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
QE
99
.A341
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 00850640
iv
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 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.) interdisciplinaryInterSociety 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 hardpressed
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 FebruaryMarch, 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, FebMar, 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 37050204429) entitled the Florida Coastal Wetlands Study, and
between the FGS and the Minerals Management Service (agreement number 37050204
422) entitled the EastCentral 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
grainsize analysis, Sedimentology, v. 27, p. 231232,
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. 9094,
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. 156164,
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. 1940.
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. 225236,
and:
Tanner, W. F., 1991, Application of suite statistics to stratigraphy and sealevel
changes: [In] Principles, Methods and Application of Particle Size
Analysis, (J. P. M. Syvitski, ed.), Cambridge University Press,
Cambridge, p. 283292.
Lecture Notes James H. Ba/si/lie
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 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, FebMar, 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 .....
SettlingEolianLittoralFluvia
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 TRANSPODEPOSITIO
The Sediment Sample and Samplini
Suite Pattern Sampling ........
The GRAN7. 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) TranspoDepositional
ication ....................
and Plot Decompositi........
NAL ENVIRONMENTS..........
Unit.......................
es, central Colo .............
d, Florida..................
rss..........................
e Offshore Data..........................
S(SELF) TranspoDeposit 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, FebMar, 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 ShortTerm Hurricane Impacts ......... 31
Kurtosis and LongTerm Sea Level Changes ..................... 32
St. Vincent Island, Florida, Beach Ridge Plain .............. 33
St. Joseph Peninsula Storm Ridge ....................... 34
Beach Ridge Formation FairWeather or Storm Deposits? ........... 34
Texas Barrier Island Study Conversation with W. Armstrong
Price .......................................35
TranspoDepositional 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 SeaLevel 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, FebMar, 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 .....................................
NonZero 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, FebMar, 1995
INDEX ........................................ ........143
APPENDICES
Appendix I. Little Known But Important Papers on GrainSize 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 SeaLevel
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, FebMar, 1995
Lecture Notes xii James H. Balsilile
Lecture Notes
xii
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry FGS Course, FebMar, 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 sandsized material.
At the outset, it is important to understand that the majority, perhaps 90% or more,
of sandsized 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, FebMar, 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 dayandage 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, FebMar, 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 nonlinear progression (square or squareroot 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. nomenclaturesize 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 sandsized 2.00 1.00
particles, or in the case of the Wentworth 1.68 0.75 very
Scale sand and granulesized 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 mineralladen 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, FebMar, 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 handheld calculator, are given by:
S= 1.442695 In d(mm)
and
d(mm) = INV In (0.69315 4) = e0o.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. InterSociety 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) Evenlyspaced division points, facilitating
ANALYTICAL plotting.
CONSIDERATIONS (2) Geometric basis, allowing equally close
inspection of all parts of the size spectrum.
Sandsized 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) Phisize 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, FebMar, 1995
Tanner has analytical results for over 11,000samples from a multitude of transpodepositional
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 30minutes 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 1/4phi 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, FebMar, 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 sandsized siliciclastic
samples are comprised of multiple line
99.9% segments (Figure 4). Each segment, in
fact, commonly represents a different
transpodepositionalprocess 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, FebMar, 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 sandsized range
response that analytical granulometric
results are allowed to become Gaussian.
Hence, transpodepositional 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
1/40 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, FebMar, 1995
Sett nEolanLittoralFuvial (SELF) TranspoDeposiional 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 transpodepositional force element is wave activity; point
a, relative to segment E, is termed the surfbreak. 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 sandsized material,
the surfbreak normally appears for low to moderateenergy wave climates. For
highenergy waves, point a moves off the graph (to the left) and segment B
disappears (i.e., the wave energy is overpowering even to the coarsest sandsized
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, FebMar, 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 flattopped
(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, FebMar, 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 midlevel 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. 1940
FIGs. 130, 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. Wellsorted 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, Sand Ttypes 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, FebMar, 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 twodimensional. For a grain
falling in water it is threedimensional. 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
laboratorytolaboratory. 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, FebMar, 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, FebMar, 1995
transcendental progression of the form:
M, Ax mly
mra=
n1
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
n1
I(x m,)3
m =
n1
and
4 f(x m,)4
n1
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, FebMar, 1995
of Figure 15. The figure illustrates that the higher moment measures are zero near the center
of the distribution, whereas nonzero values appear only as the tails of the distribution are
approached.
