A STATI‘STSCAL AND MECHAMCAL ANALYmS 0F THE MARSHALL SANDSTONE IN WESWRN MlCi‘fiGAN TO DiiflflMiNfl THE ENVKRQNMENTAL PATTERN OF THE E35909? Thesis 96? Has Dawes :59 ski. 3. MJCHIGAN STATE COW Mariam-f W i-fheém Q’Hm I954 1mm mun mnmrmmmmm L THEME” 3 1293 01013 7176 This is to certify that the thesis entitled A STATISTICAL AND MECHANICAL ANALYSIS OF THE It‘lARSnAIL SANDSTONE IN l'v’ESTErN MICHIGAN TO DETERMINE TriE ENVIRONI‘JENTAL PATTFEW OF THE DEPOSIT presented by Norbert W. O 'Hara has been accepted towards fulfillment of the requirements for Biasiena— degree in _Creolog Major professor Date June 14, 1954 0-169 A STATISTICAL AND MECHANICAL ANALYSIS OF THE MARSHALL SANDSTONE IN WESTERN MICHIGAN TO DETERMINE THE ENVIRONMENTAL PATTERN OF THE DEPOSIT By NORBERT WILHELM O'HA RA A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology and Geography 1954 *"ubts ACKNOWLEDGMENTS The author wishes to express his most sincere thanks to Dr. B. T. Sandefur for his direction, aid, and helpful suggestions through- out this investigation. Also to Dr. W, A. Kelly for his suggestions concerning the choice of the. lithologic unit analyzed in this problem The writer greatly appreciates the critical and constructive editing of the manuscript by Dr. S. G. Bergquist. Sincere thanks are also due to Dr. Justin Zinn and Dr. J. W. Trow for their critical review of the manuscript and general assis- tance. Messrs. R. M. Acker and R. M. Ives of the Michigan State Geological Survey generously helped the author obtain many of the well samples used in this study. Dr. A. D. Perejda is also to be sincerely thanked for his valuable assistance in the preparation of the maps and figures. ii 344485 ABSTRACT The use of statistical and mechanical methods of analysis ap- pears to be a means of determining the environmental pattern of a sandstone formation. In attempting to reconstruct the directions of sedimentation and conditions of deposition within the Marshall forma- tion in western Michigan, composite samples from forty wells com- pletely penetrating the formation were analyzed with respect to their roundness, Sphericity, and size distributions Numerical pictures in the form of isopleth maps, a relatively new tool in determining environmental patterns of ancient deposits, were constructed from the values obtained in the various statistical analyses. The environmental pattern of the Marshall formation was derived from these maps and general similarities in the trends of deposition are shown. Interpretation of these relationships is attempted to determine the conditions of deposition. From the results obtained in this investigation, the author has concluded that during the period of deposition, the Marshall sea was regressing and deltaic deposits were being formed. With the increased wave action, much of the material carried to the sea by streams appears to have been reworked and deposited between these delta areas to form beaches. The statistical relationships existing in variOus parts of the area are therefore directly dependent upon the agent and method of deposition. iv TABLE OF CONTENTS -------------------------- ---------------------------- Purpose of Study SAMPLE SELECTION ........................... Source of Sample 5 Selection of Lithologic Unit ..................... LOCATION AND WELL DISTRIBUTION .............. Location of Area ............................ Distribution of Wells ------------------------- LABORATORY PROCEDURE oooooooooooooooooooooo General . ._ ................................. Me thod of Sampling -------------------------- Disaggregation oooooooooooooooooooooooooooooo Removal of Iron Oxide Stain oooooooooooooooooooo Shale E xtra c tion ---------------------------- Heavy Mine ral Analy sis ----------------------- De canta ti on Sieving ................................... Mounting of Slide 5 ........................... 15 15 15 15 lb l7 18 18 19 20 Measurements and Calculatiors of Roundness and Sphericity STATISTICAL ANALYSIS ......................... Methods of Approach ........................ Cumulative Curve Analysis . . . .................. COMPARISON AND PRESENTATION OF DATA ......... Introduction ................................ Analysis of Size Distribution .................... Analysis of Roundness Distribution ................ Analysis of Sphericity Distribution ................ Summary Comparison ......................... INTERPRETATIONS ............................ Method of Deposition ......................... Shape of Sand Grains ......................... Rounding of Sand Grains ....................... Effect of Grain Size .......................... Summary Interpretation ........................ CONCLUSION ................................. Sequence of Events ........................... REFERENCES ................................ vi 29 34 34 87 87 91 98 118 124 128 128 129 131 131 132 ' 136 137 140 C TABLE II. III. IV. VI. LIST OF TABLES Well Description ........................ Data from Sieve Analysis ................... Roundness Calculations from Cumulative Curves ................................ Sphericity Calculations from Cumulative Curves ................................ Quartile Calculations from Sieve Analysis ........ Arithmetic Averages of Roundness and Sphericity .............................. vii 43 45 89 99 LIST OF FIGURES FIGURE Page 1. Generalized Stratigraphic Section of the Mississippian and Pennsylvanian, for Lower Peninsula of Michigan ................ 6 2. Methods Used for Determining Shape and Roundness ..................... ' ..... 3o 3. Cumulative Curves of Roundness and Sphericity ............................. 4O viii LIST OF MAPS MAP Page 1. Areal Extent of the Marshall Sandstones Under Investigation . . ...................... 9 2. Well Locations ............................ 10 3. Numbering of Wells ........................ 12 4. Median Size Distribution, Sieve Analysis .......... 92 5. Sorting (So) Distribution, Sieve Analysis .......... 93 6. Skewness (5kg) Distribution, Sieve Analysis ........ 94 7. Kurtosis (an) Distribution, Sieve Analysis ........ 95 8. Average Roundness Distribution ................ 102 9. Median (Mdpi) Roundness Distribution ............ 103 10. Sorting (QDVI) Distribution Roundness ............ 104 11. Sorting (50) Distribution, Roundness ............. 105 12. Skewness (Sk) Distribution, Roundness ........... 106 13. Average Shape Distribution ................... 119 14. Median (Mdd) Shape Distribution ............... 120 15. Sorting (QDd) Distribution, Sphericity ............ 121 16. Sorting (So) Distribution, Sphericity ............. 122 17. Sand Thickness Distribution ................... 125 ix LIST OF GRAPHS Well No. Page 1 — 40 Cumulative Curves of Size Distribution ....... 47-86 1 - 40 Histograms of Roundness and Sphericity Distribution .......................... 108-117 INTRODUCTION General Information Much use has been made of statistical and mechanical mc thods of analysis in correlating sandstones, determining stratigraphic hori- zons, and classifying the various types of Sediments. Little work, however, has been done with these methods to determine either the manner in which formations were deposited or the gradational corre- lation between subsurface formations. The increasing significance of marine geology in the last few years has greatly influenced the study of sedimentation. Many pro- fessional papers and texts have been published concerning the depo- sition of marine sediments and the factors controlling this deposition. Some of the country's best—known sedimentologists and oceanographers have taken advantage of the many electronic instruments developed by the Navy during World War 11. These instruments are being employed to gain a better understanding of the influence of current and wave action on marine deposition. From this increased knowledge, new methods for analyzing ancient marine deposits may be developed. One of the most recent tnethods to determine the conditions of deposition in ancient seas is to study the environmental pattern of the area. From this pattern the general areas of extreme depo— sition can be determined and more-specific directions in which to carry on drilling operations may be determined. W. C. Krurnbein stated that: Environmental patterns provide a means of reconstructing ancient environments. The localization of high—energy areas, the prevailing directions of currents, the average depth of water, and other features may be inferred, eSpecially if the faunal elements are included in the analysis, Environmental patterns also per- mit the segregations of closely related environments, as beach and dune, which cannot be distinguished by individual samples. R. A. Hobbs (1949, p. 30) has shown that the possibility of determining the main direction of sedimentation may be positive when directed toward a small area. By using sedimentary methods of anal- ysis, he was able to show a difference in the physical prOperties of rounding, sorting, skewness, and kurtosis of the samples. However, only three wells were considered, and whether these indicate the main directions of deposition or simply the result of local conditionS, can- not be determined without more extensive investigation. The Marshall formation was chosen for this study because of the excellent supply of sandstone present in Michigan. C. Rominger (1876, p. 98) described the Marshall formatiOn as a shore deposit, because "the stratification often becomes discordant and frequent changes in the material are induced by local influence; while in one place a shale