. 135, 144, 145, 147, 149, 150) are summarized below. This list is based on hand plotting of suite parameters,. two at a time, against well-known number fields (Tanner 1991-a, 1991-b): i. Fluvial: Not one sample. ii. Dune or eolian: 2 plots. iii. Swash: 5 plots. iv. Settling (from water): 7 plots. The "fluvial'' class must be eliminated (no river samples; also, no river}. "Suite statistics" methodology identifies the beach setting, without ambiguity, and also shows that the wave energy level was "low to moderate" (not "high"). Therefore there was swash action, due to low-to-moderate-energy waves, plus a settling component (perhaps the mechanism of Postma; Tanner and Demirpolat, 1988). Wind was not the primary depositional agency, but reworked a thin veneer of sand at a later date. The swash-plus-settling combination is rather common on low-to-moderate energy beaches. It has been seen in a variety of other places, including Mesa del Gavilan (near Boca Chica, east of Brownsville, Texas, U.S.A.; Tanner and Demirpolal, the Jerup-Tversted low-energy ridge systems in extreme northern Denmark (Tanner 1992-a, 1992-b, 1993-a), and the cheniers of southwestern Louisiana (U.S.A.; Tanner 1993-b). Grain-size probability plots of these six samples show two distributions which are almost perfectly Gaussian, two good examples of the "surf break" (lowto-moderate-energy swash; Tanner 1966), one example of a distinctive coarse tail which may indicate glacial debris in the area, and one problematical example, but not a single "eolian hump" (wind evidence). Analysis of eleven of Elsner's samples (the previous six plus Numbers 160, 170, 187, 189 and 190) yielded the following: i . Settling (water): five plots. ii. Beach: five. iii. Dune: two. iv. River: none. This means low-to-moderate-energy fair weather swash, and settling from water. The mean of the kurtosis, versus the standard deviation of t.he kurtosis, places these 11 samples with the Jerup (Denmark) beach ridge sands, where the beach-plus-settling interpretation is clear (154 samples). On the various crossplots, the Darss samples are not located near known continental-interior dunes, but might resemble, in some minor way, coastal dune sands with a previous beach history. Probability plots of individual sand samples show the "surf break," Lecture Notes 89 James H. Ba/sillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Coast.ai Research October 1994, Page 3 but not the "eolian hump." The entire suite (16 samples) has 12 examples of the "surf break," only minor-to-negligible evidence for wind work, and not a single "eolian hump." The entire suite indicates swash work and settling, on a low-to-moderate-wave-energy beach. Specifically, the cross-plot of kurtosis vs standard deviation (n = 16) shows a combination of swash-and-backwash, and settling from water, and matches rather closely similar beach ridges from Mesa del Gavibin, Texas, and from the Tversted-Jerup area {Denmark). The cross-plot of mean-of-kurtosis vs standarddeviation-of-kurtosis also places the Darss samples with the Mesa del Gavilan examples and with the Tversted-Jerup beach ridges. Therefore, this analysis shows that the Darss sands represent essentially the same beach environment as the Tversted-Jerup samples, even though later wind work was surficially extensive in the Darss area. This analysis also indicates that the field impression of pervasive wind influence must not be extrapolated to depth; these sand samples represent swash-built fair-weather beach ridges, but not dunes, and the granulometric data match the cross-bedding described by Ul'st. Hence Elsner's tr,ench samples provide reliable information. The surface of the Darss beach ridge plain has been modified a great deal by later "-'ind work, as shown by many published misidentifications of the ridges. Later wind influence makes sampling difficult, if one wishes to get swash-built beach-ridge sand samples; therefore it Will be impossible to collect a c 'omplete, reliable set of samples, ridge by ridge, if one Wishes to derive a detailed sealevel history, without extensive digging (Tanner 1992-a). Number of Ridges The ridges are hard to count, because of the dune cover. Schiitze (1939) summarized earlier work, cited counts from 121 ridges to 180-plus, and tried to use historical data to determine rate of growth. He adopted a figure of 35 years per ridge (the BrUckner cycle), which yields 4135 years for 121 ridges, or 6300 years for 180 ridges; he also used other numbers, obtaining younger dates (2800-3000 B.P.). lf the Darss ridges are like those in the Jerup-Tversted area, then perhaps timing from Denmark can be transferred to the Darss. If so, the Darss ridge system appears to have started about 3,200 years ago, leading to the following inferences: If 121 ridges, then '26.4 150 173 180 200 yrs each 21.3 18.5 17.8 16.0 The first, second and fifth do not match any known periodicity in any other well-studied sandy beach ridge system. The third is close to the periodicity of a beach ridge plain on the Pacific coast of Mexico (Nayarit and Sinaloa; 18.6 years). (Average periodicity in the Jerup system (Denmark) and the St. Vincent Island system (Florida) was 50-51 years.) Each swash-built beach ridge was made during, and because of, a sea level rise-and-drop pair, with a magnitude of 5-30 em (Tanner 1992-b). Various studies have produced different time intervals for beach ridges, ranging from as little as 3-4 years (Tanner 1990)' to 1,000 years or more. This is possible beCc"lUSe several di!ferent periods are available on the coast (e.g., the El Nino-Southern Oscillation, at 3-7 years, plus many other longer periods}. It appears that the Lecture Notes 90 James H. Ba/sillie

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W F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Page 4, October 1994 Coastal Research local availability of new sand selects the period that will be used, with large availability creating short map spacing and short time intervals. A transverse line (right angles to ridge crests), at the widest part of the Darss system, was measured on a map to be 5360 m long. If the ridge counts, used above, are employed, one can calculate average map spacing between ridges. This spacing, with time intervals listed above, produces an accretion rate as follows (m/yr): If 121 ridges, then 44 m and 150 35.7 173 31 180 30 200 27 1.67 m/yr 1.67 1.67 1.68 This is higher than a "typical" value Perhaps 120-173 ridges is about right. 1.69 (roughly Wind Work 1.0 m/yr), but is not excessive. Rizk (1991) studied the wide beach ridge system on St. Joseph Peninsula (Florida, Bis study area includes numerous swash-built beach ridges, many of which are covered locally by dunes. Be trenched several dunes and under lying ridges, studied the bedding, and eollected numerous samples. Granulometric analysis produced the same results as his cross-bedding study. He was able to state, with great precision, which part of each trench wall represented swash work, and which was eelian. The critical parts of his work were trenching and granulometric analysis. Chaki (1974) studied swash-built, wind-modified, beach ridges on Cape Canaveral (Florida, U.S.A.), trenching to 30-50 em for samples. She showed that it is relatively easy to get beach-type sand samples. Various other publications (e.g., Johnson, 1919) which identify the Cape Canaveral ridges as dunes, were based on surface inspection only, with no trenching and no granulometric work. Certain famous beach rid&e plains (the Darss; Cape Canaveral) are not as easy to study as some less-well known ones (e.g., Tversted and Jerup systems, Denmark). This is largely because of extensive dune decoration and eolian reworking which modifies the surfaces of many swash-built ridges. However, preliminary results from the Darss, reported here, indicate once more that dunedecoration is not an insuperable problem, although it makes sample cOllecting difficult. Conclusions Many people have identified ridges on the Darss (German Baltic coast) as wind-built dunes. A previous worker who dug trenches (Ul'st 1957), reported fair-weather beach-type cross-bedding; but this finding has been largely ignored or rejected. Sand samples, from trenches on the Darss, show clearly that the underlying ridges were built under !air-weather conditions by low-to-maderate-energy swash, plus settling from water. This is in agreement with the findings of Ul'st. The present conclusion, based on granulometric parameters of sand samples taken from trenches, is strongly supported by the facts that the suite of 16 samples shows many examples of the "sur! break" on probability plots, not a single example of the "eolian hump." Each one of these kinks is fully diagnostic. It is clear that extrapolalion of wind work, from surface dunes, downward into underlying beach ridges, was a mistake. The critical information is ob-Lecture Notes 91 James H. Bs/sillie

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W. F. Tanner --Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 Coastal Research October 1994, Page 5 ta.ined by trenching. The ridges were built by fairweather low-to-moderate swash, in combination with settling from water. Eolian decoration was added at a later date. Acknowledgement Appreciation hereby expressed to Dr. Harald Elsner, who carried out the reconnaissance on which this report is based. References Chaki, Susan J., 1974 A sedimentary investigation of the beach ridge sets com p_osing Cape Canaveral, Florida. Unpublished M .S. thesis, Florida State University, Tallahassee, Fla.; 95 p. Fukarek, Franz, 1961. Die Vegetation des Darss und ihre Geschichte. Gustav Fischer Verlag, Jena; 303 p. Gierloff-Emden, H.G., 1985. East Germany. Pp. 315-320 in: The world's coastline. E .C.F.Bird and M.Schwartz, ed.; Van Nostrand Reinhold Co., New York; 1071 p. Johnson, D.W., 1919, reprinted 1938. Shore processes and shoreline development. John Wiley, New York; 584 p. Kolp, Otto, 1982. Entwicklung und Chronologie des Vor-and Neudarsses. Petermann's Geographische Mitteilungen, Gotha; vol. 126 p. 85-94. Lobeck, A.L., 1939. Geomorphology. McGraw-Hill, New York; 731 p. Rizk, F., 1991. The Late Holocene development of St. Joseph Spit. Ph.D. dissertation, Florida State University, Tallahassee; 378 p. Unpublished Schiitze, Hans, 1939. Morphologischer Beitrag zur Entstehung des Darss and Zingst. Geologie der Meere und Binnenwasser, Berlin; v. 3, p. 173-200. Tanner, W.F., 1966. vol. 7, p. 203-210. The surf ''break.,: key to paleogeography? Sedimentology, Tanner, W.F., 1991. Suite statistics: The hydrodynamic evolution of the sediment pool. Pp. 225-236 in: Principles, methods and application of particle size analysis; J.P.M.Syvitski, ed.; Cambridge Univ., Press, Cambridge; 368 p. Tanner, W.F., 1991. Application of .. suite statistics to stratigraphy and sealevel changes. Pp. 283-292 in: Principles, methods and application of particle size analysis; J.P.M.Syvitski, ed.; Cambridge Univ. Press, Cambridge; 368 p. Tanner, W.F 1992. 3000 of sea level change. Bull. Amer. Meteorological Society, vol. 73, p. 297-303. Tanner, W.F., 1992. Detailed Holocene sea level curve, Northern Denmark. Pp. 748-759 in: Proc. Internat. Coastal Congress ICC-Kiel '92; H. Sterr, J. Hofstede and H.-P. Plag, editors; Peter Lang, Frankfurt a.m.; 808 p. Lecture Notes 92 James H. Balsillie

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W. F. Tanner-Environ. Clastic Granu/ometryFGS Course, Feb-Mar, 1995 Page 6, October 1994 Coastal Research Tanner, W.F., 1993. An 8000-year record of sea-level change from grain-size parameters: data from beach ridges in Denmark. The Holocene, vol. 3, p. 220-231. Tanner, W.F., 1993. Louisiana cheniers: Settling from high water. Trans. Gulf Coast Assoc. of Geological Societies, vol. 43, pp. 391-397. Tanner, W .. F., and S. Demirpolat, 1988. New beach ridge type: Severely limited fetch, very shallow Trans. Gulf Coast Assoc. of Geological Societies, val. 38 p. 367-373. .Ul'st, V.G., 1957. Morphology and developmental history of the region of marine accumulation at the head of Riga Bay. (In Russian). Aka d. Nauk., Latvian SSR, Riga, Latvia; 179 p. Zenkovich, V.P., 1967. Processes of coastal development. Inte.rscience Publishers {Wiley); New York; 738 p. Table I Means, standard deviations and relative dispersions (16 samples; phi measure ex-cept where n9ted): Mean Diameter 2.148 0.088 0.041 (0.226 mm) Std.Deviation 0.311 0.044 0.142 Skewness (3rcU 1.343 0.690 0.514 Kurtosis (4th) 12.989 4.929 0.379 5th Moment Measure 91.331 45.045 0.493 6th Monent Measure 845.479 425.515 0.503 Tail of Fines 0.0021 0.0022 1.050 The third column shows (small numbers) that the mean and standard deviation are the least variable of these parameters, and the kurtosis is next best, but all six of the moment measures are reliable cOo. Lecture Notes 93 James H Balsillie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 NOTES Lecture Notes 94 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Appendix VI Tanner, W. F., 1990, Origin of barrier islands on sandy coasts: Transactions of the Gulf Coast Association of Geological Societies, v. 40, p. 819-823. [Reprinted with Pennission} Lecture Notes 95 James H. Balsillie

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W. F. Tanner Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 TANNER 819 ORIGIN OF BARRIER ISLANDS ON SANDY COASTS William F Tanner1 ABSTRACT Most theories on the origin of sandy barrier islands are statements that they migrated to the positions where they are now obsaved These theories do not explain origins, but only displacements Many sand barriers were clearly not the product of displacement, hence we need a explanation for birth in siru Theories based on drowning do not apply to many sandy barriers A small sea level drop (e g a few feet) would be ample to convert a suitable shoal to a stable sub aerial island If there were an abundant nearby supply of sand this island nucleus would then expand in area Several such small sea level drops are now known from nUddleto-late Holocene time Many sandy banier islands in the srudy areas date from shortly after lhe mean sea level higb at 2,500 2 800 B P A few are earlier chan 3,000 B .P., a few are lattr than 1 ,SOO. But island nuclei are relatively common o n wide barriers that f o rmed more recently than 3 000 B P BACKGROUND How do sandy barrier islands fortn in settings where such islands did not exist previously? Many authors have offered hypotheses. King (1972) provided a sUDlJJl8iy, including the following items : 1 de Beaumont ( 184S). Build-up by landward movement of offshore matter. 2. Gilben ( 1890}. Build-up by spit growth, then later seg mentation 3 Hoyt and Henry (1967). Mass migration in a shore-paral lel direction. 4 Leontyev and Nikiforov (1966). Venical accretion on submarine bars. S Hoyt (1967}. Drowning of mainland dunes 6. Fisher (1968) Modification of pre-existing spits. 7 Otvos (J 970), Upward growth of offshore shoals 8 Shepard ( 1963) Slowing rate of sea level rise. 9 W P. Dillon (1970) Landward migration of a pre-existing island. In this list. Nos 2 3 6 and 9 undertake to explain how an island came to be located at a specific map position as a result of la!erallranSlation of some kind. but do not explain how an island can be initiated at a stared position in the tint place Nos. 4 and 7 are almost tbe same the primary difference being the choice of pre-island seometry (whether a bar or a aboal). The remaining items are: 1 Landward movement of offshore material. 4, 7 Vertical build-up, in place, by offshore material. S. Drowning of mainland dunes. 8 Slowing of the rate of sea-level rise No 8 is a statement that when sea level rise slows down, barrier islands are then builL But this provides very little, if any, explanation of what happens. In No. 1 there is no explana-1 Repms Profeuor Geology Dep.nment. Florida State University Tallahueee Fla. 32306 U S.A. Lecture Notes 96 tion of how it is that the migrating sediment become s concentrated at one locality, if not immediately adjacent to a pre-exist ing beach thus fonning a new isl and. And Nos 4 and 7 are not concerned with the problem of converting a sub-aqueous sedi ment mass into a sub-aerial island, a process which certainly has not been conspicuous in fonning islands in the last few centuries Finally No S includes the hypothesis of drowning, in order to provide for a significant amount of water landward of the new island. and to penn it the pre-existing sediment body to protrude above that water surface, but it does not appear to apply to very many sandy barrier islands. Fisher (1982) reviewed the problem, and mentioned along with some of the others cited above the following : 1 0 Menill (1890) Raising the sea floor to convert a bar to an island 11. McGee (1890) Drowning of mainland coastal ridges No 10 is epeirogenetic but could be :replaced by a sea level drop. No. 11 is a clear statement of the idea popularized later by Hoyt (1967) Evans (1942), along with many others, felt that no submerged bar or shoal could be built above water level because in due time a depth is reached at which wave action would keep the shoal (or bar} surface scoured clean, and there would be no funher upward growth. He was probably right. provided water level did not ever change significantly. In writing his sunun.ary, FJ.sher (1982} opced for multiple hypotheses and included a table giving 10 choices. This table lisu major proponent, geographic region of occurence, sediment source and primary mechanism. Under the heading "Primary Mechanism, Fisher used, at six places, words such as emergence su6mcrgence and transgression (that is, drown ing) It is hard to see bow sea level rise (drowning} can create an island, except by submerging-incompletelya pre-exist ing feature This eoncept may well have become popular James H. Ba/sillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 820 TRANSACI10NS-GULF COAST ASSOCIATION OF GEOLOGICAL SOCIETIES VOLUME XL. 1990 because island initiation has generally been assumed to. have taken place during, or at the end of, Holocene sea level rise. That is, the facts show that a rise took place, so the hypothesis must be correct. This simplistic view contains at least one major problem: sandy barrier islands are rarely built around some earlier feature which was then partly drowned. There are, at various places around the Gulf of Mexico, barrier islands the origin of which cannot be explained by any of the above hypotheses. These islands were initiated in some other way, although there is no doubt that, once they were created; many of them were augmented by material from offshore. It is the pwpose of the present paper to note certain barrier island feature.s which require a different mechanism. Energy Constraints A very narrow barrier island (less than about 500ft wide) may be subjected to sufficient overwash and wind work that it migrates actively shoreward, narrowing the lagoon behind it. Barring a major change in sea level, such an island should in due time reach the mainland beach. where it will cease to exist as an island. If the island is too wide to be migrating, it may undergo erosion on the seaward side, thus growing narrower with time. The initial rate of narrowing and the rate of migration. later, should depend on the coastal wave-energy level, provided the grain size is essentially uniform from one example to another. Therefore we should expect such a history to unfold more rapidly along high energy coasts (such as the Atlantic and Pacific shores of the U.S.) than alorig low-to-moderate energy coasts (such as around the Gulf of Mexico). At a given date, it is more likely that island migration will have destroyed all pans of its original geometry, in a high energy setting, hence one is more likely to find clues to the original island position and character in a low energy setting. Papers such as by Dillon (listed above}, iUusb'ate this commenL Many of the existing hypotheses come from high energy coasts, which are not the best places to loo.k. We therefore tum to regions of lower wave energy. Good examples should be found around the Gulf of Mexico, where low sandy shores and moderate wave energy levels are common. Island Nudei Many banier islands on the coasts of the Gulf of Mexico contain one or more nuclei; island growth bas taken place more-or-less seaward from these nuclei, which are the oldest parts of the islands. The nuclei were, at one time, separate islands; the oldest beach ridges typically "wrap around" them on two or three sides, showing that they were not remnants of spits or other earlier larger features. The grew bigger with time because of a local "equilibrium of abundance" of sand. rather than a regime of erosion. Lecture Notes 97 The younger "growth" areas are commonly marked by sequences, or sets, of beach ridges; such features are not visible in the nuclei. The question of the origin of many banier islands on sandy coasts must be closely related to the question of lbe origin of the nuclei. But the nuclei appear to have no distin guishing marks that in themselves might help explain their origin. They are small (compared with present typical island size), more-or-less oval, arranged in chains having spacings of a mile or more, and occur typically one or a few miles from the mainland shore A dune origin is hard to visualize. Certainly modem coastal dunes in the area do not have appropriate geometry Felix Rizk, who has been studying coastal sediments in the Florida Panhandle for about seven years, has had a keen inter est in island nuclei, and has sampled several of them in detail. Some of his data, kindly made available prior to his own publication, include granulometric and other work on sands from two such nuclei, with l 0 or more samples from each one. The mean size is 0.24 mm for the one, and 0.22 mm for the other. These are typical values for his study area. and reflect a general coarsening trend, in one direction, which be found in aU of his other samples The means of the standard deviations are 0.382 and 0 .378, respectively, which are typical of beaches in this pan of tbe world, where values commonly fall in the range 0.28-0.SO. These values are a bit larger, numerically, than the sands (0.35) in the beach ridges which are adjacent to, but younger than, tbe nuclei. In an evolutionary scheme, with only a single dominant transport agency (beach-and-nearshore wave action, in this cue). the adjacent beach ridges should indeed have slightly better sorting. Hence it appears that the nuclei amd the subse quent ridges fit into a single historical sequence. The skewness values for the two nuclei are -0.195 and -0.0392. These nmnbers are typical of beach or river sands, but are not close to representing dune or settling The suggestion of a drowned dune is not supported at aU. The of a river deposit must be set uidc, for several reasons, the numerically low standard deviation and the very small tail of fines being only two. The kurtosis values are 4.129 and 4.564. These indic:ar.e moderate wave energy levels (Tanner 1990), much like what can be seen in the area today. Skewness is more negative in the nuclei, less negative in the younger beach ridges, and kurtosis is the same in both cases. The changes in standard deviation and kurtosis. quoted here from the work of Rizk. are specifical ly indicative of maturing of beach sands over a period of time. Therefore the granulomeuy indicates that the nuclei were fanned in the same way as tbe beach ridges, by swuh action. In other words, even within the nuclei, the evidence is for wave -work. Yet it must be remembered that these nuclei, prior to lbe addition of younger beach ridges on two or three sides, were small isolated sand bodies a few miles offshore from lhe mainland. And the parts were not dunes. James H. Balsil/ie