This is MOMDEMO. Data source: Keyboard.. SampleTVER X46. 02061995
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 8.999999E03
.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
ni
fn m,
m n
n1
Sf(xm,)7
n1
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, FebMar, 1995
Sf (x mr)
m 
n1
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 2way 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 1Way 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, FebMar, 1995
DETERMINING TRANSPODEPOSITIONAL 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 transpodepositional 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 overandover 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, FebMar, 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. Multilevel,
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 crossbedded 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 GRAN7 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 GRAN7 program is based on a program that James P.
May wrote a number of years ago called GRANULO. GRAN7 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 GRAN7 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, FebMar, 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 GRAN7. The data source is kirkgsd.dt$.
Panel 1
02241995
This is GRAN7. File: kirkgsd.dt$. Sample: M09. Table of raw data:
MidPt(phi)
.625
.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
PAN
MidPt(phi)
Sieve(phi)
.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
Sieve (phi)
Wt. (g.)
.018
.397
4.059
15.989
16.016
19.894
16.369
14.007
8.514
2.766
1.514
.351
.071
.013
.025
Wt. (g.)
CumWt(g.)
.018
.415
4.474
20.463
36.479
56.373
72.742
86.74901
95.26301
98.02901
99.54301
99.894
99.965
99.978
100.003
CumWt(g.)
Wt(Dec.)
.00017
.00396
.04058
.15988
.16015
.19893
.16368
.14006
.08513
.02765
.01513
.0035
.0007
.00012
.0002
Wt(Dec.)
Cum.Wt(D)
.00017
.00414
.04473
.20462
.36477
.56371
.72739
.86746
.9526
.98026
.9954
.9989
.99961
.99974
.9999
Cum.Wt(D)
Cumulative weight, including pan (if any): 100.003 grams.
Panel 2
Results calculated by GRAN7. File: kirkgsd.dt$. Sample: M09
Several versions are given below, with the pan fraction either
omitted, or located at different places on the phi scale. A
widelyused 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 GRAN7 for sample M09 from
the Great Sand Dunes, central Colorado.
Lecture Notes
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry FGS Course, FebMar, 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: kirkgsd.dt$. Sample; M09
left shows screen sizes, not midpoints, in Phi.
20 30 40 50 60 %
+
+
20 30 40 50 60 %
left shows screen sizes, not midpoints, in Phi.
PAN
Panel 4
Next: Probability (decimal wt. vs Phi size). File: kirkgsd.dt$.
The column on the left shows screen sizes, not midpoints, in Phi.
0.1 1 2 5 10 20 30 50 70 80 90 95 98 99
: : : : : ~:: : :
Sample: M09
99.9 %
Eolian Hump
PAN
0.1 1 2 5 10 20 30 50 70 80 90 95 98 99 99.9
This is GRAN7.
Coarsest sieve:
Sieve interval: .25 File: kirkgsd.dt$. Sample: M09
.75 phi. Pan contents (g., %): .025 .0002
Figure 17. (cont.)
particularly good for a mature beach sand. Mature beaches have ao values of from 0.30 to
0.50 0; the lowest ao value WFT has seen is about 0.260.
The cumulative probability plot of panel 4 shows the surfbreak. The surfbreak
inflection point moves with time ... the plot, therefore, is a snapshot in the history of the
evolution of the sample. With high enough wave energy or with sufficient time, the inflection
point will move to the left and off the plot. Note, also, that there is a tail of fines. Hence, the
sample is one reflecting low wave energy. The surfbreak occurs at about 4.5% with the
settling curve comprised of less than 1 % of the sample. Hence, we are looking at only about
5% of the sample. By looking at a multitude of samples we can attempt to clarify our
James H. Balsillie
Lecture Notes
W. F. Tanner Environ. Clastic Granulometry  FGS Course, FebMar, 1995
interpretations.
Example 3: The German Darss
The Darss, a German federal nature preserve, is located in Germany fronting on the
Baltic sea, just to the east of the old EastWest German border. It is attractive to study
because it is not subject to open Atlantic Ocean waves. A series of 120 to 200 ridges
comprise the plain, although it is not possible to count all the ridges because wind work has
been pervasive. The feature has been interpreted by many investigators (20) to represent
I .
This is GRAN7.
This is GRAN7.
MidPt(phi) Si
.375 .5
.625 .7
.875 1
1.125 1.