bed formS, in another near by a sand~rock ledge may be accumulated." In the first attempt to describe the history of Marshall time, C. W. Cook (1941, p. 64) suggested that the red shales found in the lower Marshall indicate periods of stability in which the finer material is tranSported seaward and that the main feature of this geologic history was the isolation of the Michigan basin during Marshall time. V. B. Monnett (1948, p. 629) madelan extensive study of the Marshall formation and concluded that there is both a domi- nant eastern and western source of sediments. Source areas reSpon- sible for the materials deposited. in the Michigan basin, according to G. W. Pirtle (1932, p. 32), are the Wisconsin arch on the west, the Kankakee arch to the southwest, the Findlay arch to the southeast, the Algonquin arch on the east, and the pre-Cambrian complex to the north. Purpose of Study One purpose of this investigaion is to determine the possibility of reconstructing the main directions of sedimentation within a Spe- cific subsurface horizon. With this information, it may be possible to reconstructznufient shore fines of deposiuon winch umndd be of ecmnunnic value in the search for petroleuni, iAnother purpose is to show how the material forming the Marshall formation was distributed in the Marshall sea and from this information to determine the con- ditions of deposition during that period. Both purposes may be re— garded as an attempt to determine the environmental pattern of the deposit. SAMPLE SELECTION Source of Samples The well samples used in this study were obtained from the Department of Geology, Michigan State College, and the Michigan Geological Survey, Lansing, Michigan. Selection of Lithologic Unit The sands chosen for analysis in this investigation are from the Marshall sandstone formation of the Mississippian period (Figure l). The sample used from each well depends upon the thickness of the sands between the oldest nonclastic bed in the Michigan forma- tion and the first showing of the Coldwater shale. This choice was suggested by Dr. W. A. Kelly, Professor of Geology at Michigan State College. Using these boundaries, it is possible to obtain the most uniform horizon throughout the area. Another reason for this choice is that it eliminates all doubts whether to include or exclude the so-called "stray" sands which appear from place to place within the area. Many geologists include the "stray" sandstones with the SERIES FORMATION LITHOLUGY DESCRIPTION THICKNESS r..- 3 a? 'T ‘1 6) fi.'~ CW auster— W 2,,i 9., 35- gravel, sand FF . nary lsconsin *;Jf“a Jévi ani clay O“" OH' J 0“.C 33. : e;3s.;;ssa£1 sand shale s 4 __ __ _ _ _ w *3 I g Grand River;;:L;;H_-_: and coal 80 ,5 ii §§TL:LE;-:§L ?’ DIE-L m—i Barld , '3' ,. —— ————————— '— b, e . _, - ' .' Saginaw _—...—- __~__ t.___ 8‘ a1 ’ 1 SOC-sf) ”all g "fiS coal ann " c ‘ limestone Q ‘5 ear? and , ‘uy , w. .113 ' Bajport limestone h0“*’J ([111 gypsum , . ____________ v 9 3 _ Micniran 8999' Shalt: O-bOO' _L;r_ ______ dolomite and 4331 “13“”? IfIbf-fifizii: and siltetom 500””1000 EPZEZfZFZEif‘ “fEffiSE‘:”7' Sunburv :::i:§§§}{}z shale lO-QO' Berra figjfi7§3:g;§;,sand and shale 0—210' Beifori -€:€:4:§:§CE shale 10—300' Figure 1,- Generalized Stratigraphic Section of the Mississippian and Pennsylvanian, for Lower Peninsula of Michigan. (After Monnett, l9h8) MiChigan formation, while others place them in the Marshall. One group of geologists thinks that the Michigan "stray" sandstone-s were deposited as bars in the Michigan sea following erosion of the top of the Marshall formation. The other group, however, considers the "stray" sandstones to be reworked and redeposited Marshall sediments. The writer agrees with the latter group that these sands should be in- cluded within the Marshall formation and that by using the boundaries stated above, these "stray" sands will be included in all samples in which they occur. LOCATION AND WELL DISTRIBUTION Location of Area The area selected for this investigation is confined to the west- central section of the Lower Peninsula of Michigan. The western limit is confined to the area where the Marshall formation crops out beneath the overlying drift. The northern, eastern, and southern boundaries are arbitrarily set to form a semicircular pattern toward the center of the basin (Map 1). Within these boundaries is an area approximately 55 miles wide and 110 miles long, covering all or part of the following counties: Clare Muskegon Ionia Newaygo Kent Oceana Lake Osceola Mecosta Ottawa Missaukee Wexford Montcalm Distribution of W ells Forty wells were selected, all of which are located in different townships within the above-listed counties (Map 2). MICHIGAN muml AREAL EXTENT OF THE MARSHALL SANDSTONES 43~»—— UNDER INVESTIGATION