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Letter of transmittal  
Foreword and acknowledgements  
Table of Contents  
Introduction  
Particle size and nomenclature  
Analytical considerations  
Determining transpodepositional...  
Plot decomposition: Mixing and...  
Carbonates  
References  
Appendices  
Index  
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Front Cover 1 Front Cover 2 Title Page Page i Page ii Letter of transmittal Page iii Page iv Foreword and acknowledgements Page v Page vi Page vii Table of Contents Page viii Page ix Page x Page xi Page xii Introduction Page 1 Page 2 Particle size and nomenclature Page 3 Analytical considerations Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Determining transpodepositional environments Page 16 Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24 Page 25 Page 26 Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 35 Page 36 Page 37 Page 38 Page 39 Page 40 Page 41 Page 42 Page 43 Page 44 Page 45 Page 46 Page 47 Page 48 Page 49 Page 50 Page 51 Page 52 Page 53 Plot decomposition: Mixing and selection Page 54 Page 55 Page 56 Page 57 Page 58 Page 59 Page 60 Page 61 Page 62 Carbonates Page 63 Page 64 References Page 65 Page 66 Page 67 Page 68 Page 69 Page 70 Appendices Page 71 Page 72 Page 73 Page 74 Page 75 Page 76 Page 77 Page 78 Page 79 Page 80 Page 81 Page 82 Page 83 Page 84 Page 85 Page 86 Page 87 Page 88 Page 89 Page 90 Page 91 Page 92 Page 93 Page 94 Page 95 Page 96 Page 97 Page 98 Page 99 Page 100 Page 101 Page 102 Page 103 Page 104 Page 105 Page 106 Page 107 Page 108 Page 109 Page 110 Page 111 Page 112 Page 113 Page 114 Page 115 Page 116 Page 117 Page 118 Page 119 Page 120 Page 121 Page 122 Page 123 Page 124 Page 125 Page 126 Page 127 Page 128 Page 129 Page 130 Page 131 Page 132 Page 133 Page 134 Page 135 Page 136 Page 137 Page 138 Page 139 Page 140 Page 141 Page 142 Index Page 143 Page 144 Back Matter Page 145 Page 146 Back Cover Page 147 Page 148 

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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 I =_;. 1` C' 'L Li" Rt* ~ ' J' ill ~B ~. F'' .. h; .r. ' r .. 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 