1.375 1.
1.625 1.
1.875 2
2.125 2.
2.375 2.
2.625 2.
2.875 3
3.125 3.
3.375 3.
3.625 3.
3.875 4
4.125 4.;
MidPt(phi) Si
The data source is stvwei.dt$.
File: stvwei.dt$.
eve (phi)
5
25
5
75
25
5
75
25
5
75
25
eve (phi)
Wt. (g.)
.021
.146
.348
1.003
3.543
8.487
10.821
13.819
7.208
3.383
1.579
.311
.066
.017
.013
.034
Wt. (g.)
Panel I
Sample: Centr.16.
CumWt(g.)
.021
.167
.515
1.518
5.061
13.548
24.369
38.188
45.396
48.779
50.358
50.669
50.735
50.752
50.765
50.799
CumWt(g.)
02241995
Table of raw data:
Wt(Dec.)
.00041
.00287
.00685
.01974
.06974
.16707
.21301
.27203
.14189
.06659
.03108
.00612
.00129
.00033
.00025
.00066
Wt(Dec.)
Cum.Wt(D)
.00041
.00328
.01013
.02988
.09962
.26669
.47971
.75174
.89363
.96023
.99131
.99744
.99874
.99907
.99933
1
Cum.Wt (D)
Cumulative weight, including pan (if any): 50.799 grams.
Panel 2
Results calculated by GRAN7. File: stvwei.dt$. Sample: Centr.16
Several versions are given below, with the pan fraction either
omitted, or located at different places on the phi scale. A
widelyused 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 GRAN7 for sample Centr. 16
from St. Vincent Island, Roida.
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry FGS Course, FebMar, 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: stvwei.dt$. Sample; Centr.16
sizes, not midpoints, in Phi.
40 50 60 %
20 30 40 50 60 %
left shows screen sizes, not midpoints, in Phi.
PAN
Panel 4
Next: Proba
Centr.16
The column
0.1
ability
(decimal wt. vs Phi size). File: stvwei.dt$. Sample:
on the left shows screen sizes, not midpoints, in Phi.
1 2 5 10 20 30 50 70 80 90 95 98 99
99.9 %
SurfBreak
PAN
0.1 1 2 5 10 20 30 50 70 80 90 95 98 99 99.9 %
This is GRAN7. Sieve interval: .25 File: stvwei.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 lowangle, fairweather, beach
type crossbedding 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, FebMar, 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 surfbreak. 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 surfbreak 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 surfbreak 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 surfbreak. The mounds probably represent marine terrace
deposits reworked by eolian processes. That is, some degree of eolian reworking may not
always destroy the surfbreak 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 nonnuclei sediments. Hence, the sorting of the younger nonnuclei 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, FebMar, 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, FebMar, 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 TUE
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 tailoffnes diagram. The means
mature beach and nearshore 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 "lastprevious" agency, but not
The Vanabity Diagram: [ Appendix VII, p. 105, the final one.
figure 16.2]. Figure 19. Tagofines 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 lowerleft to upperright 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, FebMar, 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 welldeveloped 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 35 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 tailoffines 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 transpodepositional
mechanism above.
James H. Balsillie
Lecture Notes
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 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 razorsharp 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 transpodepositional 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, straightline 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, FebMar, 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 straightline 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 GlacialFluvial Deposit
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 1995
S Settling Basin
U Unknown
The stratigraphic column, both the target and nontarget 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 nonrecognizable 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.
Crossplots, 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 downslope 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 sandsized range. If we take our
clue from Doeglas and what we have learned about the tails of the sandsized 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, longterm sea level rise, seasonal changes, and
shortterm storm tide and wave impact events.
Lecture Notes James H. Balsillie
Lecture Notes
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry FGS Course, FebMar, 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, FebMar, 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, FebMar, 1995
divergence or "drift divide" near the eastern central portion of the island (Figure 28). A
combination refractionlongshore 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.
Fortyfour 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 lagoonside 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 highenergy
processes, as is indicated by the lower kurtosis.