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W. F. Tanner-Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 TANNER The landward sides of some of the nuclei have been cliffed by lagoon waves. The material exposed in this fashion has not, as yet, produced any evidence for dune growth A single modem barrier island may have zero to four (or more?) recognizable nuclei Barriers that arc very narrow (perhaps less than about 500ft wide) do not show any nuclei and apparently do not have room fw because it is migrating landward, nuclei on this island should have been destroyed long ago These nuclei appear to date largely from about 1,000-2,000 B P Such nuclei have not been recognized at many places, or have not been preserved for easy inspection, on islands that date back to about 3,000-3,500 B.P. This may be because the appropriate parts of these older barrier islands are now drowned (but drowning did not initiate these islands; it took place after they were already in position) Exceptions Many barrier islands do not have recognizable nuclei. There are several reasons for this (1) Some are very narrow (<500 ft.), and are migrating land -ward by a "roll-over" process ; the earliest pans have been destroyed already (such as parts of St George Island, Fla.; Schade, 1985). (2) Some are being eroded severely on the lagoon side, and the oldest parts have been lost (3) Some were initiated more than 3,000 years ago, when sea level was five to 10 feet lower than at present, and subsequent rises have pennitted either total drowning or burial by younger sand. (4) Some were created on the "annual tide tidal flat (Tonner and HununcJJ, 1989) where the water level rises and falls five to 10 feet almost every year. There probably are other reasons also. Each exception must be considered in the light of its age, location and prevailing conditions. After exceptions .of these kinds have been removed from the list tbe incidence of nuclei is still high Moving Shoal Johnson Shoal (Lee County, on the lower west coast of the Florida peninsula) may provide some insight into the origin of nuclei. The shoal appeared for the first time on maps and charts in 1863 in water 10-20 ft deep, and has been migrating landward (eastward) ever since. Seven maps and charts from various dates and many sets of black-and-white aerial photo graphs have been used to produce a history of shoal migration By December 1988 welding of large parts of the shoal onto the shore of Cayo Costa island was already under way (Tanner 1989). The migrating shoal contained more than 13 million cubic yards of sand (more than l 0 million cubic meters, with a mass of 10 trillion Kg). Known nuclei on other islands are common ly about this size 821 Part of the shoal surface has been awash in many of the aerial photographs, starting in 1944. The outline of the exposed pan has been, in general V-shaped, with the apex of the V pointing seaward. The moving shoal did not develop from dredge spoil (there has been no dredging of this magnitude in the area), a spit, a drowned dune or a fault: the water in the area was meters deep before the shoal first appeared. The initiation must have been a natural non-tectonic event: Emergence of a shoal since 1863 without notable changes in sea level or wave climate. Perhaps such events were more conunon at some moment in Late Holocene time, and account for barrier island nuclei. This statement raises two in t eresting questions : ( 1) How could such a shoal be converted into an island nucleus? And (2) How come conditions were better suited, for such events say 2,000 years ago, than they arc today? Hypothesis A small sea level drop (about 5 feet) would be enough to conven such a shoal into a small island, which would then show no distinctive markings untillarer growth added beach ridges and/or dunes. Small drops, like this in middle-to-late Holocene time, are now known (Tanner et al1989). Johnson Shoal is being welded against a pre-existing shoreline, and will not form a island This is because there bas been no suitable sea level drop in the last 130 years The central idea here is that a shoal can emerge and become an island by means of modest water level changes. Such a change in water level may be small and perbaps short-lived. as during a storm, or may last for a longer period of time In the Gulf of Mexico area, sea level dropped three feet or more at least twice in middle-to-late Holocene time: once at roughly 4,000 B.P and a second time about 2,000 B.P. Many barrier islands may have been initiated at one or the other of these times, with obvious growth histories well under way a century, or a few centuries, later The oldest known barrier islands along tbe Gulf of Mexico coast of Florida were initiated about 3,500 B.P.; two examples are SL Vmcent Island, southwest of Tallahassee (Stapor and Tanner, 1977), and Sanibel Island, southwest of Ft. Myers (Stapor et al 1988). Several other islands apparently date from about 2,000 B P ., or a bit later. A third category of islands is not represented by dated materials that define the time of initia tion, but this fact cannot be used to infer a time of nucleus-building other than the two stated in this paragraph. A fourth category includes a few examples which were initiated about 1 000 B.P.; two examples are Mesa del Gavilan and Brazos Island, east of Brownsville and south ofPon Isabel, Texas (Tanner & Hummell 1989). (1970) produced an islands from shoals" hypothe sis He stated in his abstract that .. Historical evidence and drilling results ... indicate that banier islands form by upward Lecture Notes 98 James H Balsillie

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W. F. Tanner -Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 822 TRANSACI'IONs-GULF COAST ASSOCIATION OF GEOLOGICAL SOCIETIES VOLUMEXL, 1990 aggradation of submerged shoal areas." In his text (p. 243) he stated that "Several ... examples ... took place during historic times." But in the following sentence he explained that this occurred by island migration ("Barrier islands . grew west ward by building shoals up ... while the opposite ends were reduced by erosion ... (p. 243). In contrast, the hypothesis stated in the present paper is that isolated shoals during a certain and specific sequence of events can tum out to be above water level, hence become islands. This is visualized without any effects from any adja cent island. spit or mainland. The necessary event is a small sea level drop, perhaps in the waning stages of a major stonn, but more likely over a longer period of time. The island fonns in place. If there is an abundance of sand. it may grow larger with time. After it has grown larger, the original nucleus may be preserved, on the lagoon side, as a more-or-less featureless sand mass. Along low-to-moderite energy coasts it stands a reasonably good chance of being preserved for a while. The present hypothesis may explain the origin of many coastal island nuclei, which fanned offshore without any help from dredge spoil, drowned dunes, growing spits, faulting, warping, or other such popular explanations. Once such a nucleus has been formed. there will be no problem in enlarging it, if there is a local excess of sand ("equilibrium of abundance"). Gulf of Mexico I:..,.., \J.1 0 drop in 1944 ha11e created an Island here ...,. .. J CAYO COSTA ISLAND z 8 C> I :3 of trees, 1944 \ Edge of trees, 1860 BlOCh IKM Older Beach Ridges Figure 2. The aortbem end ot Cayo Costa (lllaad), oa the lower west coat or the Florida pnlnsula, mel Jobaloa SboaJ to tbe west. The shoal was bat DOt emerpat, oo tbe IUUitical daart of 1863. Positlo of the emeJ'Ieat shoal, 11unm for 1944, 1951 and 1988, were taken 11om black-ud-wldte vertkal aerial pbotographl.lll this cae, wttbout a suitable .. level drop, tbe lboal II beiDa welded oato tbe older illaDd. A .. level drop of three to five feet, betRaD 1865 ud D40, would bave coavertecl tbe mo.J IDio u Island audeus. 3 years FJaure 3. Sea level bistory for the GuJt or Muico, IDOdJt'lecl from Taoaer et al (1989) by iDdudJaa more fA tbe dlaqa sbOWD In the prtat-out aaderlytaa their fta. 4-B thaD Ia tbetr mmm1ry (tbdr fl&. 8). Tile dalbed I1Da in tbe praeat ftaure huticate tbe adcled detaiL ACCGI'dlaa to this represeatadoo of tile origfDal data, alae formatlon of lllaDd oudel sbo1lld ban beeD coaftlltrated around 1,100 B.P., pollibly aroaad 2,5t0 B.P. or 1,210 B.P. Lecture Notes 99 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 TANNER CONCLUSIONS The bypotbesis stated here is that a small drop in sea level (e .g., three to five ft.) can conven a shallow but non-emergent shoal into a small island. which can be built up to a more stable geometry by swash action. Data now available show tbat sea level drops of about this magnitude have taken place several times during the late Holocene. It is also possible that such a drop could have taken place in the waning stages of a major storm, an event that might have been especially imponant if a given shoal had been built upward somewhat during the high-water stage of that stonn. A small island of sand, created by a small sea level drop, in an area of an abundance of sand, should then grow by addition of beach ridges (or other deposits) on sides. The original island is here tenned an island nucleus Sandy island nuclei have been found in many of those Gulf of Mexico coastal barrier islands which were initiated some 2,000 years ago at ( or not long after) a sea level drop of three to eight feet. In the study areas, very few barrier islands were formed at any other time except prior to 3,000 B .P. during an interVal for which we now have very few details. REFERENCES CITED Dillon W P., 1970. Submergence effects on Rhode Island barrier and lagoon and inferences on migration of barriers. Journal Geology vol. 78 p 94-106. Elie de Beaumont, L.E., 1845. de Geologie pratique. Levees de sables et galets. Paris. Evans, 0. F., 1942. The origin of spits bars and related struc tures. Journal Geology, vol. 50 p. 846-863 Fisher, John J. 1968. Barrier island formation : Discussion GcoJ. Soc of America Bull. vol 79, p 1421-1426. Fisher John J., 1982. Banier islands. Pp 124-133 in: Encyclo pedia of Beaches and Coastal Environments M L Schwanz, ed.; Hutchinson Ross Publishing Co. Strouds burg Penn.; 940 p. Oilben, G K., 1890. LalceBormeville U.S. Geological Survey Monograph 1. Hoyt, J H., 1967. Banier island formation. Bulletin G.S.A., vol. 78 p. 1427-1432 Hoyt, J H ., and V. J Hemy, 1967.1nfluence of island migra tion on barrier island sedimentation. Bulletin G S.A., vol 78 p. 77-86 823 King C.A.M., 1972. Beaches and Coasts (2nd ed .). St Mar tin's Press, New York; 567 p Leontyev, 0 K, and Nikiforov, L. G 1966. Reasons for the world-wide occurrence of barrier beaches. Oceanology, vol. 5 p 61-67 McGee, W J 1890. Encroachment of the sea. Forum v. 9 p 437-449 . Merrill FJ.H., 1890. Barrier beaches of the Atlantic coast. Popular Science Monthly v 37.p. 744 Otvos, E G 1970. Development and migration of barrier islands northern Gulf of Mexico Bulletin G S A ., vol. 81 p 241-246. Schade, Carlton. 1985. Late Holocene sedimentology of St. George Island Unpublished M.S. thesis, Florida State Univ ., Tallahassee; 194 p. Shepard, F. P., 1963. Submarine Geology {2nd ed.) Harper & Row New York; 557 p Stapor F W., T.D. Mathews and F.E. Lindfors-Keams 1988. Episodic barrier island growth in southwest Florida : A re sponse to fluctuating Holocene sea level? M iami (Fla ) Geo logical Society Memoir 3, p 149-202 Stapor, F. W., and W. F. Tanner, 1977. Late Holocene mean sea level data from St Vmcent Island and the shape of the late Holocene mean sea level curve Pp. 35-68 in: Coastal Sedi mentology, Proceedings 3rd Symposium on Coastal Sedi mentology, W F Tanner ed.; Geology Deparunent, Florida State Univ., Tallahassee; 315 p Tanner, W F ., 1989. Johnson Shoal : Clues to beach ridge plain origin and history. Pp. 97-106 in: Coastal Sediment Mobil ity, Proceedings 8th Symposium on Coastal Sedimentology, W F Tanner, ed.; Geology Depanment, Florida State Univ., Tallahassee, Fla.; 294 p. 'Iinner, W F., 1990. The relationship between kurtosis and wave 9th Symposium on Coastal Sedimentology; W F Tanner, ed. ; Geology Department, Florida State Univers i ty; in press Tanner, W .F. S Demirpolat, F.W. Stapor andL Alvarez, 1989. The "Gulf of Mexico late Holocene sea level curve Transactions, Gulf Coast Association of Geological Societies, vol. 39 p 5.53-562. Tanner, W. F., aDd R Hummell, 1989. The annual-tide tidal flat near Boca Chica, Texas. Transactions Gulf Coast Associ ation of Geological Societies, vol. 39 p 590. Lecture Notes 100 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar 1995 Appendix VII Tanner, W. F., 1991, Suite statistics: The hydrodynamic evolution of the sediment pool: [In] Principles, Methods and Application of Particle Size Analysis, (J. P. M. Syvitski, ed.), Cambridge University Press, Cambridge, p. 225-236. [Reprinted with Pennission] Lecture Notes 101 James H Balsillie