sous W“ 20 o 20 40 MILES 20 o 20 40 qt:— (onflld l Dun by Andros I. hulls Ikh. State College, low. of 6001. l 600.. E i i w .r O O 0 SM. (015.. In” (spyrlgh "F H 10 WELL LOCATIONS 11 The total area under investigation was divided into seven. east- west sections, each having dimensions of approximately 20 by 50 miles. Each section forms a wedge—shaped area which greatly simplifies later discussion and presentation of the final results. Four to eight wells were selected from each section. It is not possible to divide the total area in such manner that each section has the same number of wells and still obtain a complete coverage. Wells are designated by numbers from one through forty, by a method such that the wells in each section, beginning with the south- ernmost section, are completely numbered from west to east before progressing northward into the next section (Map 3). Table 1 lists the wells plotted on Maps 2 and 3, the permit number and location of each well, along with the thickness of the sand stone being inve stiga ted . 12 w No. 3 NUMBERING OF WELLS 03' . 37 o 38 32. .33 o 25 ‘34 o .27 .23 4o .55 / 0 / . .29 '39 0 l9 0 / "‘ I7 20 o . 22 030 Is l8 / .2: / .HS .23 CD / .l5 l4 l6 ,0 8 no ." . ""LGBBDd" '2 0 Well .9 Latter: Denote 7 - Section . I 4 .6 I . 5 Scale '3 . =5: 10 5 o 10 20 Kilns .2 -__.—- H _. o . - ‘_-__ fl “*0.“ 'IAJ3LEII WELL DESCRIPTION m_~_— ’ ‘ o—--‘— _~ ‘- ’7‘ w-‘_.—r..s+—'-_._—.d~. fl-_ -,-a..— -.____.J- ”H7 ’~~—'--H—.—‘_'q--_'—H s --———_.“~‘V -. Well Permit , Land No. No. county Townsmp Description 1 6624 Ottawa Tallmadge 36—T7N-R13W 2 14587 Kent Gaines 5-T5N-R11W 3 7453 Kent Ada 8-T7N—R10W 4 3144 Kent Courtland 29-T9N-R10W 5 11472 Ionia Otisco 26-T8N-R8W 6 1 3554 Montcalm Fairplain 7 -T9N-R7W 7 7099 Ottawa Wright 7-T8N-R13W 8 15241 Muskegon Moorland 9-T10N-R14W 9 14577 Kent Sparta 12-T9N-R12W 10 13168 Newaygo Grant 25-T11N-R12W 11 8149 Montcalm Pierson 23-T11N-R10W 12 12254 Montcalm Douglass l-TllN—R7W 13 9946 Oceana Greenwood 27-T13N-R15W 14 12952 Newaygo Garfield 29-T12N—R13W 15 14886 Newaygo Big Prairie 28-T13N-R11W 16 12365 Montcalm Cato 5-T12N-R8W 17 13380 Oceana Leavitt 17-T15N-R15W 18 13890 Newaygo Denver 10-T14N-R14W 19 9697 Newaygo Troy 24-T16N-R14W 20 4460 Newaygo Barton 7—T16N-R11W 21 10419 Newaygo Goodwell 8-T14N-R11W Thickne 55 of Sand (in fee t) ._—'-.—. l 4 TABLE 1 (Continued) Well Permit County Township Land , TZIFC15:::S No. No. Description (in feet) 22 13965 Mecosta Grant 20—T16N-R9W 195 23 1440 Mecosta Austin 11—T14N—R9W 255 24 12883 Mecosta Wheatland 9-T14N-R7W 280 25 9394 Lake Sauble 16-T19N-R14W 181 26 13013 Lake Newkirk 16—T20N—R12W 265 27 14960 Lake Cherry Valley 15—T18N—R12W 270 28 12379 Osceola Leroy 33—T19N-R10W 290 29 16343 Osceola Hersey 8-T17N-R9W 255 30 16329 Mecosta Fork 3-T16N-R7W 100 31 1177 Wexford Antiock 26-T23N-R11WI 230 32 12515 Wexford Cherry Grove 28-T21N-R10W 275 33 12590 Wexford Clam Lake 11-T21N-R9W 170 34 15934 Osceola Highland 19-T20N-R8W 160 35 14533 . Osceola Hartwick 36-T19N-R8W 200 36 5418 Clare Freeman 3-T18N-R6W 180 37 14307 Wexford Cedar Creek l6-TZ3N—R9W 225 38 12977 Missaukee Forest 32-T23N—R7W 105 39 7357 Missaukee Riverside 22-T21N-R7W 155 40 11444 Clare Summerfield 7-T20N-R5W 110 ,__‘ LABORATORY PROCEDURE General This investigation involves physical and statistical methods of study, using such descriptive methods of analysis as weight percent- ages and quartile measures of sorted sieve sizes, roundness and Sphericity measurements of quartz grains. M e thod of Sampling Each sample consists of eight to twenty-five vials of sand, with each vial representing a Specific interval, usually 5 or 10 feet, of formation. The samples were considered as individual composite units, and the material from each vial was sampled according to the interval it represented. One-tenth gram was selected for each foot of Marshall formation, and weighed to the nearest 0.005 gram. Di saggregation Each sample studied was either partly or wholly consolidated. To remove the cement, which for the most part was calcareous, the samples were treated with a solution of 1:1 hydrochloric acid and a 15 16 30 per cent solution of hydrogen peroxide for a period of 24 hours, and then heated over a burner for one hour. While heating, a solu- tion of 50 per cent hydrochloric acid was added so that the sample would not dry out and thus cause fracturing of the grains or baking of any cement which was still present. The above reaction, however, did not completely disaggregate the sandstone, and although the coherence was not strong, it was found necessary to separate these grains with the use of a porcelain plate and a cork, held in the vial. This method consists of placing the aggregates on the porcelain plate, soaking them with water, and then subjecting them to