Kurtosis versus Seasonal and ShortTerm 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, FebMar, 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 shoreincident storms or hurricanes, not only produce exceptionally high
waves, but also storm tides (which being a superelevated 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 LongTerm 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 shorepropagating 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 depthlimited. 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 shorebreaking (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 presea level drop case let us suppose that waves begin to
experience bed drag at point A. There is, then, the distance aA over which the waves will
attenuate to eventually shorebreak 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 bB, a
distance that is much greater C Near
Coast Beach Shore ( Offshore
than distance aA. 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 PreSeaLel 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, FebMar, 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 aA for
the prerise sea level is longer
than for the bB distance b Hbb 8
following sea level rise. a ba A
Moreover, shorebreaking wave
heights Hbb will be larger than
Hba.
If we have learned our
lessons from previous PreSea 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, FebMar, 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 3,000year
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 FairWeather 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, FebMar, 1995
outcomes. Beach ridges are, with rare exceptions, fairweather 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 shorebreaking 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 rechecked 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 stormproduced.
TranspoDepositional Energy Levels and the Kurtosis; and an Explanation:
From the preceding examples we can 100
draw some general conclusions. In general,
kurtosis and transpodepositional 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 [El] 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 sandsized 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 shorepropagating 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, FebMar, 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 FriedmanSanders 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
sampletosample within the sample suite. If the same level of energy of a force element (e.g.,
waves) is the same dayafterdayafterday, 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 multistory 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 SeaLevel 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, FebMar, 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 crosssection 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 noncoastal 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 TailofFines 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, FebMar, 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 3point 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, FebMar, 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 GRAN7 ... when
the results are tallied, have never resulted in a tie between transpodepositional 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 GRAN7 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 tailoffines. 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,
glacialfluvial 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 glaciofluvial (GLF). A
capital X signifies assured environmental identification of the transpodepositional
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 shorebreaking storm wave activity. W. F. Tanner,
however, resampled (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 GRAN7 contained 5 parameters with the pan fraction
James H. Balsillie
Lecture Notes
W. F. Tanner Environ. Clastic Granulometry FGS Course, FebMar, 1995
This is SUITES. Data source: kirkgsd.7p5. No. of Samples: 21 02241995
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: kirkgsd.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
T01
T02
T03
T04
T05
T06
T07
M08
M09
M10
M11
M12
M13
M14
B15
B16
B17
B18
B19
B20
B21
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, FebMar, 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 4phisieveandfiner.
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 kirkgsd.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 SINGLEX lines and their site meanings. NOTE that the
TailofFines tends to identify the lastprevious agency.
For best results, plot numerical data by hand on proper bivariate charts.
MB=Mature Bch; Sett=Settling (Closed Basin); Tflat=Tidal Flat; GLF=GlacioFluv.
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 TailsofFines: X
StdDev of TailofFines: X
TailofFines diagram: X
Inverted RelDisp (Sk vs K; Min. usefulness): x
Eolian hump (definitive!): X
This is SUITES. Data source: kirkgsd.7p5.
The End.
N 21 1 to 21 02241995
Figure 36. (cont.)
Lectue Noes Jmes H Ba/i/li
Lecture Notes
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry FGS Course, FebMar, 1995
This is SUITES. Data source: stormrdg.5p5. No. of Samples: 21 02271995
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
SJ8920
SJ8921
SJ8922
SJ8923
SJ8924
SJ8925
SJ8926
SJ8927
SJ8928
SJ8929
SJ8930
SJ8931
SJ8932
SJ8933
SJ8934
SJ8935
SJ8936
SJ8937
SJ8938
SJ8939
SJ8940
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, FebMar, 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 4phisieveandfiner.
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 SINGLEX lines and their site meanings. NOTE that the
TailofFines tends to identify the lastprevious agency.
For best results, plot numerical data by hand on proper bivariate charts.
MB=Mature Bch; Sett=Settling (Closed Basin); Tflat=Tidal Flat; GLF=GlacioFluv.
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 TailsofFines: X
StdDev. of TailofFines: X
TailofFines diagram: X
The Storm Ridge on St. Joseph Peninsula, FL. Tall ridge.
This is SUITES. Data source: stormrdg.5p5. N = 21 1 to 21 02271995
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. 3334) found from 249 first quadrant (in terms of event impact)
Lecture Notes
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry  FGS Course, FebMar, 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 subparallel, lowangle, crossbedding planes sloping
6 to 8 degrees down in the seaward direction. It, again, shows good homogeneity (Figure 38)
This is SUITES. Data source: rremb$.5p5. No. of Samples: 11 03011995
This program produces suite, or group, statistics for a suite, or set, of
samples, presumably all representing the same depositional environment.