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W F. Tanner-Environ. Clastic Granu/ometry-FGS Course, Feb-Mar, 1995 16 Suite statistics: The hydrodynamic evolution of the sediment pool WIILIAMF. TANNER Introduction For a century or so the purpose of making grain size measurements was to determine the diameter of a representative particle. This useful when one is studying reduction in grain size along a river (e g Sternberg, 1875) But it is a simplistic approach, and one is entitled to ask: -Is the mean diameter the only information that we wish to get? Or does the simplicity of this first step make us think that we have now described the sand pool? When we measure grain size, what do we really want to know? This does not refer to whether we measure the long axis or the short axis of a nonspherical particle, or whether we approximate the diameter by measuring a surro gate (such as fall velocity) Rather, we ask this question in order to get a glimpse of how far research has come in understanding transport agencies or conditions of deposition, and of the degree to which we might reasonably expect to improve our methods of environmental discrim ination. Can a set of parameters that describe a size spectrum for one sample permit us to compare this sample with some other, perhaps from a different transport or depositional environment? A positive response implies that a single sample may be adequate to describe the parent sand body. Do we want to know about variability within the sand body, thereby requiring a suite of samples? This might suggest that there is only one kind of variability (hence a single parameter will do), or it might mean that we will have to explore many kinds of variability Do we wish to see if there is more than one sand pool contributing to the sediment body? "Sand pool" needs an improved definition but presently includes : (a) material presently being added (but not necessarily depos i ted) at the site; (b) material located upstream" of the site and in transport toward it; and (c) material already present. This concept is more easily applied to river sands than to a wide, shallow near-shore depo sitional area. Do we wish to identify any characteristics of the transporting agency? Moving from "sim ple diameter of one sample" to "transport agen cy" is a big step, and it cannot be done by using simple theory If we are going to undertake to answer questions such as these, we must make determinations beyond simply specifying a rep resentative diameter." A good deal of work has been undertaken on trying t o answer such questions much of it at Florida State U niversity Many environment s have so far been sampled, with thousands of samples The basic environmental identitie s have been as follows : dune, mature beach, river, tidal flat, settling (or closed basin: lake, lagoon, estuary interior seaway, etc.), offshore wave, and glaciofluvial. Not all have been treated equally; for instance, glaciofluvial materials and offshore wave sediments are poorly represent ed. Both modem and ancient environments have been studied and sampled in the field Most of the terms used here are familiar ones, such as mean and standard deviation (but as calculated numerically with the method of moments ); two, however, require a note of c au tion (Hoel, 1954; Blatt, Middleton & Murray 1980) "Skewness" and "kurtosis" refer to some form of the third -and fourth-moment measure s, respectively. The actual words have been taken, i n part of the literature, to identify specific geometric features of a plot of the distribution ; this is not the intent here. For present purposes, skewness and kurtosis are convenient labels for certain moment -not graphic -parameters. They do not require, but may correlate with, a specific curve shape An additional point should be made regarding skewness This term is used to mean (in general) an asymmetry of the distri bution Positive and negative skewness cannot be defmed from a priori considerations. But Folk (1974, p 52) and Blatt et al. (1980, p 46) used upositive skewness" to identify a sample Lecture Notes 102 James H Balsi/lie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 William F. Tanner with many classes in the fine tail, and this usage has been followed here. Phi measure has been used throughout, unless indicated otherwise. Control factors Air versus water The mass density of a singie grain in air is quite different from that in water. The practical effect is that realistic local variations of air ve locity, by a stated amount, are more important in moving a specified grain (such as quanz sand) than are the same variations in water ve locity A unidirectional flow of water typically transports a greater range of grain sizes (provided that they are available) than does a unidirec tional flow of air. The standard deviation of the grain size tends to be numerically larger in uni directional water transport than in unidirectional air movement One cannot take a simple state ment of the standard deviation of a single sample and translate that number to "transport agency" because some of the other influences mentioned here complicate the system too much. On the other hand, with suitable treatment, the standard deviation can be the basis for a powerful tool for discriminating among certain environments. One should note that in_ a few instances (e .g on a beach), back-and-forth motions over a long period result in much better sorting than can be obtained in ordinary water or air currents. 226 any kind of dead-end setting: a category that can be identified as the closed basin (perhaps even an interior or geosynclinal seaway). Settling may be the main hydrodynamic process. A sim ple example is the site where a high-energy, fine-sand-laden river flows into a coastal zone having very low wave-energy density. A large supply gives roughly the same results as a closed basin: probable dominance of the finer sizes, up to the limits of availability Winnow ing, on the other hand, tends to reduce the proportion of fmes, as is well known Back-and1orth shuffling (BAFS) and net unidirectional sediment transport (NUST) The basic concepts of back-and-forth shuf fling (BAFS) and net unidirectional sediment transport (NUST) lead to an unexpected obser vation confirmed in both field and laboratory. Transport in an ordinary river is clearly char acterized by NUST, and one can observe the result: Sand introduced upriver is carried downstream Under a wave field, however the primary effect is BAFS. There is commonly an asymmetry in transport effectiveness of water motion near the bottom, so the BAFS phenome non leads to movement of grains of the same mineral (two different sizes) in opposite direc tions (see May, 1973). On a low-to-moderate energy beach without a new supply, BAFS may New supply from upstream; through-flow; be so efficient in and near the swash zone that trapping; winntiwing the standard deviation of the grain size may A river carrying a large sand and/or coarse reduced to (or close to) what may be the minisilt load may have an abundant new supply so mum value for quartz: -o.26. This is even low that winnowing cannot be very effective On the er than is found in most dune environments, other hand, a more-or-less isolated sand shoal where the mass density difference between air perched on a wide shallow shelf have no and sand (rather than BAFS) produces very new supply of sand, so winnowing can be very good sorting. important. Through-flow has to do with the ability of a transport system to cany certain sizes more or less continuously (time sense), such as the wash load concept dealing with fine silt sizes in an energetic stream: They are "washed" for long distances rather than resting on the bottom for lengthy time intervals on their way along the channel. Trapping clearly can take place in ponds, lakes, and lagoons, but likewise is important in Multistory (multitierlmultilevel) turbulence structure A single grain of quartz sand, settling in water, generates an eddy system with dimen sions controlled largely by the size of the sand grain (Tanner, 1983) Eddies of a different scale may be formed adjacent to bedforms such as ripple marks and/or giant ripple marks. Sand bars and sandbanks are typically responsible for a third scale, and river bends create turbulence Lecture Notes 103 James H. Balsillie

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W. F. Tanner Environ. Clastic Granu/ometry -FGS Course, Feb-Mar, 1995 Suite statistics: Evolution of the sediment pool 227 at a fourth level. It is not known how many sto ries may exist, but the number could reach six or more In certain environments, the structure generally has only one or two levels. The turbu lence structure is much more complicated (of higher numerical order) in a large, energetic riv er than on a low-energy beach. The standard deviation of the grain size distribution tends to be numerically smaller as the number of stories decreases (within the limits of availability). A high-order system (many stories) typically pro duces greater mixing of sizes at any one locality (if such sizes are available) sample; cutting across many adjacent laminae); 2 lab procedure (using whole-or half-phi screens instead of quarter-phi sieves; making more than one split, thus escalating the splitting error, using too short a sieving time; putting too large or too small a sample on the coarsest screen; and so on); 3. graphic or other low-precision parame ters (e.g., the sorting coefficient instead of the standard deviation); 4. overlimited options (e g beach versus river, as if dunes and other settings can be ig nored) In Friedman & Sanders (1978, p. 78) Grain-grain interactions beach samples are compared with river samples Because the eddy system generated by a by plotting "simple skewness measure" against single grain may occupy a volume orders of "sorting measure" (their terms for graphic mea magnitude larger than the grain itself, interacsures). The dividing line that was drawn be rions between grains may be frequent and imtween the two number fields is far from straight, portant (Tanner, 1983). These include trapping, does not emphasize anything like a natural divi tailgating, and ejection, and involve the motion sion, and for some twenty-seven samples gives of one grain fairly close to another, perhaps of the wrong answer. Use of moment" measures dissimilar size; the two may then be deposited (p. 81) produces an improvement (perhaps together. The result is a significant numerical innineteen misidentifications), butthe dividing line crease in the standard deviation with is still complex, many samples of both types what would have been obtained had there been cluster on or near it, and the number field for no such interactions. beaches is centered within that for rivers. One Transport directionality Unlike BAFS (under one wave train) this has to do with differences arising from varying wave approach angles and the mixing of two (or more) sand pools that may result. Such mix ing tends to increase the standard deviation nu merically, and generally modifies other parame ters as well Bivariate plots Sedimentologists have long tried td make environmental sense out of bivariate plots of pa rameters that describe a sample size spectrum. The investigator selects two parameters (such as mean size and standard deviation), and plots them against each other. There are many ples in the literature (see, e.g., Friedman & Sanders [1978, pp. 78-81], where skewness is plotted against sorting) The results have been less than enchanting, for several reasons (Socci & Tanner, 1980): 1. sampling technique (taking too large a understands why many workers have given up on the procedure However, the basis for this kind of diagram is hydrodynamic (BAFS for beaches vs. NUST for rivers); it lacks only a small modification to become a valuable tool An obvious way to improve the graph is to define sample suites, by field or subsurface study, and plot only suite-mean values for each parameter. This greatly reduces the scatter, min imizes (perhaps eliminates) overlap and pin points the center of gravity of the measurements for any one suite. Aberrant or anomalous val ues, still available to the investigator, no longer appear as clutter Ideally a suite contains perhaps flfty or more samples, but this is commonly impracti. cal. Experience has shown that, for sand and C
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W. F. TannerEnviron. Clastic Granulometry -FGS Course, Feb-Mar, 1995 William F. Tanner )J 0 .001 0 .01 0 1 cr o.J Figure 161. The tail-of-fines diagram. The means and standard deviations of the weight percents on 'ihe 4 screen and finer are shown here. Four fairly distinct number fields. appear, as labeled above, with relatively little overlap Many suites plot neatly in a single field. In certain other cases the apparent ambiguity mJy be useful; for example, a point at a mean of 0 .01 and a standard deviation of 0.017 might indicate either dune or mature beach, and not formed in a closed basin This diagram commonly gives a "river" position when in fact the river was the "last;. previous" agency. but not the final one. 228 Figure 16.2. The variability diagram, showing the suite standard deviation of the sample means and of the sample standard deviations. Except for the extremes, the plotted position indicates two possi ble agencies (such as swash or dune). The decision between these two can be made, in most instances, by consulting other plots (such as Fig 16.1). This diagram considers specifically the variability, within the suite, from one sample to the others. This diagram has four reasonably distinct number fields : mature beach, dune, river, and closed basin (settling). The tail-of-fmes plot works well because it depends on hydrodynamic factors: 1. The number field* is smaller. The suite mean tends to separate "large new 2. Anomalous points (although still pressupply" (river or closed basin) from winnowing ent). do not clutter the plot (beach and dune), and the suite standard devia3. Distinctions between transport agencies tion tends to separate BAFS (mature beach and are more obvious. near-shore) and "large mass-density difference" 4. Transition suites or mixtures may be (dune) from settling and poor winnowing. Fur easy to identify thermore, mature dunes (large mass-density dif-5 or more sedimentary environference) are generally readily distinguished from ments may be represented conveniently on one mature beaches (BAFS) because the number of graph. transport events per year on the beach may be Doeglas (1946) observed that the tails of lOS or 106Iarger than in a dune fieldthe distribution provide much of the important A plot (not shown here) of standard devi information that is available to us; so we are ation (S.D.) versus kurtosis K is commonly less likely to be able to make fine distinctions useful because a river, dune, or beach suite may by using the mean (surrogate for the first moappear within a small distinctive area, whereas ment) than by using higher moments (such as tidal flat or other settling suites may plot in a the third and fourth). Therefore, we can conlong narrow band showing a very closely con struct one or more bivariate plots of tail data, trolled relationship between the two parameters using weight percents in the fine tail (material (form: InK= a exp(-b where a and b on the 4,P screen and finer) For a suite of sam-are numerical values to be determined for any pies, one can plot the mean weight percent of given suite of samples; R2 about the fine tail (4t; and finer) against the standard Thestandarddeviationneednotbe small for this deviation of the same fine-tail data (Fig. 16.1) relationship to hold On one well-studied tidal Editor's note: nus is a numerical matrix of distribution parameters. flat, settling effects produced a straight line of data points (Tanner & Demirpolat, 1988). Lecture Notes 105 James H. Balsillie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Suite statistics: Evolution of the sediment pool 2 2 9 K .6 SK 4 . . -0. 4 -0.2 0 . ..... ........... 0 2 0.4 0 6 r'-I I -----.... ........ I / b Figure 16 3 Skewness vs kurtosis. The suite means of these two parameters are used. Positive skeWness, as used here, identifies a geometrically distinctive fme tail; if there is also a distinctive coarse tail, it is the smaller (weight percent) of the two The closed basin (settling) environment typi cally produces an obvious fine tail, much more so than beach or river sands. Eolian sands commonly have, instead of a well-developed fine tail, a feature called the eolian Jwmp (cf. Fig. 16.5), which the skewness indicates in the same way as it does a distinctive fine tail 1berefore the two tend to plot together. Negative skewness identifies a distinctive coarse tail, either fluvial coarse tail (large K) or surf break" (=kink in the probability plot; Kin the range of 3-S or so) Many river and beach suites appear in the same part of the diagram but are ordinarily easy to identify by using this figure fust and then the tail-of fines diagram (Fig. 16.1). The variability diagram (S.D of means vs. S.D. of standard deviations) typically places any given suite in one or perhaps two categories (e. g., dune or beach). Figure 16.2 identifies variability from sample to sample in a band ranging from "very small variations" (dune) to "very large variations" (high-energy stream), perhaps because it identifies the multistory tur bulence level. Skewness indicates the balance between the two tails. If the coarse tail is well developed and the fine tail small or nonexistent a negative skewness (as defined here) results. H, on the other hand, the fine tail is dominant, skewness is positive Experience to date is that beach sands (surf break on the probabilitY plot) and river sands (coarse fluvial tail) tend to show skewness Sk <0. 1. Settling or closed basin de posits, with a well-developed fmc tail but little or no coarse tail, typically show Sk> 0.1. Ma ture dune sands commonly have the eolian hump SEGMENT ANALYSIS; WT.% FINE TAIL R S E : TAIL Figure 16.4. The segment analysis triangle The procedure for picking segments and obtaining the necessary numbers is outlined in the text. The apex is characterized by very small or negligible distinc tive tails ("no tails"). and the base (not shown) connects distinctive coarse tail (to the right) with distinctive fme tail (to the left). Four different environments are distinguished reasonably clearly, except for one area of overlap; in. this area one ex amines the probability plots for the eolian hump in order to see which of the two is indicated. (a convex-up inflection, coarser than 50%, on the probability plot) Because the skewness pa rameter may see the main part of the sample as a large fine tail, it generally exceeds 0 1 for these sands Therefore skewness can be combined to good advantage with some other parameterperhaps kurtosis, as shown here to make a use ful diagram (Fig. 16.3). The probability curve (see next section) can be divided into three convenient parts: A central segment (straight line) is identified first, and whatever is left over is then assigned to either the coarse tail or the fine tail. The percentages of these three parts can be averaged for the suite, and the resulting point can be plotted on a threedimensional (triangular) "segment analysis" diagram, which separates mature sandy beaches (minimal tails) from rivers and dunes Sand and-gravel rivers are likewise separated from dunes and silt-and-clay rivers because the former tend to have larger coarse tails, and the lat ter, larger fine tails (like settling) Mature dunes can be identified provided the eolian hump is on some of the probability plots (Fig. 16.4). Lecture Notes 106 James H. Balsil/ie

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W. F. Tanner-Environ. Clastic Granu/ometry --FGS Course, Feb-Mar, 1995 W i lliam F Tannu There are four well-studied moment mea sures (mean through kunosis), several parameters derived from one or two tails, higher moments the meaning of which is not always clear, and other numerical values. Taken two or three at a time, these provide the bases for many bi variate plots, which are valuable tools for interpretation of agency and environment 230 Probability plot The grain size distribution may be de scribed by a package of parameters of various kinds (the early goal of achieving this with only one or perhaps two has not been realized) A graph may be used as a complement ; for many size distributions the complicated nature of the data makes a graphic display helpful. On such a graph one normally plots a transform of size Contradictions? (typically phi measure) versus weight, weight In some cases many of the bivariate plots percent or cumulated weight percent. provide the same result -a single environment Histograms and cumulated S-curves fall inof deposition These are the easy cases; but in to this category but suffer from a defect: They many cases things are not that simple either display a slope reversal (which is comusHowever, what might appear to be contra-ing in highly detailed work) or exhibit marked dictory is commonly correct throughout, and curvature In well sorted sediments having few helpful as well, because not all sand masses data points these curves can be drawn in vari were moved by only one transport agency Samous ways without violating the points and thus pies from the inner continental shelf (see Arthur may be works of an rather than tools for study et al., 1986) may give a river or fluvial identifi-The purpose of a plot of a single sample is cation, despite the marine location because a to provide information o r an impression not sand mass delivered by one agency to another readily gotten from the various numerical pamay not lose the granulometric fingerprint of the rameters One therefore seeks a procedure that first until some considerable time has passed. shows neither modal peaks nor artistic curveDune sand may be blown into a river or creek, fitting, and several are available. Well-known and be reworked by ruruiing water. Suite analy examples are the probabili t y plot (Otto 1938; sis of the creek sands might then give a primary Pettijohn, 1975), the Rosin-l a w plot \'crushed dune indication yet also show that there have particle" distribution applicable to milled or been complications. The analyst should not in-ground-up material [Rosin & Rammler, 1934 ; sist on selecting a single agency, but instead be Irani & Callis 1963; Pettijohn, 1975]) and a aware that there may be_ two or more. Analysis method based on the log-exponential concept of beach ridge sands commonly indicates both (Bagnold, 1941 ; Bamdorff-Nielsen, 1977) Any beach and dune origins, since sand beach ridges additional variety can be created simply by not are typically built by both agencies (swash, ing that one must pick one or two transforms A mix of dune and beach indices might for the data (e g the probability plot uses a log be formed in ways, but unless there is transform for size [phi] and the Gaussian transother evidence for dune buildup one should form for cumulated weight percent) The Rosinpick the beach as the preferred site. law plot has not been exploited much : Crushed Wind deposits. filtered down from above, materials follow it, but transported sediments do without any dune migration, have been identi-not The Bagnold procedure has not been popu fied correctly (see Tanner & Demirpolat, 1988) lar, perhaps because the computations required by suite methods as eolian plus settling, al-are time consuming, even on a computer though beach and river components were sugThere are cenain advantages to using the gested (also correctly) by the analysis. probability plot: There are many" kinds of transitions and Several varieties of suitable paper are already mixing, and the different suite parameters proavailable commercially vide different kinds of clues to this -the hydroIt is easy to make. dynamic basis for any one parameter is not nee-Modes and saddles are relatively easy to spot. essarily the same as for the others. Rarely, an Cenain parameters unavailable via ordinary staenvironmental decision cannot be made. tistical techniques can be read directly. Lecture Notes 107 James H. Balsil/ie