a rubbing process, using the cork and a twisting motion of the wrist. This action was found adequate to almost completely disaggregate the quartz grains. No fracturing or other wearing effects were observable when the grains were examined under a binocular microscope. Removal of Iron Oxide Stain The hydrogen peroxide employed in disaggregation was used also for the purpose of removing the iron oxide stain which occurs in lenses ranging between 5 and 150 feet in thickness in most of the wells used in this study (Hobbs, 1949, p. 7). This method of removal 17 was highly successful in most instances; however, in those cases in which it was not, no serious consequences resulted because, as noted by Hobbs, this stain had no appreciable effect upon the roundness and Sphericity value 5. Shale Extra c tion With the material now mostly unconsolidated, it was found nec- essary to remove a large amount of shale which, during drilling, had fallen into the Marshall samples from the overlying Michigan forma— tion. This was accomplished with bromoform, a heavy liquid having a Specific gravity of 2.87 at 20° C. Alcohol was mixed with the bromoform to lower the Specific gravity to the point where the shale would float and the quartz grains sink (Kropschot, 1953, p. 25). A large funnel, with a piece of rubber tubing attached and closed with a wire clamp, was filled with the diluted bromoform. The sand and shale was Sprinkled upon the bromoform and time was allotted for the sand to settle to the bottom. The clamp was then released and quickly replaced after allowing the sand and some liquid to flow into a lower funnel containing a filter paper. The sand was finally washed with alcohol and allowed to dry. 18 Heavy Mine ral Analysis Heavy mineral separations were conducted by the same method performed in the shale extraction, the only difference being in the specific gravity of the bromoform, which, in this case, had a gravity of pure bromoform. The sand fractions used for the heavy mineral studies was that between the sieve sized 65 and 100 mesh per inch. M. D. Stearns (1933) stated that few heavy minerals are present in the Marshall sands, This statement was checked in ten of the well samples obtained in this investigation and found to be correct. In as much as very small amounts of muscovite, garnet, and Opaque minerals were found, it was decided that the heavy mineral study would not be extended. De cantation Prior to the sieving analysis, all material finer than 1/32 mm. was decanted from each sample. Decantation was accomplished by filling the beakers, containing the forty samples, with water, to a height of 10 cm., and allowing them to stand for a period of 1 minute and 56 seconds. At this instant all water and sediment finer than 1/32 mm. was poured off, since all larger particles had settled to the bottom. This rate of settling was computed according to Stokes’ 19 law for sediments with a Specific gravity of 2.65 (Krumbein, 1936‘, p, 16(1). Sieving Each sample was examined for traces of gypsum and shale, which were extracted with a pair of tweezers. The samples were then weighed to the nearest milligram. Tyler sieve sizes 35, 48, 65, 100, 150, and 200 mesh per inch were first employed to divide the sample into seven different fractions. It was later found in many samples that the sand below sieve size 35 contained too large a per- centage of material to make accurate cumulative curves below the ten percentile. This material, therefore, was passed through sieve size 28, thus establishing another point for plotting the curve below the ten percentile. These sieve sizes, when compared with the Went- worth grade scale, include coarse, medium, fine, and very fine sand. During the initial sieving Operation, the sample was placed in the tOp Tyler sieve, size 35, which allowed all material finer than this size to pass through. That which remained on this sieve was found to consist mostly of sand aggregates. These aggregates were then dis- persed by rubbing them over the sieve with a piece of rubber hose. The next grade size, between sieves 35 and 48, was then examined 20 to determine the aggregates still present. A surprisingly small amount was found, and it was felt by the author that any aggregates still prevailing would have little effect upon the end results. The sieving was finally completed by placing the individual samples in the ro—tap automatic shaking machine for a period of ten minutes. Each grade size was then weighed, recorded (Table II), and placed in ten-gram vials for possible future reference. Mounting of Slide 3 It was found that the sand between Tyler sieve sizes 65 and 100 mesh per inch was the most desirable grade for projecting and measuring roundness and Sphericity values. Airaform (n-1.66) was used as the