Panel 1
Tabulation of data:
Sample
RR1
RR2
RR3
RR4
RR9
RR13
RR19
RR20
RR7n
RR6n
RR3n
Sample
Mean Std.Dev. Skewness Kurtosis 5thM.M. 6thM.M. T.of F.
2.782
2.583
2.158
2.703
2.463
2.545
2.422
2.583
2.195
2.262
2.44
Mean
.32
.389
.473
.333
.375
.325
.382
.353
.434
.398
.341
Std.Dev.
.211
.176
.113
.163
.093
.128
.018
.128
.204
.201
.172
Skewness
3.882
3.177
2.416
3.117
3.523
3.461
3.196
3.24
3.1
3.414
3.52
Kurtosis
1
1
1
1
1
5thM.M.
1
1
1
1
1
1
1
1
1
1
1
6thM.M.
0
.0001
.0001
0
.0001
.0001
.00001
0
.0001
.0001
.0001
T.of F.
Panel 2
Suite homogeneity, in terms of departures of sample means and
standard deviations from the suite mean values (of means & std.devs.)
as an evaluation of uniformity. Crosses represent numbers on far right.
Mean and Std. Dev. of Means: 2.466 .191 and of Std.Devs.: .374 .045
Dep.of Std.D.
.098
.059
.023
.014
.007
0
.022
.034
.042
.05
.055
Dep.of Std.D.
Dep. of Mean
.309
.273
.204
.115
.046
.005
.115
.028
.236
.078
.314
Dep. of Mean
Evaluation of homogeneity. Crosses represent numbers on far right.
Outliers, if any, should be obvious. Data Source: rremb$.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, FebMar, 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 4phisieveandfiner.
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 rremb$.5p5. N= 11 Samples, 1 to 11
Means Std.Dev. Skewn. Kurtos. 5th.M.M. 6th.M.M. T.Fines
Mean of the: 2.466 .374 .126 3.276 0 0 0
Stnd. .Dev.: .191 .045 .092 .35 0 0 0
Skewness: .134 .731 1.481 .82 0 0 .577
Kurtosis: 2.02 2.654 4.295 4.16 0 0 1.343
Fifth Mom.: .277 4.131 10.234 6.667 0 0 1.372
Sixth Mom.: 4.657 10.105 26.508 22.244 0 0 2.175
Rel.Disp.: .077 .121 .74 .107 0 0 .727
Invrtd.R.D.: 12.901 8.235 1.353 9.338 0 0 1.374
StdDev/Ku. = .114 Kurt./Mean = 1.328 .
T.of F. Mns & StdDevs as Percent: 0 ; 0
Mn & StdDev of Mn/Ku & of SD/Ku: .752 .071 .114 .029
The Relative Dispersion (or Coefficient of Variation) is the
Standard Deviation divided by the Mean.
Panel 4
The primary use of the next display is to minimize the weight of certain
interpretations (e.g., no X's). Of those that are left, a single line
with 2 X's must not be taken to demonstrate either one alone; FIRST,
identify SINGLEX lines and their site meanings. NOTE that the
TailofFines tends to identify the lastprevious agency.
For best results, plot numerical data by hand on proper bivariate charts.
MB=Mature Bch; SettSettling (Closed Basin); Tflat=Tidal Flat; GLF=GlacioFluv.
Parameter (below) Environment: Dune MB Riv Sett TFlat GLF
Procedures giving 1 or 2 answers: . . . . .
Mean of the Skewness: x x
Variability diagram: x x
Procedures generally giving one answer: . . .
RelDisMn vs RelDisStdDev: X
Mean of the TailsofFines: X
StdDev. of TailofFines: X
TailofFines diagram: X
Inverted RelDisp (Sk vs K; Min. usefulness: x
Railroad Embankment, near Cape San Blas, FL. Tall. ridge
This is SUITES. Data source: rremb$.5p5. N = 11 1 to 11 03011995
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 surfbreak which was not interactively logged in the SUITES data
entry section.] The Railroad Embankment is a fairweather swash/runup deposit, or beach
ridge.
The Storm Ridge versus the Railroad Embankment and the ZTest.
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, FebMar, 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 ZTest are listed
in Table 6. The ZTest 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 (RREMB$.5P5). Input data are listed under the heading "summary of means and
standard deviations". The column with the header "Z VALUE" lists the Z value results; the
larger the Z value, the greater the statistical difference between averages tested. Exceedence
probability and significance of the ZTest results are shown by the Z and P rows near the
bottom of the table. Moment measures for a, p, and the tailoffines (T of F) are significantly
different to the less than 0.00005 confidence level, K is significantly different to less than the
0.05 confidence level. Hence, the two deposits are not the same.