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W. F. Tanner-Environ. Clastic Granulometiy --FGS Course, Feb-Mar, 1995 Suite statistics: Evolution of the sediment pool 2 31 w N u; Figure 16.5. Diagrammatic probability plots. (1) The Gaussian, rare among sands. (2) The distinctive eolian bump (E.H.) is common, but not universal, in dune sands, and so far has not been observed in other sands that did not bave any previous eolian history. (3) The surf break (S B ) has been demonsttated to form in lhe :urf zone, as the sorting improves (4) The fluvial tail is geometrically distinctive, but cannot be distin guished in every case from the surf break. (5) This curve bas both a fluvial coarse tail and a fluvial fine tail; the central segment (C.S.) is the line between the two small squares. However, it is not the modal swarm (see text) (6) 1be modal swann (a grain size concept, not a graphic one) obtained by subtraction from the original distribution; it shows the actual size distribution of the central segment (graphic device) of line 5. Lines of these kinds help one visualize the effects summarized in the bivariate plots. Interpretation is fairly easy once the operator is used to its distinctive properties. The main disadvantage (shared with some other methods) is that the learning period may be long The rationale for the probability plot may have been the idea that many (if not most) sands and coarse silts should be essentially Gaussian; therefore, one would quickly learn to distinguish "standard" sediments (straight line on probabili ty paper) from anomalous ones. In fact, very few samples are perfectly Gaussian, but segments of the grain size distribution curve indeed are. Therefore, a better approach might be to study the probability plot in order to identify these particular segments, with an eye to providing an improved interpretation (as long as one remem bers that they are segments of the plot, not com ponents of the population) (Fig. 16 5). Moss (1962-3) identified three common segments on such a plot and designated them by capital letters (A, B, C). Two of these are tails, and one is the central part of the curve. Rather than letters, the present writer prefers descrip tive terms: coarse tail (segment), central segment, andfine tail (segment). The central seg ment commonly {but not in every case) crosses the 50% line, and generally shows numerically smaller (i.e., better) standard deviation (sorting) than the other two. Distinctive kinks, or inflec tions, mark their mutual boundaries (The fine tail [segment] does not have the same definition or use as the tail of fines discussed earlier; here, it is set off by a kink in the curve, rather than by a stated size.) The central segment must be distinguished from the modal swarm, which is a sample com ponent (not segment) having a purely Gaussian form on probability paper. This component can be separated, in most instances, by simple sub traction. When combined with the pertinent tail components, the modal swarm yields the com plete curve, which now shows segments (Tanner, 1983). Components, made of actual grains, are generally not visible on the plot. Segmnts are visible on the plot, but represent the effects of combining two or more components in one sample, and do not show quantities of various sizes actually pieSent in any one component There is a widely used procedure based on the assumption that each straight-line segment on probability paper is also a component that has combined with its neighbors via butt-end joining (e.g., Visher, 1969). Because grain-Lecture Notes 108 James H. Balsillie

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W. F Tanner--Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 William F Tanner grain interactions in water provide results that, in tum, include significant misrepresentation of true grain diameters as part of creation of the perceived size spread, the butt-end-joining con cept is erroneous. On the other hand weighted addition of components, to create a segmented curve, is a better analytical concept than the sim plistic and mistaken idea that segments are also the components. LeRoy (1981) stated one of several objections to the assumption that seg ments (rather than components) represent actual sand grain clusters in transport Bergmann (1982) examined significant set tling effects on perceived grain diameter and Tanner (1983) studied the hydrodynamic pro cesses (capture, tailgating, ejection, and others). Their results show that butt-end joining is not possible but that addition of overlapping com ponents is not only possible but common. The resulting curve is, indeed, made up of two or more segments, but these segments are not the same as the actual components A few grain size curves are almost Gauss ian on probability paper-mostly mature beach or dune sands, where long-term winnowing has been effective without the addition of new sup plies. Other curves show the adjustment from one Gaussian form to another (Stapor & Tan ner, 1975). Most curves have at least two seg ments and many have three, four, or more (The number of segments does not specify the number of components; combining two' well sorted sands having considerable disparity in mean size may well produce a three-segment curve ) The probability plot can be used: to identify distinctive inflections (e g., eolian hump, surf break) to separa:te components where mixing is sus pected, to permit quick estimation of internal sorting to allow easy reading of certain useful parame ters, and to pennit (where a linear suite is taken along the travel path) direct analysis, on the plot, of important hydrodynamic changes. The linear suite A suite of samples may be taken in any pattern prefem:d by the investigator: areally ran232 dom grid intersections, nested multilevel sam pling or othe rs. One useful and time honored procedure i s to take the samples (in one suite) in a historically or hydrodynamically meaningful way. The latter is done when sampling a creek sequentially from headwaters to mouth. The former is done when a sandstone formation is sampled systematically from the oldest (base) to the youngest (top) A variant of the latte r is to sample along a suitable horizontal line a geo logically y oung and growing deposit, such as an aggrading beach The linear suite provides much more infor mation than the same set of samples with rela tive positions in time or space unknown. A long stream without tributaries should yield a linear suite in which various size parameters (e.g., the mean) change in a predictable way from one end to the other If tributaries are samplecL sedi ment mixing processes can be studied to good advantage in such a suite If it is not known to be linear, this kind of work cannot be done. Linear suites, unless the line is too short, c:ommonly show changes Down the river pro me, tributaries may make important contribu tions The changes in key parameters should correlate with the fact that not even the river profile itself is smoothly cmving from one end to the other (Tanner 1974) In time-dependent linear suites, historical events may be evident in the data. The presence of changes or contributions as stated in the previous paragraphs, may well preclude the use of simple regression models. One does not get high assurance by trying to force a nonlinear curve with several peaks into a simple linear model. If the nature of the change can be identified or assumed in some acceptable way, then detailed study can be undertaken on the separate segments of the line Again, a good example is a linear suite along a stream profile: Peaks (or troughs) on the curve may correlate closely with tributaries If so, the analyst should recognize this fact and adjust the treatment ac cordingly Demirpolat, Tanner, & Clark (1986) stud ied a line of samples across a beach ridge plain that has had a history of adding one new sand ridge every 20-25 years (roughly 180 ridges). In addition to areal sampling they focused on a Lecture Notes 109 James H Balsil/ie

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W. F. Tanner Environ. Clastic Granulometry --FGS Course, Feb-Mar, 1995 Suitt statistics: Evolulion of the stdiment pool single ttansverse line, along which they sampled each available ridge (on that line) Because the ridges were clustered in visibly and measurably distinct sets, each containing some eight to twenty ridges, these workers were able to treat their samples in separate suites One also can look at the whole sequence as a single linear suite and examine quasi-cyclical changes with time (oldest to youngest) Changes along the sample line are clear when plotted (sample by sample) in terms of standard deviation and/or kunosis. Each of these two parameters showed striking changes having a quasi-regular periodic ity of some centuries (two or more), and each change is associated with a change in ridge-set altitude. Because each set was deposited over an interval of centuries, these changes cannot re flect storms (or even stonny seasons) ; therefore these two parameters appear to identify small changes of sea level (of a meter or two, from plane-table profiling ). This work also produced other interesting results. On the tail-of-fines diagram (Fig 16 1), successive sets of ridges plot as follows : D, river (perhaps closed basin) ; E 1, mature river sediment; E2, more mature river; F, even more mature river; G, beyond the river number field to the edge of the "mature beach" number field. Because this plot typically provides about the "next to last agency, the conclusion is drawn that set D reflects early reworlcing of riv. er (probably deltaic) sands, and that by the time set G was being deposited, waves had come pretty close to producing mature beach or near shore sand. This, of course, is correct, but could not have been deduced from the samples had they not been handled in linear fashion. Storm data Rizk (1985) studied beach sands along a large spit in the Florida Panhandle and deter mined grain size parameters along five ttansects taken at right angles to the beach far both the highand low-energy seasons of the year. His work provided a baseline data bank represent ing almost ten years since the area had last been struck by a hurricane (in 1975, by Eloise) Shortly after he completed his analysis, 233 three hurricanes (Elena, Juan, and Kate) affect ed the coast at intervals of only weeks (all in 1985) He therefore resampled his earlier tran sects at more or less regular time intervals : once shortly after Elena once shonly after Juan and twice within a month after Kate (Rizk & Demir polat, 1986). Juan was the mildest of the three and did not produce any significant changes This left six sample dates : two following a hurricane-free period of nearly a decade two between Elena and Kate and two after Kate The data for each traverse and da t e were examined in terms of the range for each moment measure; for example, for Traverse A immedi ately after Kate, the range was calculated for the size mean, for the size standard deviation, and so on The smaller the range, the less heteroge neity in that traverse on that date The range of the mean size (in phi units) on Traverse A dropped from 1.0 prior to Elena to slightly less than 0 3 immediately after Kate, then climbed back to about 0 4 a month later The standard deviation behaved in the same fashion (smaller values immediately after the storm) Changes were minor or not clear in the other parameters From their data the conclusion should be drawn that high storm energy resulted in mixing (homogenization) in contrast to the well-defined areal banding that existed after nearly a decade of relative calm and that was being reestablished a month or so after the third hurricane Fo r lin ear suites, this suggests that storm effects on this kind of coast are minimized in a matte r of weeks to months, and therefore should not be expected to show up clearly in samples taken at much greater intervals than this. If major storms were common in the sample area (e.g., weekly intervals), then one would not expect the kind of recovery seen by Rizk & Demirpolat, and there would be no evidence for occasional vio lent storm activity. Rizk & Demirpolat (1986) noted that what ever is represented (locally) by fair weather pro vides important long-term influences on the grain size distribution The beforeand after storm data were also studied in terms of other suite parameters The effect was greater suite uniformity after each storm. This is the same ob servation made from comparing traverses, but the presentation is different and the conclusions Lecture Notes 110 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 William F. Tanner appear to be more general when seen in suite form. Evolution of the sand pool A suite may be taken in areal, linear, or some other fashion. An areal suite should ap proximate a fairly narrow time slice, spread over an area. If the area is large, local suites should be taken at various places (perhaps only a few meters to some hundreds of meters across). The suite analysis should provide roughly the same kind of information produced by isoplething each parameter, such as mean size, but with less variability and more different kinds of informa tion. An isopleth map of mean size (or of coars est median diameter, or of some similar mea sure) commonly pinpoints the part of the study area closest to the source. If this is all one wants to know, and if the simple isopleth map is clear, 234 ST VINCENT 0 2 GULF OF MEXICO 16.6. Sketch map of St. Vincent Island, Florida, showing twelve beach ridge sets easy to recognize on air photos or by plane tabling. Some of these sets, each consisting of ten to fifteen ridges and representing a few centuries, stand high er than others. Grain size parameters identify cor reedy those sets that slalld high (or low). then sUite methods are not indicated. On the othseen by inspecting the standard deviations : The er hand, suite procedures for a full house of pamean for E2 is four standard deviations larger rameters provide a great deal more information. than the mean for G. The history of the offshore The linear suite may be geographical (e.g., sand pool, for these ridges, includes an early along a river), as stated earlier, or it may have fining sequence (the model of May [1973]) fol a time dimension If the sample line goes, say, lowed by coarser sediments after much of the from oldest to youngest, then one has the opfine-sand population had been depleted (not inponunity of studying the evolution of the sand eluded, but implied, in the model) The time is pool. One can plot various parametersfor in-2, 000 years (Figs 16.1, 16.6). dividual samples or for small suites -along the Sets D-G are almost parallel with each oth time line, and observe the changes. If small er in map view (although set boundaries are dis suites (e g., eight to twenty closely spaced samtinct); however, they do not cover the full histo ples each) are used, suite methods provide that ry of the island. Younger than G are sets H-L. there is very little noise, and one worries about Sets a t and 1 are located at the eastern end of neither the validity of statistical "lumping" tech. the island, have distinctive map patterns includ niques nor the proliferation of num-ing very short ridges, and do not parallel any bers of samples in any useful nested-sampling thing older; therefore, they do not belong in the design. same history as D-G. In fact, the suite-mean Beach ridge sets on a central traverse on St. mean size for H-J is 2 3, an apparent fming af Vincent Island have suite means and standard t.er the previous coarsening. The offshore sand deviations of mean sizes (phi units) as follows: pool has been isolated for longer than the histoSet F G ry of St Vincent Island; hence it is unlikely that this is merely a "new wave" of fine materials, but from the same source as older ridges. Alternatively we can see if sets H-J repreMean 2.2867 2.3812 2.4750 2.3045 2 .1750 sent introduction of finer material from the east S D 0.0925 0.1014 0 0682 0 1324 0 0787 (StGeorge Island). The suite mean of H-J is D E1 This produces a relatively smooth history of fming, followed by coarsening, from oldest (D) to youngest (G). The changes are real, as can be clearly within the range of D-G, so it is not fin er than the offshore sand pool may have been at an earlier date. It is finer than set G. Other parameters may be helpful The stan-Lecture Notes 111 James H. Balsillie

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W. F. Tanner Environ Clastic Granu/ometry FGS Course, Feb-Mar, 1995 Suite sUJlistics: Evolution of the pool dard deviation of H-J is numerically large r (mean value 0.414, with a suite standard devia tion of only 0 025) than any set in D-G (maxi mum, 0.39) The kurtosis of H-J is larger (3. 936) than anything in and equally large with G For low-to-moderate wave energy, these are distinctive results. The map patterns show that these short, almost isolated ridges were supplied from the east; but the granulometry alone, with linear methods, indicates that a new source of sand became important in the study area between G and H The history of this one island is really not the topic here. The key item is the chain of trends shown by sequential suites (or samples) in a linear system. Such a study yields more in formation than can be obtained by sampling in a nonlinear fashion. Conclusions The grain size distribution of a sand contains much infonnation about transport, deposi tion, or both. Analysis of a single sample of that sand may not provide very much of the infonna tion since variability from one sample to another may be an important facet of the nature of the sand body The joint study of ten or more sam ples from the same sand is much more useful Several effects or controls operate so that the suite of samples shows distinctive character istics. Among these effects are the following : 1 the mass-density contrast between mineral in air and mineral in water; 2 supply rates, through flow, trapping, and winnowing; 3 back-and-forth shuffling (BAFS) and net unidirectional sediment transport (NUST); 4 multistory turbulence structure; 5 grain grain interactions ; and 6 transport directionality New have been developed based on the concept of the sample suite: a set of closely related samples taken from a single transport and/or depositional system. Suite data include the means and standard deviations of the usual statistical parameters, plus additional measures such as the mean and standard devia tion of the weight percent in the tails-of-fmes (4' and finer) These can be plotted to good advantage on bivariate diagrams, where intcrpre-235 tation is reasonably clear. These diagrams are particularly useful because they show certain aspects of hydrodynamics, sediment supply and resupply, trapping (settling ; closed basin), and similar items The result is a markedly improved analysis Some of the advantages over traditional plots, which show all of the data points, are as follows: 1. The number of plotted points is now much smaller and easier to visualize. 2. Dubious or anomal9us points, due per haps to sampling problems, do not clutter the diagram 3 The effects of various transport agen cies are easier to differentiate 4 Transitions (in a historical sense) from one agency to another are easier to identify. 5 Four or more environment.s are conve niently placed on any one plot, without confu sion. The use of five or six properly selected bi variate plots commonly provides additional in formation such as "last previous agency," and may also give strong clues as to the reliability of the analysis The use of linear suites, where ap propriate, can pay off in terms of important geo graphic or historical information: for example the maturing of a sediment pool, the change from one agency to another, changes in energy level or in sea level, or the advent of short-term contributions from outside the system. REFERENCES Anhur, J Applegate, J., Melkote, s .. & Scott, T (1986). Heavy mineral recomaissance off the coast of the Apalachicola River delta, Nonhwest florida Florida Geological Survey, Report of Investigation no. 95, Tallahassee, 61 pp Bagnold, R A (1941). TM physics of blown sand and desert dunes. London: Methuen and Co., 265 pp Bamdorff Nielson, 0. (1977) Ex ponentially de creasing distributions for the logarithm of par ticle size Proceedings Royal Society of London, Ser. A, 353 : 401-19. Bergmann, P C. (1982). Comparison of sieving, settling and microscope determination of sand grain size Unpublished M.S thesis, florida State Univ Ta11abusee, 178 pp. Lecture Notes 112 James H. Balsillie