mounting medium in order that the quartz grains (n-1.544-1.553) would. have greater relief when projected, and thus produce more distinct outlines. Approximately one gram of airaform was placed on each glass slide. These slides were then placed on a metal plate and warmed with a bunsen burner. Centinued heating of the airaform for three minutes drove off all air bubbles. Approximately 150 sand grains were flicked from the vial onto the airaform; cover glasses were added and the airaform permitted to harden. Xylol served as the cleaning agent to remove any excess airaform from the slide. monwm 965 .8388 88.2: - 8888: 8:88 8N8 8.8 8888 8.: 888 88.8 08.880 88.2: 28 88 88.8 88.8 8.8 8.8 8.8: 88 $8 08 43 88:8: 888 8888 888:: 88.8 .888 2.88 888.: 888.8 8888 :8}; 88 8.2: - 888: 8888 88.88 8888 8.8:. 88.8: 88.: 88.8 8.886 8888: 888 :N: 8:. 8:8: :888 8:.8N 88.8: 88.: $8 .8 is 8.8.8: 8888 2.88 888 888 88: 888.8 8888 888 8888 3.; 88 88.88 - 88.88 8.8.8 8.8 8.88 888:. 8.8.8: 88.8. 888 08.880 :82: $8 888 88.8: 38: 8.8: 8:88 8:8: 888 888 .8 is 88.8.88 8:8 888 888.8. 888.8 8:88 2.88 8.88.8. 8:88 2.8 3.83 88 8.2: - 8.2: 88.88 8.8.88 8.8.88 3.8 88:: 88;: 888 1.8.880 $88: :88 888 $8: 8.8 3.8.8 8:8N 88.8 8.: 88.8 08 as 88.: ~88 88:: 8888 88.8 83.8 8.888 88.: 08:8 888 333 N» 88.88 - 88.88 88:88 88.88 888 ::.:N 88.8 888 888 0.8.880 888:: :88 8.8 8.8: 8888 2.8: 8:8: 888 88 88.8 .8 as 8888: 888 888 888.8. 8:88 888 8888 888.: 2:8 888 :83? 2a -888. .womw memo” mm“ 8-8:. 88-8.8 88-88 mm- :Soh wood :03 mHmMr1HHHm 20mm 06 poi-H. $85300: :: mam-8:. 29 Measurements and Calculations of Roundness and Sphericity The most time-consuming portion of this study was involved in measuring the quartz grains for roundness and Sphericity. This was accomplished by mounting a petrographic microscope in a hori- zontal position, removing the lower prism and reflection mirror, and directing the beam of light, from a BOO-watt lamp, through the slide. A prism attached to the ocular of the microscope projected the grain images onto a concentric circle protractor, where they were measured. The method devised by Wadell and modified by Schmitt (1949, p. 47) was used to measure roundness and Sphericity. This method employs the use of a concentric circle protractor drawn on white paper, rather than on plexiglass as suggested by Wadell. Measurements are made directly from the grain images, and therefore it is not necessary to draw each grain before measuring it. The roundness of a sand grain, as defined by Wadell (1935), is a measure of the angularity of its corners, and may be expressed as the arithmetic average of the radii of curvature of its individual corners, divided by the maximum inscribed circle (Figure 2). As roundness increases, the radius of curvature of the corners also increases. This may be stated mathematically by the formula used in this investigation to determine roundness. 30 Radii in mm. Wadell's Roundness (P): P:— ElizflLiz .1420 R 25 Riley's Sphericity (3): :-1—: 32—5-2 3 VC— V35 '833 whore: R1: radius or maximum inscribed circle. r = radius of curvature of individual corners. n =-number of corners measured. 1 = radius of largest inscribed circle. C = radius of smallest circumscribed circle. Figure 2.- Methods Used for Determining Shape and Roundness 31 P : (Zr/n)/R where: P : degree of roundness; R - radius of maximum inscribed circle; r = radius of curvature of individual corners; n = number of corners measured. Roundness, therefore, is a function of the sharpness of the corners, and is entirely independent of shape which has to do with the form of the grain. Although Wentworth (1922) recognized the difference between flatness (shape) and roundness, it was Wadell (1932) who first pointed out these two geometrically independent variables included in the general shape concept. Since a Sphere has the smallest surface area in proportion to volume of any other shape, Wadell defined this as the unit measurement, and referred to the shape of a particle as having a Specific "degree of Sphericity." Wadell‘s original formula for determining Sphericity may be expressed: Q5 d/D where: Q5 = degree of Sphericity; d = diameter of circle equal in area to that of the grain obtained by planimeter measurements; D 2 diameter of smallest circle circumscribing the grain. In the above formula it may be seen that in order to determine Sphericity, it is necessary first to measure the exact area of the grain. This proved a most time—consuming procedure. Therefore, Wadell 32 developed a. more practical formula which gives satisfactory results closely approaching those obtained when planimetric measurements are made. Wadell's short-method formula is: s : R/D where: S 2: degree of Sphericity; R = radius of largest inscribed circle; D = diameter of smallest circumscribed