Table 6. ZTest for the Storm Ridge (STORMRDG.5P5) and Railroad
Embankment (RREMB$.5P5) deposits of Gulf County, Florida.
This is ZTEST Data sources: STORMRDG.5P5. RREMB$.5P5 N = 21 11
Summary of means andstandard deviations:
File Mn and SD, STORMRDG.5P5. File Mn and SD, RREMBS.5P5.
Variable 1: A 2.056429 .1085852 2.466909 .1912094
Variable 2: o .3134762 3.138014E02 .3748182 4.551521E02
Variable 3: Sk .0224762 .1067845 .1255455 9.283353E02
Variable 4: K 3.521572 .3742375 3.27691 .3508905
Variable 5:TofF 2.080952E04 6.751506E05 6.454546E05
4.697459E05
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 6.233131E02 30
Second Variable: o 3.999623 1.533693E02 30
Third Variable: Sk 4.064234 3.642056E02 30
Fourth Variable: K 1.830617 .13365 30
Fifth Variable: T. of F. 7.024088 2.043679305 30
If the degrees of freedom > 25to30, then largesample 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 ZTEST. Sources: STORMBDG.5P5, RREMBS.5P5 02151995. 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, FebMar, 1995
This is SUITES. Data source: stvinak.4p5. No. of Samples: 59 03011995
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, FebMar, 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: stvinak.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, FebMar, 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 4phisieveandfiner.
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 stvinak.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 SINGLEX lines and their site meanings. NOTE that the
TailofFines tends to identify the lastprevious agency.
For best results, plot numerical data by hand on proper bivariate charts.
MB=Mature Bch; Sett=Settling (Closed Basin); Tflat=Tidal Flat; GLF=GlacioFluv.
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 TailsofFines:
StdDev. of TailofFines:
TailofFines 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: stvinak.4p5. N = 59 1 to 59 03011995
The End.
Figure 39. (cont.)
suite of samples represents a mature beach deposit. The majority of probability plots did show
the surfbreak, although it was not interactively so noted in the SUITES program.
The relationship between 1/K and relatively small sea level changes (12 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, FebMar, 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.
GrMnSD/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)
GrMnSD/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: 08031990. 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, sealevel changes.
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 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 ZTest 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 3277
Suite Statistics in
Following
Order: A
Sk
K
GULF OF MEXICO
St Joseph Peninsula
Apalachicola Bay
I I
Figure 41. Ztest 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 Ztest; 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, FebMar, 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. ZTest 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 ZTEST 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 7.652164E02
Variable 2: o .388718 3.638637E02 .4141539 2.594015E02
Variable 3: Sk .1130769 8.397658E02 6.907693E02 .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 9.257903E03 50
Third Variable: Sk .8499909 5.176528E02 50
Fourth Variable: K 3.784773 .1964417 50
If the degrees of freedom > 25to30, then largesample 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 ZTEST Sources: STVIN.4EE, CLARK.5P5 10241989. 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 timetotime, 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 latitudelongitude.
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 1995
2. Paleogeography:
Granulometric suite OPEN SEA
statistics and the inherent Noncrossbedded alternating shales.
variability within is nds & limestone > 100 marine
variability within is invertebrate species
correlative with
paleogeographic evidence. ARRIE
For instance, Tanner ISLAND H crossbeddedsandsupto
(1o988, d ontrabbles, several species of fresh water
(1 988), demonstrated the gastropods, microfossils, 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 ( Finegrained sediments, approx 12
42). nonmarine 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 ZTest.
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, FebMar, 1995
that little, if any, sand is escaping from beachtobeach in the longshore direction.
6. Sea Level Rise:
Kurtosis correlates inversely with even small changes in sea level (rise and fall). This
applies to longterm 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 zigzag 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. Multisegmented, zigzag, or multicomponent
sand distributions have been discussed by a multitude of investigators. However, in a series
of papers, Tanner (1964; Appendix X, p. 134) found that zigzag modifications of the straight
line plot include mixing and selection which, in turn, can be subdivided as follows:
Mixing: Nonzero 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, FebMar, 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).