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W F. Tanner --Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 William F Tanno Blatt, H. Middleton. G ., & Murray, R. (1980). Ori gin o/sedimentary rocks Englewood Cliffs, N.J. : Prentice-Hall, 782 pp. Demirpolat,S Tanner, W F., & Clark, D. (1986). Subtle mean sea level changes and sand grain size data In: Proceedings 7th Symposium on Coastal Sedimentology, ed. W F Tanner Geology Department, Florida State Univ Tallahassee, 113-28 Doeglas, D. J. (1946). Interpretation of the results of mechanical analyses. JoU11J/Jl of Sedimenta ry Petrology. 16: 19-40. Folk, R. L. (1974). Petrology of sedimentary rocks Austin, Texas : Hemphill, 182 pp Friedman, G., & Sanders J (1978) Principks of Sedimentology New York John Wiley, 792 pp. Hoel P G (1954) Introduction to mathematical stiJtistics. New Yolk: John Wiley, 318 pp. Irani, R. R & Callis, C F. (1963) Particle size : Measurement, interpretation and application New York : John Wiley,l65 pp. LeRoy, S D (1981) Grain-size and moment mea sures: A new look at Karl Pearsori's ideas on disttibutions Journal of Sedimentary Petrolo gy 51: 625-30. May, James P (1973). Selective transpOrt of heavy minerals by shoaling waves Sedimentology, 20: 203-12. Moss, A. J. (1962-3) The physical nature of com mon sandy and pebbly deposits American Journal of Science 260: 337-73; 261: 297-343 Otto, G. H. (1938). 1be sedimentation unit and its usc in field sampling. JollTNll of Geology, 46: 569-82. Pettijohn. F (1975) Sedimentary rocks (3rd ed.). New Yolk: Harper and Row, 628 pp. Rizk, F. (1985). Sedimentological studies at Alli-236 gator Spit. Franklin County, Florida Unpub lished M S thesis, Florida State Univ ., Talla hassee, 171 pp. Rizk, F ., & Demirpolat. S (1986). Pre-hurricane vs. post-hurricane beach sand. In: Proceedings 7th Symposium on Coastal Sedimentology, ed. W F Tanner. Geology Department. Flor ida State Univ Tallahassee, 129-42 Rosin. P 0., & Rammler, E. (1934). Die Komzu sammensetzung des Mahlgutes im Lichte der W ahrscheinl i chkeitslehre. Kolloid Zeitschrift 67: 16-26 Socc i A ., & Tanner, W. F (1980) Little-known but imponant papers on grain size analysis Sedimentology 27 :231-2 Stapor, F W & Tanner,W F (1975) Hydrody namic implications of beach, beach ridge and dune grain size studies Journal of Sedimenta ry Petrology, 45:926-31. Sternberg H (1875) Untersuchungen Uber gen-und Quer-profil geschiebefUhrende FlUs se Zeitschrift Bauwuen. 25: 483-506 Tanner, W. F (1974). Bed-load transportation in a chain of river segments. Shale Shaker, Oklahoma City, Oldtz., USA, 14: 128-34. (1983). Hydrodynamic origin of the Gaussian size distribution. In: Nearshore sedinuntology: Proceedings 6th Symposium on Coastal Sedi mentology, ed. W. F Tanner Geology De partment, Florida State Univ ., Tallahassee, pp. 12-34 . Tanner, W. F., & Demirpolat, S (1988). New beach ridge type : Severely limited fetch, very shallow water. Transactions, Gulf Coast Associtllton of Geological Societies 38: 367-73 Visher G. S. (1969) Grain size distributions and depositional process Journal of Sedimentary Petrology, 39: 1074-106 Lecture Notes 113 James H. Balsillie

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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 NOTES Lecture Notes 114 James H. Ba/sillie

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W. F Tanner--Environ. Clastic Granulometry-FGS Course, Feb-Mar, 1995 Appendix VIII Tanner, W. F., 1991, Application of suite statistics to stratigraphy and sea-level changes: [In] Principles, Methods, and Application of Particle Size Analysis, (J. P. M. Syvitski, ed.), Cambridge University Press, Cambridge, p. 283-292. [Reprinted with Pennission] Lecture Notes 115 James H Balsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 20 Application of suite statistics to stratigraphy and sea-level changes WILLIAM F. TANNER Introduction The methodology underlying the work de scribed in this chapter is given by Tanner in Chapter 16. Development of the basic proce dures has at all times been coupled with field and laboratoiy work on modem sediments, in a variety of environments Over the course of al most fifteen years, the bank has grown greatly The plots and other devices that have evolved have been based on that data bank. These methods are considered to represent an improvement over traditional procedures (inter preting one sample at a time) Because the suite of samples contains more useful information than can a single sample, the results obtained by using suite parameters should provide better, more detailed answers. Certain standards have been observed : lam inar sampling (where possible) precision siev ing, S 100 g of field sample, not more than one spli4 S50 g for sieving using 0 .25 tP screens, and 30-min shaking time (Socci & Tanner, 1980). All of the work has been focused on quanz-rich clastics in the coarse silt-fine gravel size range; sediments made of chemically mo bile materials are not discussed heze. Modern environments Many environments have been studied using suite statistics: inner continental shelves, beaches, beach ridges, coastal dunes, interior river channels, tidal flats, delta fronts, aeolian nondune deposits, and others. A few deposits are even though they accumulated in late Holocene time and have not been altered very since deposition. Except for the latter group, all of the modem examples arc of known (observed) origin; thus the results of using suite methods are necessari ly coiTCCi in the simplest, most obvious cases (criteria were based on these cases). Only one easy example will be given, followed by a pre sentation of a few marginal and perhaps contra dictory examples Cape San Bias Cape San Bias is located on the Gulf of Mexico coast of Florida southwest of the city of Tallahassee and southwest of the village of Apa lachicola. All samples were taken from the mid tide position on the modem (medium-energy) sand beach The suite means (and standard de viations) of sample means and standard devia tions were 2 517 4> (0.175 f>) and 0 3 6 8 (0 .046 2.3 Dune sand is blown by the wind along what is generally a west-to-cast path Therefore the creek has two main sources of sediment the dunes to the west and the mountain range to the north and east. The creek bed. was sampled at 100-m intervals, producing fifteen samples in what was pre sumed to be a single suite. The basic measures for the suite (suite mean and standard deViation) follow: diamea2.195fP (0.218tJ>), staridardde viation0.396; (0.053), skewness 0.1 (0.25), kurtosis 6.882 (3. 952), and tail of rmes 0.001 (0.0005). The standard deviations of the Lecture Notes 116 James H. Balsillie

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W. F. Tanner-Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 William F Tanner Table 20.1. Summary of suite statistics parameters for Cape San Bias Mean of the skewness (two choices): Variability (of mean. of S.D.; two) : Relative d i spersions (mean. S.D. ): Skewness and mean of tail of fines: Skewness and S D of tail of fines : Tail-of-fines diagram: CQmparison of tails : river dune means and standard deviations (0.053 that this is a uniform suite. Never theless the analysis was run with fifteen sam ples, then with thirteen and finally only eleven samples Discarding was done on the basis of anomalously high fifth and sixth moments The mean and the standard deviation of the tail of fines (Fig 20. 1) coupled with the skewness, indicate that these are dune sands, if only two treatments are used (n = 13 or n = 11 samples) Likewise, the large standard dev:iations of skewness and kunosis indicate a dune origin Two other plots show a settling process; but settling, as used here covers several environ ments including aeolian, small lake, lagoon, or other closed basin setting-hence this finding i s not helpful The variability diagram (Fig 20.2) gives a choice of or mature beach Prob ability plots show a faint but sharply developed coarse fluvial tail, not at. all representative of mature sand beaches or dunes There is a single aeolian hump on the probability plots; this (by itself) is modest evidence for dunes. The analy sis indicates that these sands are probably aeolian(duneand/orsettling),buturlghthavefonned on a beach. The probability plots provide the additional Clue that there is a small (but not dominant) influence of stream type. The beach evidence vanishes when the suite is reduced to n = 13, and so is rejected. A suite of samples is. available from the dunes proper. 'This suite characterized by: great homogeneity. Suite parameters clearly indicate dune and many prob ability plots show the aeolian hump. Two obvi ous differences can be seen on the probability plots: humps are common in the dune sands and a faint but sharply developed fluvial coarse tail appem in the aeek samples. 284 )J 0 .001 0 0 1 0 1 T F WT% -(j 0.1 s t----+----+---1 Figure 20.1. Tail-of-fines diagram : means versus standard deviations of sample values The tail of fines is taken as the weight percent resting on the 4; screen, and fmer The closed basin (CB. set tling), river dune, and mature beach number f&elds are defined. 0 modem environments; o. ancient environments Abbreviations: B Cape San Bias beach; C Medano aeek; D Great Sand Dunes; K, Oklahoma sandstones; 0, Florida offshore; R, river; X New Mexico sandstones Figure 20.2. The variability diagram: standard de viations of sample means and of sample standard deviations. High energy is in the upper right. low energy in the lower lefL Except for some dunes and high-energy streams there are commonly two possibilities for any one point; this amb i guity can be resolved in Figure 20.1, Figure 20.3. or with some of the otber melbods given in texL See Fig ure 20 1 for key. If the creek sands were lithified and ex posed in an : ordinary stratigraphic section the environmental intcipretation would probably be dune, :but there would be a necessary note that them had been a minor fluvial influence of some kind. The analyst might consider the suggestion of a mature beach (hence the ocean coast) and Lecture Notes 117 James H. Ba/sillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Application of suite statistics might wish to opt for coastal dunes (a serious error), but a little attention to suite homogeneity would avoid this mistake. Florida shelf Arthm et al . (l986) studied surficial conti nental s helf sediments south of the panhandle (extreme nonhwestem pan) of the state of Flor ida in the Gulf of Mexico Their study area ex tended from a point south of Tallahassee, west ward almost to the the westernmost boundary of the state. The east-west extent of the area is roughly 300 km, and the north-south width of that band is about 18 lcm, extending from 5.5 km offshore to almost 24 km offshore. Water depths were mostly in the range 3-30 m. There were 32 north-south sample Jines, spaced about 9.5 km apart in the east-west direction, with 250 samples collected from the entire area. The published report contains: I. loran coordinates, water depth, and longitude and latitude for each sample; II. the firSt four grain size moments, the tail of fines, and the median diameter for each sample; m. running four-point averages, for each transeCt, showing smoothed mean, standard de viation, and weight-percent heavy minerals in each of three size classes; IV occurrence data for each of twelve heavy minerals in each sample; and V. modal analyses for each of twelve minerals, in one size fraction (3-4,), for thirtyone selected samples. In general, mean grain size coarsens to the west, but with large excursions, nearly as great as the entire range of values. The coarsest sizes were foimd opposite estuaries, and appear tore flect river channel positions when sea level was somewhat lower than it is now. The fmest sizes, at the eastern end of the study strip, found in an area where mean wave-energy density is extraordinarily low Breaker heights are typical ly only 3 or 4 em, despite the fact that this is an open sea coast (Tanner, 1960). Standard deviations (running averages) of these size spectra decrease from about 0.94 at the eastern end to close to 0.67 at the western end, but with large excursions. Sediment was best sorted on a large shoal off of Cape 285 George, where wave refraction and energy con vergence are important A plot of skewness versus standard devia tion from individual size spectra indicates sam ples in a beach or river regime, but fails to sepa rate the two. The kurtosis versus skewness plot of Friedman & Sanders (1978) also did not make a clear distinction between these environ ments. In this particular study, the large area clearly contains two or more sample suites, but the exact boundaries of the latter are not known. Therefore small subareas were treated, arbitrari ly, as suites. Several results are apparent. The variability diagram of Anhur et al. (1986: cf. Fig. 20.2) placed the grand mean in the off shore wave or coastal plain stream category, but subareas also extended into the swash regime. The area is presently being reworked by off shore waves; it was subject to surf action in middle-to-late Holocene time ; and the sands were indeed delivered to the region by one or more rivers. The tail-of-fines scatter plot placed each subarea within the fluvial regime, and showed that these sediments are much more nearly like various rivers than they are like typical beach sands. The two environments, on the diagram, are separated by a factor of 10. This approach largely eliminates the uncertainty between river and wave (or beach). The location of the aeolian area on this scatter plot is well known, and these samples are in no sense aeolian. Probability plots of representative samples show no aeolian hump, most having the obvious tail of fines (which eliminates the mature beach category) and a distinctive coarse tail (more typ ical of rivers than wave-dominated environ ments). These samples were all obtained from the continental shelf, yet scatter plots of their suite statistics identify them as beach or river sands that still exhibit grain size characteristics of river sands The apparent environmental interpreta tion is that these stream-deposited sediments date largely from a lower stand of sea level, and that there has not been enough time since they were laid down, and the water has been too deep, for the local waves to rework them to any great degree. Thus we should not expect that Lecture Notes 118 James H Balsil/ie

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W. F. Tanner --Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 WiUiam F. Tanner a sand mass, delivered from agency A to B, should instantly acquire the characteristics of the latter environment, which in due time could be impose
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W F Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Application of suitt statistics I( 6 SK 4 . . . -0. 4 -oi .. .. . . 0 .. ................ : 0.2 0 4 0 6 -----..,.., 1'-........ .,.....-! ......_ ____ _..-I Figure 20.3. Suite skewness versus suite kurtosis. The primary dividing line is at a skewness value of 0.1, separating aeolian or settling sediments (to the right) from river or beach sediments (to the left). The skewness provides a comparison of lhe two tails, and lhe kurtosis indicates their size. In some instances, river and beach sediments can be distinguished on the basis of kurtosis. The latter (K) also provides a general clue to energy levels: small K suggests high energy, and large K low energy. On the rigbtband side, dune sands typical ly have K 3, and closed basin sediments may haveK <3. SeeFigme 20.1 for key. 287 Table 20.2. Mean/kurtosis of ridges Topographically low ridges 1, 2. 3, 4, 5, 6 15, 16, 17, 18, 19, 20 46,47,48,49,50,51 Ridges with low meanlkuttosis 2, 3, 4, 5, 6 14, 15, 16, 17, 18, 19 48,49,50,51 each has a vertical position that does not reflect stonns or even stormy decades. Where the mean/kunosis parameter is nu merically low, the ridge set was found to stand low This is demonstrated in Table 20.2, where ridge numbers are from oldest to youngest. A critical mean/kurtosis value of 0 68 was used here; data were examined in terms of a three point moving average (Fig. 20 4). Other statis tical parameters successful in distinguishlrlg be tween topographically high and low sets, using three-point moving averages, were !/kurtosis (0.3), S D /kurtosis (0.115<;), the differences of the standard deviations (which show changes only, but not positions), and differences of leur four sets span about 2,000 yr of more or less tosis (which also show changes only) Each of simple evolution of the sand pooL these five plots identifies either changes and po. At the southeastern tip of the island are sitions, or changes, correcdy. several small ridge sets that do not belong with Set means of the means and set means of the main body of the island. These shon ridges the standard deviations provide some additional also indicated (with various criteria) senling, information. The sand got finer and better sort river and mature beach, but also an aeolian in-ed from ridge 1 to 15 (a boundary value, as fluence. The combination of swash and aeolian seen above); then coarser and less well sorted effects is essentially standard in sand beach from 15 to 32 (another boundary value); and ridges (not necessarily in single massive coastal finally fmer better soned from 32 to 45 ridges [Tanner, 1987]) However, the primary There were matching changes in skewness and agency was wave action (swash) with secondakurtosis, also. Ridges 15 and 32 appear to mark ry wind work. This is true of most sand beach important boundaries in tenns of these size pa ridges that I have studied, where obvious wind rameters. deposition typically represents 5%-20% of the Each of these sets covers hundreds of years entire coastal ridge. (e.g., ridges 15-20, plus any ridges missing on The ridges crossed by the central transect the traverse, times roughly 20 yr each). There were deposited in an unambiguous sequence fore the numerical results show sand-pool ef from oldest to youngest. This fact provides fects, regardless of whether a low set represents much mare information than can be obtained a slightly lower mean sea level. Seasonal or from a suite of random sampies. Several param -storm events are too brief to be shown, but.there etcrs are of interest here, because set boundaries is evidence for slower (few-century) modifiare clearly visible (e.g., on air photos), and cations of the sand-pool history. Wave-climate therefore ridge sets can be studied as such. Cerchanges are also not shown since differences in tain ridge sets stand low relative to others Each set heights are too large to be due to long-tenn ridge set spans a few centuries, and therefore wave changes. It is concluded that suite size Lecture Notes 120 James H. Balsil/ie