circle. From this short-method formula, N. A. Riley (1941) has de— rived another formula using the diameter of the largest inscribed circle, and dividing this by the diameter of the smallest circumscribed circle; the square root of the product is then taken as the degree of Sphericity (Figure 2). Riley's short—method formula is: s = i/C ‘where: S = degree of Sphericity; i : radius of largest inscribed circle; C = radius of smallest circumscribed circle. The writer selected the method of calculating Sphericity derived by Riley, because it is believed to compare more closely with the true Sphericity. Also, it proved to be the most rapid method. The writer found by using Riley's method with tables constructed from results computed with the aid of a slide rule, that considerably more Speed was obtained than when the alignment diagram, suggested by Wadell (1934), was employed. Krumbein (1938, p. 294) allowed one-}1alf 33 minute for each calculation with the alignment chart, whereas the writer made several calculations within this same period by using tables. A total of four thousand quartz grains, one hundred from each of the forty wells under investigation, were measured to determine roundness and Sphericity. Although Krumbein (1941, p. 69) suggested the measuring of fifty grains for each sample, R. C. Perry (1951, p. 10) stated: "After measuring 200 grains of the St. Peter sand the average Sphericity and roundness were computed for the first 75 grains, the first 150 grains and the total 200 grains." In comparing the resultS, it was found that little, if any, additional accuracy was to be gained by counting more than 75: "It was decided therefore, that the measurement of 100 grains from each sample would result in a representative figure for the sample as a whole." STATISTICAL ANALYSIS Methods of Approach Krumbein (1939, p. 559) described two main approaches to a statistical sedimentary analysis. The first and earliest method is that employed by workers who prefer to consider their data in terms of the original grade sizes used in the analysis. These investigators usually employ histograms in describing and comparing the modal class, number of grade sizes present, and the symmetry or asymmetry of the figures. This method, however, serves more as a picture to be compared visually than mathematically. The second approach, which is far more popular and valuable, is to consider the data in terms of a continuous frequency distribution. This approach may be divided into two methods: using either cumu- lative curves or frequency curves as the basis of interpretation. The former is considered the most popular. In this investigation, the author has endeavored to present mathematical results which could later be represented as isopleth 0 maps and numerically comparable figures. For these reasons, cumu- lative curves were drawn, using the weight percentages of size 34 35 distribution (pp. 47-86) and the frequency distribution of roundness and Sphericity measurements. Histograms were also drawn to rep- resent more clearly a visual picture of the cumulative values obtained in the roundness and Sphericity measurements (pp. 108-117). Cumula tive Curve Analy sis In order to obtain the geometrical ratios directly, cumulative curves representing the data secured from the sieve analysis (Table II) were drawn on semilogarithmic paper. The diameters of the grains in millimeters are plotted logarithmically along the horizontal axis and the cumulated weight percentages are plotted arithmetically along the vertical axis (pp. 47-86), The curve is drawn by erecting an ordinate at the first grade (Tyler sieve size 28), equal in height to the percentage of material in that class; at the end of the second grade, another ordinate is measured, equal in height to the sum of the percentages in the first two classes, and so on. The curve is then drawn through the upper limits of these ordinates. Krumbein (1938, p. 563) described a cumulative curve as, in effect, equivalent to setting a histogram block above and to the right of its predecessor, so that the base of each block is the total height of all preceding blocks. 