NonZero 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 twocomponent
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, FebMar, 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 twodimensional
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 pingpong 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 threecomponent
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, FebMar, 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 1/4phi 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, FebMar, 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 1/4phi classes, or for a Phi, to
number of missing items (i.e., n number of
sand grains within a 1/4phi 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 
anderror 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 straightline probability
Lecture~ Notes Jmes H. alsilli
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 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, FebMar, 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 1/4phi 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, FebMar, 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, FebMar, 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 trialanderror 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, FebMar, 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 = 4T3B B = (4T A)/3
xaxis] 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 = 4T3B 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 = 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 < 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 = 4T3B 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, FebMar, 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 resieve 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 (dashdot
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 twosegment 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, FebMar, 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 reprecipitated. 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 plateshaped particles significantly change the hydrodynamic response of the
quartz particles. Platy particles exhibit significant lateral movement when settling in water.
Consequently, the grainsize 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.
6778.
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, Poststorm report: Hurricane Elena of 29 August to 2 September 1985:
Florida Department of Natural Resources, Beaches and Shores PostStorm Report No.
852, 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, FebMar, 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. 17181731.
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 bedmaterial sampling: Journal of Hydraulic Research,
v. 8, p. 523534.
Doeglas, D. J., 1946, Interpretation of the results of mechanical analyses: Journal of
Sedimentary Petrology, v. 16, no. 1, p. 1940.
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 beachfill evaluation: U. S. Army Corps
of Engineers, Coastal Engineering Research Center, Washington, D. C., Technical Paper
No. 776, 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. 165172.
Neale, J. M., 1980, A sedimentological study of the Gulf Coasts of CayoCosta 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. 569582.
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, Prehurricane vs. posthurricane beach sand:
Proceedings of the 7th Symposium on Coastal Sedimentology, (W. F. Tanner, ed.),
Department of Geology, Florida State University, Tallahassee, FL, p. 129142.
Savage, R. P., 1958, Wave runup on roughened and permeable slopes: Transactions of the
American Society of Civil Engineers, v. 124, paper no. 3003, p. 852870.
Lecture Notes
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry  FGS Course, FebMar, 1995
Socci, A., and Tanner, W. F., 1980, Little known but important papers on grainsize analysis:
Sedimentology, v. 27, p. 231232.
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. 926931.
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. 3567.
Sternberg, H., 1875, Untersuchungen Ober LAngen und Querprofil geschiebef0hrende FlOsse:
Zeitschrift Bauwesen, v. 25, p. 483506.
Tanner, W. F., 1959a, Examples of departure from the Gaussian in geomorphic analysis:
American Journal of Science, v. 257, p. 458460.
1959b, Sample components obtained by the method of differences: Journal of
Sedimentary Petrology, v. 29, p. 408411.
_, 1959c, Possible Gaussian components of zigzag curves: Bulletin of the
Geological Society of America, v. 70, p. 18131814.
,__ 1960a, Florida coastal classification: Transactions of the Gulf Coast Association
of Geological Societies, v. 10, p. 259266.
1960b, Numerical comparison of geomorphic samples: Science, v. 131, p.
15251526.
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. 28412844.
1963, Detachment of Gaussian components from zigzag curves: Journal of
Applied Meteorology, v. 2, p. 119121.
1964, Modification of sediment size distributions: Journal of Sedimentary
Petrology, p. 34, p. 156164.
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, FebMar, 1995
1971, Numerical estimates of ancient waves, water depth and fetch:
Sedimentology, v. 16, p. 7188.
1978, Grainsize studies: [In] Encyclopedia of Sedimentology, (R. W. Fairbridge
and Joanne Bourgeois, eds.), Dowden, Hutchinson and Ross, p. 376382.
,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. 114117.
1982b, High marine terraces of MioPliocene 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] NearShore
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. 6266.
1990a, Origin of barrier islands on sandy coasts: Transactions of the Gulf Coast
Association of Geological Societies: v. 40, p. 819823.
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.4150.
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. 225236.
1991 b, Application of suite statistics to stratigraphy and sealevel changes: [In]
Principles, Methods and Application of Particle Size Analysis, (J. P. M. Syvitski, ed.),
Cambridge University Press, Cambridge, p. 283292.
1992a, 3000 years of sea level change: Bulletin of the American Meteorological
Society, v. 83, p. 297303.