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W. F. Tanner--Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 William F Tanner 288 This is LBIJ::AR. Data N is 37 Mn/Ku Cut-off: .68 Std.D/Ku Cut-off: .125 !1n/Ku Window: 3 and mean: .7131271 1 Std.D./K Mean Kurt. Mn/1\urt. !1o\'. A\'i, (incl. s) I Mean value of Mn/Kurt.: .. 1 .096 2.318 3.928 1 2 .106 2.362 3.578 .619 LOW? s ., .. 3 .103 2.274 3.728 667 LOW? s 3 4 .12 2.346 3.158 .662 LOW? s 4 5 .135 @ 2.23 3.459 .677 LOW? s 5 6 101 2.381 3.658 .665 LO"'? s 6 'i .119 2.392 3.403 .692 $ 7 8 .113 2.445 3.355 .729 s 8 9 1 3 @ 2.473 3.266 .765 $ !J 10 .15 @ 2.338 2.861 7 .92 s 10 11 .143 @ 2.434 3.019 .793 s 11 12. .136 @ 2.315 3.048 .74 $ 12 13 .109 2.303 3.455 .703 13 14 .123 2.297 3.33 .649' LOW'? s 14 15 096 2.355 3.924 .643 LOW? s 15 16 .12 2.293 3.542 .63 LOW'! s 16 i7 .122 2.212 3.406 .615 LOW? s 1i 11i .11 2.14 3.8H .613 LOW? s 18 19 .088 2.435 3 . 819 .651 LOW? s 19 20 .138 @ 2.306 2.897 .704 s 20 21 .106 2.416 3.449 .741 s 21 22 .156 @ 2.203 2.992 .796 s 22 23 .146 @ 2.415 2.39 .813 s 23 24 .112 2.365 3.198 .772 s 24 25 .106 2.427 3.742 .71 s 25 26 .112 2.454 3.255 .731 s 26 27 .116 2.518 3.121 .785 s 27 28 151 Iii 2.238 2.8 .817 s 29 .126 @ 2.468 2.918 .817 s 29 30 .117 2.531 3 .136 .834 s 30 31 .135 Iii 2.474 2.901 .817 s 31 32 .132 @ 2.35 2.962 .807 s 33 .116 2.457 3.153 .78 s 33 34 .11 2.566 3.327 .766 s 34 35 .151 @ 2.188 2.931 7 s 35 36 .096 2.228 3.714 .649 LOW'! 36 37 .107 2.19 3.523 37 Mean value of Mn/Kurt.: f I Std.D./K Mean Kurt. Mn/Kurt. !1ov. A ''i (incl. s) I This is LINEAR Data source:STVIN.4AE; N is 37 Mn/Ku Cut-off: .68 Std.D/Ku Cut-off: .125 The latter helps identify boundaries. Figure. 20 .4. The ralio of mean to kurtosis, for each sample, along a time line across part of the SL Vincent Island beach ridge plain. The full output covezs ridges 1 (oldest) through 59, but is not shown here for space reasons. The note WW?, derived from the ratio itself, idemifies topograpbically low ridge sets (not low indi vidoal ridges; these ue three-point moving averages) In this area as on other sand ridges that have been stud ied, this ratio, or any of several other parameters listed in tbe text, identifies set vtltical position changes and precnmably small sea-level changes data provide useful clues to long-term wave energy level changes and therefore to small (1-2 m) changes in mean sea level. That this is not a geographically localized effect is shown by the fact that the same relationship between suite data and ridge height appears in data from Mesa del Gavilan, a beach ridge plain located southeast of Port Texas (Tanner & Demirpolat, 1988). What if this sand sheet were lithificd and then exposed at some future date? Almost com pletely without marine fossils, it might contain a few thin peat layers. Ripple marks aie nonexist ent; cross-bedding if visible, would be largely Lecture Notes 121 James H. Ba/sillie

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W. F Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 Application of suiu statistics in the 8-20 range, dipping southward (at present, toward the open sea), but having a uni fonnity that might very well be puzzling. Per haps the best information would be granulomet ric. One should be able to identify the sand as having been placed on the beach rather than in some other environment River influence should be obvious, and one should even be able to point toward the river mouth (nonh of the old est sands, by present coordinates). Identifying modest sea-level changes con ceivably would be possible, but the investigator would not be able to select sample sites on the basis of ridge geometry (as was actually done}, and perhaps would not even be able to establish a linear suite Ancient environments Oklahoma The Vamoosa formation, of late Pennsylva nian age, was chosen for sampling. This sand stone and conglomerate unit is well exposed along several roads in Seminole County, in east centtal Oklahoma. It was selected because pre vious work (e.g., Tanner, 1953) showed that it contains (from north to south) sediments that represent seafloor, barrier island, and lagoon (or estuarine) environments of deposition. As part of a larger project, five sample suites, to taling forty-eight samples, were collected (Tan ner, 1988) The suites were taken along two lines that cross the axis of the banier island at about 60 One of these lines, representing the basal, or oldest, part of the formation, was 23 Jan long and included three suites: A on the northern (seaward) flank, B near the middle, and E on the southern flank of the barrier. There were ten samples in suite A, fifteen in B, and five in E. The other two suites (fourteen and four samples) were collected near the middle of the formation, on the northern flank of the barrier island. There were twenty-nine more samples from rock units higher in the section (slightly younger). The three suites from the basal v amoosa formation contained tail of fines with weight percents and standard deviations of those per cents in the closed basin or settling category: quantities of sediment on the sieve (and finer) greater than found in most rivers. The tail-of289 SEGMENT ANALYSIS, WT. % FINE TAIL Figwe 20.5. The segment analysis triangle. The raw dala were taken from the probability curves for individual samples Each curve was dissected into a straight-line central segment and two tails (wheth.:. er straight lines or not). This provided three segments for each sample. Percentages were read for each segment, and the three mean values then calculated and plotted. The "B" near apex marks mature beaches; other environments are labeled clearly. The main overlap involves dune (aeolian) sediments and clay-or silt-carrying streams; this ambiguity can be resolved, in most inscances, by checking for the aeolian hump on the probability plots.. and/or by comparing the mean and standard deviations. See Figure 20.1 for key. fines plot (Fig 20.1) commonly shows the penultimate transport agency; therefore, these data may indicate a fluvial source. The suite mean values of skewness for the three suites plot as follows (Fig. 20 3) : B and A (closest to the sea), settling or aeolian; E (clos est to the fluvial source to the south), river. There was no clear evidence for an aeolian origin, so this option was discounted. The standard deviations of suite means and suite standard deviations indicate beach, offshore wave, or low-gradient stream (Fig. 20.2). The lack of coarse tails in these sand units coupled with high weight percents in the ce ntral segment on probability plots (typically places A and B (seaward suites) with beaches, and E Oand ward suite} with rivers (Fig 20.5) The relative dispersions of means and standard deviations (Fig. 20.6) indicate a beach origin forB, a prob able beach origin for A, and a probable river SO\D'Ce for B. Lecture Notes 122 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry -FGS Course, Feb-Mar, 7 995 William F. Tanner ).J* 0 .03 0.()5 0 1 0.4 0 .05 02 / /s Figure 20. 6 Relative dispersions of means and standard deviations showing settling (S), river (R), beach, and dune areas There is a small overlap at two places See Figure 20 1 for key. Suite E, taken within the lagoon (or estuary), appeared on bivariate plots with river en vironments Suites A and B, on the other hand, showed clear beach characteristics but also evi dence of settling This l8st indication is here tak en to match the restricted (interior) seaway in which these sediments accumulated. The penul timate agency for all of the suites was indicated as fluvial. Because the suite analysis provided the same intetpretation as had been made on the ba sis of other information, the conclusion is drawn that the methodology was useful (Tanner, 1988) The suite approach did not produce as much detail as did the combination of fieldwork and paleontology, but in the absence of the latter would have reached essentially the same general conclusions. 290 Two suites (eight and twelve samples) have been processed from the Yeso ; they are desig.: nated A and B The two were collected within about a kilometer of each other, horizontally, but the former represents the middle of the for mation, and the latter, the upper third. Tail-of-fines data (Fig. 20. 1) place both suites in the closed basin or settling category. This is taken to indicate the geosynclinal sea way in which Yeso sediments accwnulated. The suite mean skewness value (Fig. 20. 3) also in dicates settling for each suite, although the two do not have similar values. The alternative is aeolian, but the fairly uniform thin bedding, the very small wave-type ripple marks, and the ab sence of any positive evidence eliminate this possibility. Each of the two suites provides one clue suggesting a tidal flat depositional environment: the ratio of suite mean standard deviation to suite mean kmtosis (0.19 in each case) The relative dispersion of the means and of the standard de viations (Fig. 20.6) puts each suite in the beach category, and the variability plot (Fig. 20.2) shows each as beach or low-gradient stream. The latter, along with the wind possibility, must be rejected for lack of support; but most of the criteria indicate settling, which is consistent with the low-energy tidal flat environment. The interpretation to be drawn from the suite statis tics analysis is closed basin or settling, prob ably beach or tidal flat, but with a possible river episode in its history. The ripple mark data indi. cate very small fetch values, in general only New Mexico hundreds of meters or a few kilometers at the The Yeso formation of Permian age is well most. The Permian sea in Yeso time was actual exposed in many places in San Miguel County, ly much larger than a few kilometers, so the rip in north central New Mexico. It is typically a ple mark measurements are taken to mean re thin-bedded sandstone, with lesser amounts of stricted ponds on the tidal flat, such as are coarse siltstone and shale, and a few thin limeactually observed on low-relief, low-energy, stone beds. It lies immediately above the Sangre modem examples (Tarmer&Demirpolat, 1988) de Cristo formation, mostly of continental origin in this pan of the state, and directly below the Glorieta sandstone, which contains wave type ripple marks indicating fetch in the hun dreds of kilometers. The Y eso itself also con tains wave-type ripple marks, but all small, ranging down to < 1 em in spacing Based on this information, the Y eso was identified earlier as of tidal flat origin (Tanner, 1963). Conclusions The suite statistics procedure requires that a suitable set of samples, from a given sand body, be used for analysis, and that suite param eters (such as the mean of the sample means) be employed for environmental intexpretation. The results of such a study typically include one or more of the following: identification of a domi-Lecture Notes 123 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 Appllcadon of suite statistics 291 Table 20.3. Summary of suite statistics results for examples in the text CSB Mcd GSD Off StV Okla NewM Skewnus > 0. 1 (2 possibilities) Variability Tail of fines Aeolian .hump Skewness < 0. 1 (2 possibilities) Variability Tail of fines Fluvial coarse tail Segment analysis Relative dispersion Summary D,S D,S D D B,R B B,D B 1 R B B,R s 1 o D,S D,S s s s s B,R B,R B,R B,R B R S R B,R B,R S B,R ? B,R,S B,R B,R,S B,R,S Note: Only the first colurrin shows a simple case: obvious uncomplicated mod em beach. 1be other columns Wusttate problems, commonly due to mixing of environments, or sequence of environments (such as dune-to-creek, or river-to sea). A more detailed analysis is given in the text Abbrevii:llions: CSB, modem beach; Med, modem creek in Great Sand Dunes; GSD, modem d1mes; Off, florida offshore, modem shelf; StV, modem beach ridge plain; Okla, ancient barrier island, lagoon, and estuary; NewM, ancient near-shore tidal.flat; B, beach; D, dune or aeolian; R, river or creek; S, settling (closed basin. lagoon, estuary, lake, interior seaway, delta). nant agency or environment (if there was only one), identification of a penultimate agency, evidence for combination of two agencies, details on maturing of the sand pool, and evidence for small changes in mean sea level. Only one easy modern example has been included in this study. The other modem exam ples were selected to illustrate the kinds of prob lems commonly encountered. Although interpre tation is not invariably easy, the results (Table 20.3 gives a summary) are nevenheless superior to what one getS by making single-sample statistical studies. The ancient examples are representative of various projects that have been undertaken in that kind of work: Where other evidence has been available, suite methods have given essen tially the same results. This provides some couragement that, when other information is scarce or ambiguous, suite methods provide useful tcsults. However, some of the lithified sandstones (of unknown or uncertain origin) studied have not provided satisfactory answers: some because of pervasive silica cement, precluding lab analysis, and others because suite procedures yielded indicators of too many different env.i ronments. This is not a statement that the suite parameters were erroneous, but only that no clear intmpretation appeared in the course of the work. Many modem sands represent mixed agencies, or transition from one agency to another (e.g., river to marine). The suite meth ods have been usefut in general, in these cases; the examples given are representative of the more difficult suites. Despite problems that one encounters in using suite statistics methods, the results are much better than are generally obtainable by trying to base an analysis on data from individ ual samples. The method is not foolproof for various reasons, including inadequate number of samples, inadequate areal coverage, poor Ympling technique, absence of a single well-' defined environment of deposition, and (for an cient rocks) pervasive silica cementation Per haps the most important difficulty lies in the fact that certain sand bodies have been studied at a Lecture Notes 124 James H. Ba/sillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 William F. Tanner moment of transition; that is when there is in fact no single responsible agency or environ ment. This may be problematic for our wish to erect sharply defined class boundaries, but it is not a problem in the method of study. R.EJ4ERENCES Arthur, J Applegate, J., Melkote, S & Scott, T. (1986) Hea v y mineral reconnaissance off the coast of the River delta, North west :florida Florida Geological Survey. Report of Investigation no 95, Tallahassee. 61 pp. Demirpolat, S ., Tanner, W. F ., & Calk, D (1986) Subtle mean sea level changes and sand grain s ize data. In: Proceedings of Seventh Sympo sium on Coastal Sedimentology, ed W F. Tanner. Geo l ogy Deparunent, Florida State Univ Tallahassee pp. 113-28 . Friedman, G & Sanders, J. (1978) Principles of sedimentology Ne\Y York: John Wiley, 792 pp. 292 Socci A & Tanner W F (1980) Little-known but important papers on grain size analysis. Sedimentology 27: 231-2. Tanner, W F. (1953) Facies indicators in the Up per Pennsylvanian of Seminole County, Okla : Journal ofSetl.imentary Petrology 23: 220-8 (1960) Florida coastal classification Transac tions, Gulf Coast Association of Geological Societies, 10 : 259-66 (1963). Permian shoreline of central New Mexi co. Bulletin of American Assoc i alion of Petroleum Geologists, 47: 1604-10 (1987) Spatial and temporal factors controlling overtopping of coastal ridges. In : Flood h y drology, vol V ed P Singh. Dordrecht: Rei del, 241-8 (1988) Paleogeographic inferences from suite statistics: Late Pennsylvanian and early Penni an strata in Central Oklahoma. The Shale Shaker (0/dahoma City, Oklll ) 38(4) : 62-6. Tanne r. W F ., & Demirpolat, S (1988) New beach ridge type : Severely lim i ted fetch, very shallow water Transactions, Gulf Coast As sociation of Geological Socktiu, 38: 553-62 lecture Notes 125 James H Balsillie

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W F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 NOTES Lecture Notes 126 James H Bals i llie

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W. F Tanner--Environ Clastic Granulometry-FGS Course, Feb-Mar, 1995 Lecture Notes Appendix IX Sedimentologic Plotting Tools 127 James H. Balsillie

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W. F. Tanner Environ Clastic Granulometry -FGS Course, Feb-Mar, 1995 T F 1.0 0.5 BEACH 0.01 0.1 Jl Tal-of-Fines Plot. OFFSHORE WAVE BASIN ...._. __ 1 10 tT, 0 1 Lecture Notes 0.05 0.1 0.5 1.0 tTII v.n...., OU.gram (Suite Standard Deviation of S.mple Mens nd Stanurd Deviations). 128 James H. Balsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 K 6 5 4 -0.6 .. RIVER . ..... ..... -' -0.4 -0.2 0 Sk ,__.. ---I I EOUAN; I SETTUNG I I 0.2 0.4 Skewness versus Kurtosis Plot (Suite Means). SEGMENT ANALYSIS WtOk RIVER Silt + Clay; 80 . . . 60 RIVER ; _,. -0.6 CLOSED BASIN . . . . . . .... 40 . . . ............. Lecture Notes ... : Segment Analysis Triangle. 129 James H. Balsillie

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W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb -Mar, 1995 0 5 /). '';;! ,, / ___ / / .l //) II ,d*'t:J 1.0 I "--/ 0.5 0.02 0.05 0 1 0.2 0.5 J.l Relative Dispersion of Means and Standard Deviations Plot 30 20 K 10 8 6 4 Lecture Notes 0.2 0 4 0 6 IT Standard Deviation versus Kurtosis (lncividual Samples or Suite Statistics) 130 0.8 James H. Balsillie

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W. F. Tanner--Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 0 of K Lecture Notes 30 20 10 5 3 2 I 0 9 0 8 0 6 0 5 0 4 0 3 0 2 (/) (l) (/) 0 (l) 0 c: -(l) (f) 2 3 5 10 20 Isolated 30 Shallow Values Suite Offshore Statistics Settling 20 IE = energy Louisiana Cheni 10 Low-IE beach plus settling Sangamon H Beach Ridges..-
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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 40 30 20 15 10 /mo6 9 8 7 6 5 4 3 2 E =energy 1 2 3 4 5 K 10 20 Kurtosis versus Square Root of the 6th Moment Measure (Suite Means). Lecture Notes 132 James H. Balsillie