Lecture Notes
James H. Balsillie
W. F. Tanner Environ. Clastic Granulometry FGS Course, FebMar, 1995
1992b, Late Holocene sealevel changes from grainsize data: evidence from the
Gulf of Mexico: The Holocene, v. 2,p. 258263.
1992c, Detailed Holocene sea level cuve, northern Denmark: Proceedings of the
International Coastal Congress Kiel '92, p. 748757.
1993a, An 8000year record of sealevel change from grainsize parameters: data
from beach ridges in Denmark: The Holocene, v. 3, p. 220231.
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. 7184.
1993c, Louisiana cheniers: settling from high water: Transactions of the Gulf
Coast Association of Geological Societies, v. 43, p. 391397.
1994, The Darss: Coastal Research, v. 11, no. 3, p. 16.
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. 367373.
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. 377392.
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, FebMar, 1995
NOTES
Lecture Notes JamesH. Balsilli
James H. Balsillie
Lecture Notes
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 1995
Appendix I
Socci, A., and Tanner, W. F., 1980, Little known but important papers on
grainsize analysis: Sedimentology, v. 27, p. 231232.
[Reprinted with permission]
Lecture Notes James H. Ba/si/lie
James H. Balsillie
Lecture Notes
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 1995
Srdimentology (1980) 27. 231232
SHORT COMMUNICATION
Little known but important papers on grainsize 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 sievevssettling 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 (4050 g, after no more than one split).
The most practical aspect of Mizutani's paper, in
00340746/80/04000231 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 05 mm
diameter (84% of the sample is finer than 05 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 60100 g (or, in rare cases,
where two successive splits must be taken, regardless
of the error introduced, 120200 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 II Balihi
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry FGS Course, FebMar, 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 everincreasing 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.
299312. 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. McGrawHill, New York. 508 pp.
MIZUTANI, S. (1963) A theoretical and experimental
consideration on the accuracy of sieving analysis.
J. Earth Sci. Nagoya. Japan. 11, 127.
PETTIOHN, F.J. (1975) Sedimentary Rocks. Harper and
Row, New York. 628 pp.
PrlruoHN, FJ.. PoTTER, P.E. & SIEvER, R. (1972)
Sand and Sandstone. SpringerVerlag, 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 bedmaterial
sampling. J. Hydrand. Res. 8, 523534.
(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, FebMar, 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, FebMar, 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 halfway position.
7. Dig to a depth of about 3040 cm.
8. Use a spatula to collect a laminar sample, or nearlylaminar 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 ziploc bag (heavy duty); put sample number on highadhesion
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, FebMar, 1995
12. Clean cup thoroughly after collecting each sample. No single grain of sand, from
one sample, should be allowed to contaminate the grainsize 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 halfway 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 halfway 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, FebMar, 1995
NOTES
Lecture Notes James H. Ba/si/lie
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry FGS Course, FebMar, 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, FebMar, 1995
Laboratory Analysis of Sand Samples
In North America sieve nests are everywhere standardized and comprised of halfheight
U. S. Standard sieves, 8 inches in diameter.
The initial sample should be 4560 grams. If it is 80120 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 4550 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
ultrasound. Normally, clay and/or very fine silt, up to about 1520% of the total, can be
handled, more or less satisfactorily, in the sieving process. However, one gets more accurate
results by separating the clayandfinesilt 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 siltandfineclay 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 graintograin 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 8inchdiameter, halfheight, steelscreen sieves having a
quarterphi 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 sizefraction 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 (GRAN7 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, FebMar, 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, FebMar, 1995
NOTES
Lecture Notes James H. Ba/si/lie
Lecture Notes
James H. Balsillie
W. F. Tanner  Environ. Clastic Granulometry  FGS Course, FebMar, 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, FebMar, 1995
Example Calculation of Moments and Moments Measures
for Classified Data
(After Fogiel, et al. 1978)
Mean
Frequency MidPoint Mean f(X )2 f (X, )4
ClassR Deviation f, (X2 f. (X1 X)3 f (X X
f, (X X)
4954 6 51.5 66.5 15 6(225) =1350 20250 303750
5560 15 57.5 66.5 9 15(81)=1215 10935 98415
6166 24 63.5 66.5 3 24(9)=216 648 1943
6772 33 69.5 66.5 3 33(9)=297 891 2673
7378 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, FebMar, 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, FebMar, 1995
NOTES
Lectue Noes Jmes Basihi
James H. Balsillie
Lecture Notes