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W. F. Tanner-Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 Appendix X Tanner, W. F., 1964, Modification of sediment size distributions: Journal of Sedimentary Petrology, v. 34, no. 1, p. 156-164. [Reprinted with Permission] Lecture Notes 133 James H. Balsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 }OURNAL OF SEDIKENTAJlY PETROLOGY, VOL. 34, No. 1, PP. 156-164 FIGS. 1-8, MARCH, 1964 MODIFICATION OF SEDIMENT SIZE DISTRIBUTIONS1 WILLIAM F. TANNER Geology Department, Florida State University, Tallahassee, Florida ABSTRACT Sediment size distributions commonly plot, on probability paper, as zig-zag lines. Nevertheless, the hypothesis that the basic distribution is normal (i.e., Gaussian) and will therefore plot as a straight line, is specifically retained. Possible modifications of the straight line plot include the following: simple mixing (adding of two or more basic components), censoring of a single component, truncation of a single component, filtering of a single component, or a combination of these. Simple mixing is the simplest, and therefore the one most likely to be successful in explaining zig-zag curves. Filtering is, in some ways, a negative version of mixing. An additional factor in the wide-spread appearance of zig-zag curves is the seemingly universal deficiency of certain sediment sizes (minima which separate gravel bed load, sand bed load, and wash load). A variety of methods are available to the analyst who wishes to determine the "original" basic components in a given sample. These include a graphical method, and the method of finite differences. However, experience and intuition are more important than methodology in effecting a successful separation. Bimodal distributions having a sharp inflection point near are conceivably the result of mixing sands from two different sources (such as a river, and wave erosion of standstone exposed on the near-shore sheH), or of transporting sands in the same area by two different agencies (water currents; wave motion). A possible sand dune history of sands such as this is examined and rejected. If the dual-transportation suggestion is correct, the "break" may be useful in interpreting environments of deposition of sands of the past. The abundance of zig-zag curves, in sediment size distribution studies, makes clear the necessity for examin ing the detailed plot, rather than two or three statistical parameters (such as the mean and the standard devia tion) which do not represent the zig-zag curve very well. INTRODUCTION The distribution of sediment particle diam eters is generally reported, in the geologic literature, in terms of means and standard deviations. This practice is a tacit assumption that each sediment has a distribution of diameters which is, more or less "normal" (or, alternatively, log normal). If the assumption were correct, most sediment size studies would plot on probability paper as straight lines. Many studentsof sediments have known, for some time, that this is not true. If a size distribution plots, on probability paper, in some fashion other than a straight line, three problems arise: 1. What does this "non-normal" plot mean, in terms of physical characteristics of the sediment? (For example, do we have previously unsuspected hydrodynamic prin ciples at work, or do grains of different sizes have different shapes and therefore behave differently, or are we dealing with mixed, or otherwise altered, sediments?) 2. Once a physical explanation of the non normality is obtained, what does this ex planation tell us in our efforts to reconstruct the environment in which the sediment accumulated? 3. What parameters can be used to character ize these non-normal distributions? 1 Manuscript received january 24, 1963. Bagnold (1941) observed that certain desert sands appear to be mixtures of two components. He used a semi-logarithmic plot in an effort to make these components separable. Doeglas (1946) studied departures from the normal law, concluded that many sediments are mixtures of two or three components, and proposed three basic components designated as the R, Sand T distributions (fig. 1). More recently Doeglas (1955) has sought other methods of handling this general problem. Tanner (1958) noted the well-known de ficiencies of clastic sedimentary materials of certain sizes, and suggested that these deficiencies alone would require that many sediment dis tributions plot as zig-zag curves rather than as straight lines. The critical sizes are those be tween about 34> and 4.5q>, and those between about0.5q> and -,3(p; these deficient sizes produce minima between more abundant sizes, which were labelled "gravel bed load," "sand bed load," and "wash load." Later (1959, 1960a, 1962a) Tanner outlined a method, using first and second finite differences, for attempting to separate components of a zig-zag distribution. He also suggested (Tanner, 1960b) that filtering, censorship, and truncation may be important, along with simple mixing, in combining com ponents. Curray (1960) attempted to trace sediment masses along the continental shelf of Texas and Louisiana by separating and identifying various Lecture Notes 134 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 7 995 SEDIMENT SIZE DISTRIBUTIONS 157 modes within each sample. He was.able to show that distinctive mixtures appear to maintain their identifying characteristics across tens or hundreds of miles of shelf. From this study, he identified four types, or modes : I 0 to 2.94: II, 3.0 to 4.2(j); III, 4 3 to 7.1(j); and IV, smaller than 7 .'J.4. Walger (1962) observed that single-layer sedi ment samples invariably show three normally distributed components, each of which is sorted more efficiently (smaller dispersion numerically) than the total layer sample, and that the latter is better sorted than a cross-section or channel type sample taken at the same locality His plotted results show minima (deficiencies) in the vicinity of 3 or 44, 1 or 24, and -14; the present writer interprets these figures to mean modes in the granule, fine-to-medium sand, very fine sand, and silt size ranges Harris (1959) reported multi-component sands from beaches in Suez Canal Zone Fuller (1961) observed an inflection point near 24 in shallow marine sand size distributions and wondered if this represents a "break" be tween the "impact law" and Stokes' settling velocity formula. He followed this up (Fuller, 1962) with a more detailed treatment, in which he considered the possibility that such samples have been wind-handled at some time in their recent history Van Liew (1962) has illustrated the graphical analysis of semilogarithmk plots, providing two or more straight-line components; this pro cedure does not appear to work for sediments. Bfezina (personal communication) has pro posed that Kapteyn's normalizing transforma tion can be used on all distributions, even the polymodal ones, thereby making them plot as straight lines. He has treated this procedure in detail, for sediments which settled through still water. Application of his log-hydrodynamic transformation does not appreciably alter ob vious cases of truncation, filtering, or mixing, but may be of value in more difficult cases, where still-water settling can be inferred. PHILOSOPHY It is certainly not known that a normal (or, log-normal) distribution is superior to any other available to the earth scientist (Middleton, 1962). The normal curve is actually a special case of a more general distribution and it is not even known whether or not the latter is the most desirable one. Additional investigation, however must al ways be predicated on some general statement. Therefore, for purposes of study and contempla tion, the following is offered: The normal distri-99 COARSE R FINE FIG. 1.-Three bas i c sediment size distribution types according to Doeglas (1946). bution is adopted as the basic type; those curves which depart from the normal will be analyzed in an effort to catego r ize, in some way, the de partures, and geological significance will then be sought in the various categories. This modus operandi will, it is thought, pro duce interesting and valuable results It is con ceivable that it may even aid in the whole busi ness of clarification of the meaning of distribu tion curves in the earth sciences. It is, however, specifically contrary to the position taken by Friedman (1961, 1962). SIMPLE MIXING Fallowing the early experimental work of Bagnold (1941), Doeglas (1946) developed the i dea of mixing in relatively great detail. He desig nated three bas i c types, or curves, as R, S and T (fig 1). R identified the "continuous current" depositional area, such as in a river or under a strong marine current. S was applied to currents having decreasing capacity in the down-stream direction, such as on the lee sides of dunes, river bars, shoals, and shallows. T was used to mean stagnant water conditions, and hence total dep osition. Doelgas considered that many sands are combinations of two or more of these basic types: R+S, S+T, or R+S+T . It is true that, by combining these types, one can duplicate the size distributions of many modern sediments. However, the present approach is somewhat different. We assume here, that the Gaussian (or normal) distribution is basic, and then ob serve that each of Doeglas' three types can be obtained by proper treatment of a normal curve. In other words, we do not try to analyze a sedi ment curve in terms of R, SandT, which appear to be modifications of the assumed basic dis tribution, but rather we tum directly "pure" normally-distributed components, in an attempt to see if the total sediment can be "explained" in this way. Two (or more) normal distributions can be plotted on probability paper, and then "mixed" Lecture Notes 135 James H. Balsillie

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w. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 > 158 WILLIAM F. TANNER so COARSE -....;: ........ ................ I \ ,. \ :'COMBINATION .................... FINE ........ I Ftc.2 -Two c omponents (I and II) having equal variances and means; the combination obtamed by s1mple mlXmg. Two mftection points appear. (by simple addition) in any desired proportions. Doeglas presented examples of this process. Essenwanger (1960) has the same idea in order to make rainfall analyses The present writer has made many combinations of this kind on an electronic computer Several things quickl y become apparent. . If only two distributions are combmed by stm ple addition, characteristic cur:ves These commonly have inflection pomts whtch can be located with an accuracy of about 5 percent (on the probability scale), or better. in flection points typically indicate the proportions in which the components were combined If both variances are essentially equal, the combined curve has three segments: two nected by a third segment havtng a steeper m clination (as plotted for the present paper) (fig. 2). If the variances are markedly unequal, the comoination typically has two segments, one of which is sub-parallel to the component, and the other of which is steeper than either com-ponent (fig. 3)_. The.inflection point may have a spunous, but nevertheless important, sharpness : where closely spaced points are computed (i.e. at tenth-4> in tervals) a sharp, but smooth curve where widely-spaced (and hence realistic) pomts are computed, a definite inflection point is cated Inasmuch as sizing is m whole-4>, half-4>, or quarter-4> uruts, curye should for practical purpose:s be .out an the same fashion The inflection pomts whtch are so produced are artificial in sense, but is nevertheless what one obtams for real sedt ments. The method of finite differences (Tanner 1959, 1960a, 1962a) can be used in many in stances to effect separation of two components A graphical method has been quoted by Fuller (1961). M. Shim rat has devised a program !or machine differentiation which might be applied to this problem However skill and experience often permit an analysis to be made when mechanical or rote methods fail. Regardless of the method, whether electronic, mathematical or intuitive a successful separation is achieved when the several components recombine to make the original distribution There is no question of whether or not the separation is "correct. The only question remaining is, does it mean anythi ng? Three components are more difficult to detach than are two four more difficult than three, and so on. Nevertheless, one examp l e has been studied in which at least 10 distinctive components could be identified and (in this case) largely verified by non-statistical means. Ex amples having three four or five components appear to be fairly common, and in many in. stances relatively easy to manipulate. Fuller (1962) considered a group of near-shore, shallow marine sand samples which have size distributions showing two segments. He ob served that typical curves have two segments each, and an inflection point not far from op. His plotted example looks like many similar two component curves which the present writer has obtained either from sediments or by computer methods (such as fig. 3) Fuller examined two possibilities : (a) that the inflection is due to v change of hydrodynamic processes, at about 2t/>, or (b) that the 2,P fraction was selectively re moved by wind action at some time in the recent past when this sample was exposed along a beach A third possibility should be emphasized also : (c) these samples are produced by simple mixing of two components having unlike yari ances. It is possible, of course, that the two differ ent components might have been separated originally hydrodynamically, and hence Item (c) is closely related to Item (a). The second sug gestion, that statistical selection of some kind was operative, is discussed under head ing 19 50 COARSE FINE FIG. 3 -Two components (I and II) equal proportions, but means and and the combination obtamed by mmple mtxmg. The single sharp inftection is at about 50 percent. Lecture Notes 136 James H. Balsillie

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W. F. Tanner -Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 SEDIMENT SIZE DISTRIBUTIONS 159 The published example (Fuller's fig. 1) shows in analysis, one component having a mean of 1/>, contributing3.75 percent, and a second component having a mean at 3 .25/>, contrib uting 96.25 percent. The second more important component has much better sorting than the first If this is an example of simple mixing, how could the mixing have been accomplished? There are several possibilities : (1) a shelf area, fed by two streams, each of which delivers a sediment load having distinctive parameters, might show such mixing in various proportions; or (2) might involve two components, one derived from stream flow and one from wave erosion of sandstones exposed beneath the shelf waters; or (3) mixing might reflect two different hydrodynamic regimes. The sediment-transport diagram presented by Hjulstrom (1939) has three divisions: erosion, transportation, and dep osition. Erosion, with minimum current veloc ities, is specified for sand-sized materials Clay and gravel are shown as requiring higher velociti es in order to put material into transit. Hjulstrom's diagram was constructed for water currents and particularly for rivers and canals It might very well apply to shelf cur rents, also But it probably does not hold for wave action In the latter instance, stirring ap pears to be more important than lateral trans port, and hence the three .areas of the current diagram should be revised This is equivalent to saying that minimum orbital velocities necessary to initiate transportation may not be adequate to maintain transportation, inasmuch as each bottom orbit does not operate with constant v elocity, and furthermore the periodic reversal of direction should have the effect that sorting would be more efficient. The proposal is made, therefore, that the minimum-velocity erosion" area, for a wave version of Hjulstrom's diagram, be narrower, and to the finer side of the minimum velocity "erosion" area for the water current diagram (fig. 4) If this concept is correct, a shelf area where both currents and waves operate effectively should be marked by bimodal sediments or nega tively skewed sediments The finer mode (wave moved) should have better sorting and the coarser mode (current-moved) should have poorer (numerically higher) sorting : The propor tions in which the two components have been combined should be an indicator of the relative strengths of the two agencies. Fuller's published plot could thus be interpreted as showing a water-curre .nt mode, 3.75 percent, and a wave-mode, 96.25 percent. Vause (1957, 1959) examined over 100 samples FIG. 4 -Hjulstrom's diagram showing erosion (E), transportation ( T), and deP.osition (D), for currents (heavy l ines), with poss1ble processes for waves added (dashed lines). from the shallow shelf southwest of Tallahassee. All of these were taken one mile or farther from shore Although they are commonly weakly bi modal, the secondary mode occurs in the fines. A significant secondary mode coarser than the primary component was not observed Waskom (1957, 1958) studied a suite of sam ples from the same general area. These were taken along the beach from lagoons and marshes, and within the breaker zone. The breaker zone samples show str ong bimodality, much like that of Fuller's published example. Inasmuch as Vause and Waskom were working in the same area, on different parts of the same sand sheet, one must conclude that the coarser secondary component is due to the operation of some marine process which is not effective in deeper water (i.e., 15 feet or more). From bottom observations carried out by diving during the Vause and Waskom projects, it can be suggested that this difference is one of the following : (a) bottom currents are too weak, outside the breaker zone to produce the second ary mode, or (b) breaking waves operate in some fashion unlike ordinary waves of oscillation In either case, the secondary mode reported by Waskom was formed within, or very close to, the breaker zone, and did not appear in any other samples taken from a strip about ten miles wide on each side of the beach Brockman (1962) prepared analyses of anumber of Upper Cretaceous sands from Alabama These are largely bimodal. Their asymmetry must be taken to mean that the coarser, less im portant component is less well sorted than the finer, more important component. The present writer has held that much of the Cretaceous sedimentary section of Alabama is transitional or marine rather than continental (Tanner, 1955, Lecture Notes 137 James H. Bslsillie

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W. F. Tanner-Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 160 WILLIAM F TANNER 1962b). This conclusion was based on a com parison of cross-bedding directions with pinchouts and truncations, as well as a consideration of how coastal currents should have moved if present concepts of Cretaceous wind and wave attack directions are correct. Brockman's study tends to support this conclusion. CENSORSHIP Simple mixing is not the only way of com bining components Three additional methods, described broadly as "statistical selection" are censorship, truncation, and filtering Mason and Folk (1958) have used the term "amputation" for one or more of the various selection processes. Censoring involves the suppression of all of the information of one variety, concerning the sam ple with a certain range of values. The missing information normally belongs to one or both tails, but in some instances might be taken from the middle. There are two types of censorship: Type I where the number of suppressed classes is known, and Type II, where the number of suppressed measurements is known. In Type I censorship, the investigator does not know what numerical values are to be assigned to the sup pressed classes. In Type 11 censorship, the numerical values to be assigned to the individual items (i. e diameters) are not known. Many sediment curves p11blished in the liter ature show single censorship; that is, informa tion as to the nature of the distribution, below the finest screen size, is not conveyed, but the total amount of sediment, within that part of the distribution is nevertheless known (it was caught in the pan). This is Type II censoring: the number of suppressed classes is not known, but the total number of items from all of these suppressed classes is available. The analyst has no difficulty in working with the distribution so obtaine
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W. F. Tanner Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 SEDIMENT SIZE DISTRIBUTIONS 161 A doubly-truncated distribution appears at first glance much like a plot made by combining two components having similar variances : two flat tails connected by a steeper middle segment. The bimodal plot, however has inflection points (typically), whereas the doubly truncated plot does not. The Rand T types of Doeglas look like singlytruncated curves. He later adopted the "truncation" terminology (Doeglas, 1955). The T plot, representing stagnant water and total deposi tion looks as though the coarse fraction were missing This is logical, inasmuch as the coarse fraction probably could not have been intro duced into truly stagnant water. The R plot, representing steady currents (such as in rivers) looks as though the fine fraction were missing . This is also logical, inasmuch as the finest ma terials should not settle out in strong currents. The S type of Doeglas looks like a doubly truncated curve. Both coarse and fine fractions appear to be missing. The statistical literature is not as helpful with regard to truncation, as it is in connection with censorship. That is because of the inherently greater difficulties in the case. A censored sediment curve looks quite ordinary: in actual prac tice the analyst makes the necessary adjust ments more or less automatically. A severely truncated curve, however, looks quite strange, and trial-and-error manipulation may be re quired in any effort to approximate the original. A beginning has been made, however, with truncated data (Cohen, 1955, 1957, 1959, 1960). FILTERING The two previous forms of selection affected continuous ranges of values. Filtering is a more drastic modification, in which the suppressed items were not necessarily a continuous part of the original measure spectrum. This can be visualized by thinking of a capricious geologist, who toys with the sediment after the sieving is complete but before weighings have been made. He removes various amounts of sediment from each of several sieves. When he is through, the total original weight cannot be determined, and the analyst does not know what pattern was used, if any, in making his alterations. The pat tern, of course, has a statistical distribution of its own, and this is completely unknown. Two kinds of filtering can be distinguished. In simple filtering, the missing data have been sup pressed according to some specific (but unknown) pattern. In some instances the filter may be in fiuenced by the original sample, so that both components are altered, each by the other; the result is mutual filtering. Quartz-and-carbonate sands may owe part of their character to a filtering process. The total sample may produce a single straightline plot. Separation into two components by hand may produce two straight line plots. Yet removal of the carbonate by leaching with acid may produce a bimodal curve. In the latter instance, fine in soluble grains, formerly masked because they had been incorporated within the shells pr shell fragments, now appear in the quartz component These grains were removed from an original sam ple by organic filtering (the animal which secreted the shell appropriated them from among whatever other sizes may have been present). The final "insoluble" component is really a mixture containing the true quartz fraction plus a fine fraction which, as far as natural hydrody namic processes are concerned was added in the laboratory. Experience with filtered distributions is, to date, inadequate for rules to be laid down. The literature offers essentially no guidance; the problem is inherently exceedingly difficult. It may not even be possible to recognize harshly filtered distributions. Nevertheless, analysis of samples must proceed; hence it may be simpler to reject the hypothesis of filtering, sample by sample, unless strong evidence to the contrary, either statistical or geological, can be adduced. NATU1l.AL SELECTION The simplest procedure which will yield ac ceptable results is probably the best procedure. Therefore a workable program might be to ig nore the effects of censorship (which does not, generally, alter the appearance of a curve), toreject the hypothesis of filtering (unless other evi dence is available) and to attempt to dis tinguish, by inspection, between the results of truncation and simple mixing. Inasmuch as the two processes commonly produce quite different distributions, this should not be too difficult. Once a decision has been made, the task of re solving the components can be undertaken. This will include the identification of points and agencies of truncation, if present. Fuller suggested that his bimodal shelf Sa.nds might have acquired their zig-zag distribution as a result of removal of certain sizes by wind ac tion. He posttJlated that the suppressed, or re duced, classes were those near the middle of the distribution The number of affected classes is unknown, the total amount of information re moved is unknown, and there are no data regard ing the continuity of the missing sizes. The "wind removal" hypothesis is, then, a suggestion that a single original sample has been. filtered (by a specific agency: wind). This is, of course, a very real possibility. It might be rejected on the grounds that the distribution can be explained, Lecture Notes 139 James H. Bslsil/ie

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w. F. Tanner __ Environ. Clastic Granulometry -FGS Course, Feb-Mar, 1995 162 WILLIAM F. TANNER 50 COARSE FINE FIG. 7 .-Filtered distribution, where the filter mean is larger than (i.e., coarser than, in terms of grain size), and the filter variance is equal to, the com parable parameters of the main component. adequately, by assuming simple mixing, and therefore we have no need of the more difficult hypothesis of filtering. lntead, it may be more profitable to examine the notion of filtering by wind to see what results might be obtained in this The most obvious gap in reconstructing a filtered distribution is a knowledge of the char acter of the filter This same gap, however, occurs in many other instances, where the analyst is not particularly annoyed by the fact that he doesn t really know what kind of a distribution he is studying. Therefore, it should be almost a matter of routine to assume that the filter has a normal (Gaussian) distribution, and that a normally-distributed filter can be treated as if a negative component were being added to the primary component. By means of this assumption, filtering can be handled by the same method:; which are used in separating simple mixtures. Application of this procedure can be done in three different ways; in each instance the filter is assumed to have a mean of about 2t; (following the of FuJJer). The possibilities are these: (1) Filter variance is numerically greater than sample variance, and the filter mean is equal, or close, to the sample mean. This has the effect of eliminating sample tails, thereby reducing the sample variance. No zig-zag curve is produced (2) Filter variance is numerically equal to sample variance. This produces a result which looks like a singly-truncated dis tribution: straight in one tail, and curved in the other. If the filter mean is coarser than. the sample mean, the apparent truncation will appear in the coarser tail of the sample (fig. 7), and positive phi skew ness appears. If the filter mean is finer, negative phi skewness is obtained. I 13,..,, ITQ NntP-.t:: {3) Filter variance is numerically smaller than sam pie variance. If thefil terisstrongenough to have any appreciable effect, the result is a curve which is more complex than any discussed previously in the prese .nt paper, with perhaps four segments, or at least two straight segments plus one arc (fig. 8) Fuller's published example does not match any one of the three possibilities. The wind blown sand described in his Figure 2 has essen tially the same variance as his main sample. Filtering by this mechanism should produce the results of Example No.2 above; instead, it yields a two-segment inflected line. The conclusion which must be drawn is that application of a normally-distributed filter, through wind ac tion, is not warranted. The hypothesis of mixing (that is, the adding of one component to another) is therefore adopted for this marine, near-shore sample. Sev eral suggestions to account for simple mixing were advanced in another paragraph (two rivers as sediment sources; a river plus wave erosion of the sea fioor as sediment sources; water-current action and wave action as two different trans porting mechanisms). It should be possible by of other samples from the same shelf area to determine which of these is the pre ferred explanation. CHARACTERIZATION Three questions were posed in the introduc tion. Tentative answers for the first and second have been expressed in the preceding paragraphs. The third question was: How do we characterize these non-normal distributions? Until more sophisticated procedures are available, the most direct method is to specify the mean and stand ard deviation of the total sample, plus the mean, standard deviation, and percentage of each comCOARSE FINE FIG. 8 .-Filtered distribution, where the filter mean is larger (i.e., coarser, in terms of grain size), and the filter variance is smaller than comparable parameters of the main component. 140 James H. Balsillie

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W. F. Tanner--Environ. Clastic Granu/ometry-FGS Course, Feb-Mar, 1995 SEDIMENT SIZE DISTRIBUTIONS 163 ponent, plus the method of comb i nation or modi fication which appears to have operated CONCLUSIONS The notion that sediment size distributions are essentially normal (Gaussian) is adopted as a working hypothesis On the basis of this concept, zig-zag curves are considered to be combinations or modifications of ordinary normal distribu tions. It is observed that several operations are available, whereby straight-line normal com ponents can be altered to match observed sedi ment distributions : simple mixing, truncation and filtering Filtering i s, in some respects an operation much like siinple mixing (adding). (Censoring does not appear to alter a sample plot.) Various methods can be used in the analysis of zig-zag curves Some of these are graphical, some are a .rithmetic (m e thod of differences), and some are primarily a combination of experience and intuition. A surprisingly large number of examples yield to one or more of these methods, despite the apparently insurmountable mathe matical difficulties which seem to be inherent in the basic problem Bimodal shallow shelf sands are possibly the result of mixing of sediment from two different sources, or of mixing sediment carried by two different agencies (waves; currents) If the second of these two suggestions is borne out by later experience, an additional tool will be made available for interpreting some of the sands of the past. Deflation of selected sizes from beaches is rejected, at least for the present, as a means of obtain i ng a sharply-inflected plot. Continuing study of sediment size distribu tions makes even clearer the necessity for examining the detailed size plot, rather than relying on a hand ul of elementary parameters, such as the median and standard deviation, which mask about as much information as they reveal. REFERENCES BAGNOLD, R. A 1941, The physics of blown sand and desert dunes: London, Methuen, 265 p. BROCKMAN, GEORGE, 1962, Late cretaceous stratigraphy of western Alabama Masters thesis Univ ersity of Alabama. CoHEN, A. C., ]R. 1955, Censored samples from truncated normal distributions Biometrika, v 42, p 516-519. ---, 1957 On the solution of estimating equations for truncated and censored samples from nornial popula tions : Biometrika, v 44, p 225 236. ---, 1959, Simplified estimators for the normal distribution when samples are singly censored or truncated: Technometrics v 1 p 217-237 ---, 1960, An extension of a truncated Poisson distribution : Biometrics v. 16 p. 446-450. CUR.RAY, J. R., 1961, Tracing sediment masses by grain size modes : XXI International Geological Congress, Report, part 13, p 119-130. DoEGLAS, D J 1946, Interpretation of the results of mechanical analysis : Jour. Sedimentary Petrology, v 16, p. 19-40. . ---., 1955, An exponential function of size frequency distributions of sediments : Geologie en Mijnbouw (nw. ser .), v 18, p. 1-29. EssENWANGER, OsKAR, 1960, Frequency distributions of precipitation: Monograph No.5, American Geophya. ical Union, p. 271-279. FRIEDMAN, G M. 1961, Distinction between dune, beach and river sands from their textural characteristics : jour. Sedimentary Petrology, v 31, p. 514-529. ---, 1962, On sorting, sorting coefficients, and the log-normality of the grain-size distribution of sandstones: jour. Geology v 70, p 737-753. FULLER, A. 0., 1961, Size distribution characteristics of shallow marine sands from the Cape of Good Hope, South Africa : Jour. Sedimentary Petrology, v 31, p. 256-261. ---, 1962, Systemic fractionation of sand in the shallow marine and beach environment off the South African coast: Jour. Sedimentary v. 32, p 602-606. HARJUS, S. A., 1959, The mechanical compositton of some intertidal sands: Jour. Sedimentary Petrology v. 29, p 412-424 . HJULSTRoK, Fn.IP, 1939, Transportation of detritus by mov ing water, in Trask P. D. ed, Recent Marine Sediments-A symposium; Soc. Eco Paleontologists and Mineralogists, Special Publication No. 4, Tulsa, p. 5-31 MASON, C. C AND FoLK R. L ., 1958, Differentiat ion of beach, dune and aeolian tlat environments by size analysis, Mustang Island, Texas: jour. Sedimentary Petrology v. 28, p. 211-226 MIDDLETON, G. V., 1962, On sorting, sorting coefficients, and the log-normality of the grain-size distribution of sandstones: a discussion : Jour. Geology, v 70, p 754-756. TANNER, W. F., 1955 Paleogeographic reconstructions from cross-bedding studies: Am. Assoc. Geologists Bull. v. 39, p 2471-2483 ---, 1958, The zig-zag nature of type I and type IV curves: Jour. Sedimentary Petrology, v 28, p 372-375 ---, 1959, Sample components obtained by the method of differences: Jour. Sedimentary Petrology, v. 29, p. 408-411. 1960a, Possi.ble Gaussian of zig-zag: curves: Ql!antitative Terrain Studies, published by U S. Army Engtneer Waterways Expenment Sta., Vicksb u rg, MlSS.: Part I, No. 5. Lecture Notes 141 James H Ba/sillie

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W. F. Tanner Environ. Clastic Granulometry FGS Course, Feb-Mar, 1995 164 WILLIAM F. TANNER --, 1960b, Filtering in geological sampling: Amer. Statistician, v. 14 no. 5, p 12. --, 1962a, Components of the hypsometriccurve of the earth: Jour. Geophysical Research, v. 67 n. 7, p. 2841-2844. --, 1962b, Upper Cretaceous coast Georgia and Alabama: Georgia Mineral Newsletter; v. 15, nos. 3 4. VAN LIEW, H. D., 1962, Semilogarithmic plots of data which reflect a continuum of exponential processes: Science, v. 138, p. 682-683. VAUSE, J. E., }a., 1957 Submarine geomorphic and sedimentological investigations off part of the Florida pan handle coast: Unpublished M S. thesis, Florida State Univ., Tallahassee --, 1959, Underwater geology and analysis of recent sediments off the northwest Florida coast : Jour. Sedi mentary Petrology, v. 29 p. 555-563. WALGER. E ., 1962, Die Komgrtsssenverteilung von Einzellagen sandiger Sedimente und ihre genetische Bedeutung: Geologische Rundschau v. 51, p 494-506. WASKOM, joHN D., 1957, Quartz grain roundness as an indicator of depositional environments of part of the coast of panhandle Florida: Unpublished M.S. thesis, Florida State University, Tallahassee ---, 1958 Roundness as an indicator of environment along the coast of panhandle Florida: Jour. Sedi mentary Petrology, v. 28, p. 351-360. Lecture Notes 142 James H. Balsillie

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W. F Tanner--Environ. Clastic GranulometryFGS Course, Feb-Mar, 1995 Apfel E. T. 16, 65 Arithmetic Probability 6 Arthur, J D 22, 65 Backwash 36 BAFS 24, 105 Balance accuracy 5 Balsillie, J. H. 8, 43, 65 Bar graph 5, 19, 21 Barrier islands 22, 96 Beach ridges 18, 33, 34 38, 88, 119 Bergman, P. 11, 12, 65 Bivariate plots 24, 104, 117, 128 Brownsville, Tex. 35 Campbell, K. M. 35, 69 Cape San Bias, Fla. 36, 116 Carbonates 63-65 Cayo Costa, Fla. 23, 96 Censorship 54-ff, 138 Cheniers, La. 131 Coefficient of variation 17, 38 Components 1 0 Corpus Christi, Tex. 35 Cumulative graph 6 Demirpolat, S 66, 69 Darss (The), 20, 88 Decomposition 6, 10, 54-ff Denmark 29 Diagrammatic Probability Plots 25, 108 Differences, Method of 59-63 Doeglas, D.J., 10, 66, 135 Dog Island, Fla. 30 Elsner, H. 21, 88 Eolian hump 8, 19, 22, 26 Filtering 54-ff, 139 Florida coast 29 Florida offshore 22, 117 Florida shelf 22, 117 Lecture Notes INDEX 143 Fluvial tail 8 Fogiel, M. 66,84 Friedman, G. M., and Sanders, J. E. 15, 66, 104 Froude Number 36 Gauss, K.F. 6 Gaussian 6, 7, 9 GRAN-7 17 Granule 3 GRANULO 17 Granulometry, definintion 1 Graphic measures 17 Great Sand Dunes Colo 17-19, 37, 39-41 Gulf of Mexico, sediments 22 Higher moments 14, 132 Hobson, R. D. 4, 11, 66 Hurricanes (see Storms) 31, 43-44 Hydrodynamics 28 Indian mounds, Fla. 22 Inter-Society Grain Size Study Committee 4,68 Island nuclei, Fla. 22, 96 Johnson Shoal, Fla. 23, 96 Karman, von, T. 11 Kattegat (Europe) 29 Kurtosis 9, 13, 25, 28-31, 35, 38, 50, 53,84,104,129 Lacustrine 35 Lakes 35 Laguna Madre, Tex. 31 Leptokurtic 9 Line segments 6, 8, 9 Louisiana 131 Medano Creek, Colo. 37, 116 James H Ba/sil/ie

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W. F. TannerEnviron. Clastic GranulometryFGS Course, Feb-Mar, 1995 Method of differences 59-63 Mixing 54-ff, 135 Moment measures 12-15, 84 Moments 12-15, 84 Moments, higher 14, 132 North Sea 29 Nuclei, island 22, 96 NUST 104 Oklahoma 53, 122 Otto, G. H. 16, 66 Paleogeography 53 Particle size 3-4 Pennsylvanian age sandstone 53, 122 Phi scale 3 Platykurtic 9 Price, W. A. 35 Probability plot 6, 19, 21, 26, 104, 108 "Railroad Embankment, Fla. 44, 45 Relative dispersion 17, 38 Reynolds Number 36 Rio de Janeiro, Brazil 53 Rizk, F. 22, 31,66 RSA 11 Sample collecting 76 Sample size 5, 72, 76, 80 Sample splitting 5, 72, 76, 80 Sample suites 16, 23, 36 Sanibel Island, Fla. 30 Savage, R. P. 8, 66 Sea level change 32-36,50,54 Sedimentology, definition 1 Sedimentation unit 1 6 Segment analysis 26, 27, 129 Segments, line 6, 8, 9 Selection 54-ff, 1 38 Settling 11 Settling tail 8 Settling tube 17, 72 Sieve interval 5, 80 Sieving 11 80 Sieving time 5, 72 Sixth Moment Measure 132 Lecture Notes 144 Skewness 9, 13, 25, 38, 84, 106, 120, 128 Skewness vs kurtosis 25, 1 06, 120, 129 Sorting 7 Splitting 5, 72 Splitting error 5 Standard deviation 9, 13 St. Joseph Peninsula, Fla. 34, 39 St. Vincent lsi., Fla. 18, 33, 38, 40-47, 111,119 Storm (see Hurricane) 39, 43-44 Storm ridge, Fla. 34, 39, 42, 43 Suite samples 16, 23, 36 Suite statistics 23-ff, 36, 1 02, 116 SUITES 39 I 40-50 Surf break 8, 19, 21, 22, 26 Tail of fines 17, 24, 26, 37, 104 Time series 17, 1 8 Truncation 54-ff, 138 Ul'st, V. G. 21, 69, 88, 93 Uniformity Principal, corollaries 2 Uprush 36 Variability plot 24, 117, 128 Variance 13 von Karman, T. 11 Vortex trail 11 Wave energy 29-32 Wentworth scale 3 Yeso Formation (N. Mex.) 123 Zenkovich, V. P. 21 Zero-component 59 Z-test 45, 46, 51, 52 James H. Balsillie

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FLORIDA GEOLOGICAL SURVEY 903 WEST TENNESSEE STREET TALLAHASSEE, FLORIDA 32304-7700 Telephone: (904) 488-9380 FAX: (904) 488-8086 Walter Schmidt, Chief and S t ate Geologist Sandie Ray, Administrative Assistant Jessie Hawkins Custodian Deborah Mekeel, Librarian Cindy Collier, Admin i strative Secretary GEOLOGICAL INVESTIGATIONS SECTION Thomas M. Scott, Assistant State Geologist Jon Arthur, Petrolog ist Martin Balinsky, Research Assistant Jim Balsillie Coastal Engineering Geologist Paulette Bond, Geochemist Jennifer Branch, Research Assistant Ken Campbell, Sed imentologist Joel Duncan, Sed i mentary Pet rologist Rick Green, Research Assistant Mark Groszos Research Assistant Alex Howell, Research Assistant Jim Jones, Engi neer Lance Johnson, Res earch Assistant Ted Kiper Engi neer Dar l ene Lasalde, Secretary Specialist Li Li, Research Assistant Tom Miller, Rese arch Assistant John Morrill, Driller Steve Palms, Research Assistant Jim Trindell, Assistant Driller Frank Rupert Paleontologist Lorene Whitecross Research Assistant MINERAL RESOURCE INVESTIGATIONS AND ENVIRONMENTAL GEOLOGY SECTION Jacqueline M. Lloyd, Assistant State Geologist Joe Aylor, Research Assistant Henry Freedenberg, Environmental Geologist Cliff Hendrickson, Research Assistant Ron Hoenstine, Environmental Geologist L. Jim Ladner, Coastal Geo l ogist Ed Lane, Environmental Geologist Steve Spencer, Economic Geologist Candy Trimble Research Assistant Holly Williams Research Assistant Zi-Qiang Chen, Research Assistant OIL AND GAS SECTION L. David Curry, Administrator Robert Caughey, D istrict Coordinator Ed Gambrell, District Coordinator Ed Garrett, Geologist Don Hargrove, Engineer Evelyn Jordan, Sec r etary Carleen Jones Secretary Becky Wilkes Secretary

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