30 Although many workers use cumulative curves purely in a descriptive manner, much the same as histograms, the greatest ad— vantage of them is in obtaining statistical values. Five values may be obtained: the median, Md; the first and third quartiles, Q1 and Q3; and the ten and ninety percentiles, P10 and P90 (pp. 47-86). The median represents the value obtained at the point where the cumulative curve is intersected by the 50 per cent line, and is defined as that value which is largerithan 50 per cent of the material and smaller than the other 50 percent. This value also is commonly used as the average. The first and third quartiles lie on either side of the median and correspond to the intersections of the curve with the 25 per cent and 75 per cent lines, reSpectively. These may be considered simi- lar to the median, depending upon their frequency values. In like manner, the ten and ninety percentiles yield values correSponding to the position of an ordinate projected downward at the intersection of the 10 and 90 per cent frequency lines and the cumulative curve. The first use of quartile measures in sedimentary analysis was made by P. D. Trask (1930). With them, he was able to express three different relationships: the quartile deviation, quartile skewness, and quartile kurtosis. The quartile deviation or "sorting" of a 37 sample may be expressed as the measure of the spread of a cumula- tive curve. This may be expressed mathematically in any one of three forms. The first is the arithmetic quartile deviation: on = (Q3 - Q )/2 a l The second is the geometric form introduced by Trask (1932) as the sorting coefficient, "80," and used here to represent the data obtained from both the sieve analysis and the roundness and Sphericity calculations. This form may be defined as; QDg = So : MOI/Q3 Trask has reversed the quartiles in the above relationship. By plac- ing the largest quartile‘value in the numerator, positive values are obtained. The advantage of this form is that it eliminates the size factor and units of measurement. The third form is logarithmic, and may be expressed: log QDg = log 80 = (log Q - log Q1)/2 3 In a similar manner, the quartile skewness, used as a measure of the asymmetry of the curve or the departure of the quartiles from the median, may also be expressed in three forms: SK : (03 + Q1 - 2Md)/2 a SK = /Q Q /1va g 3 1 + log Q1 - 2 log Md)/2 log SKg = (log Q3 38 The subscripts "a" and "g" are used to distinguish between the arithmetic and geometric cases. Geometric skewness has the same advantage as geometric quartile deviation in that size factors and units of measurement are eliminated. It was this independence of the size factor and the di— rect ratios between quartiles in the case of "So" and between quar- tiles and medians in the case of skewness, which prompted Trask to introduce geometric measures for sediments. Geometric measures, however, are not the best method of comparing data. In other words, it cannot be said that a sediment with a sorting of 2.0 is twice as well sorted as a sediment with a sorting of 4.0. When the logarithmic values of the above two sediments are found, however, they may be compared in such a manner, This is possible because as "So" in- creases geometrically, "log 50" increases arithmetically. Unlike the two previous quartile ratios considered, the quartile kurtosis is generally expressed only in the arithmetic form derived by Kelley (1924, p. 77): an = (Q - Q3)/Z(P10 - P ) 1 90 This measure is essentially a comparison of the Spread of the cen- tral portion of a frequency curve to the spread of the curve as a whole. It is the measure of the degree of peakedness 'of a curve and ,9 is similar in expression to that of sorting, in, that a well sorted sand should form a more peaked curve than a poorly sorted one. Kurtosis, as defined here, yields values which decrease with increasing peaked- ness; this should be kept in mind when comparisons are made. At present, this method has received little attention in sedimentation. Krumbein (1936) has developed another method, represented by what is known as the "phi" scale, to secure quartile measures. This method consists of plotting the cumulated weight percentages against the logarithmic values of the grain diameters to the base 2, rather than to the base 10, as is done to obtain geometric values. In this method, arithmetic graph paper may be used and will show directly, in the case of size "frequency distribution, how many Went- worth grade scales are present between the various quartiles. Each Wentworth class limit is an integer and is plotted on the "phi" scale along the horizontal axis, size increasing to the right. The cumu- lated weight percentages are plotted along the vertical axis in the same manner. This method has been employed in the statistical analysis of the roundness and Sphericity measurements made in this study by substituting for the Wentworth grade scale 0.05 intervals of roundness and Sphericity values (Figure 3). Well N0. 1 40 100 N KIT Percentage tn <3 / (U U1 0:50 0.55 0.70 0.75 0.80 0.-5 0.90 # Sphericity Distribution 10 Well No. l r”" I 75 j p 5 so 0 £4 0 (L 25 0.10 0.15 0.20 0.25 0.30 0.35 0.h0 0. 5 0.50 gZ-—a> Roundness Distribution Figure 3.- Cumulative Curves of Roundness and Sphericity 41 The advantage of the "phi" scale is that quartile deviation, QDQf, and quartile skewness, Skggfi} may be compared both visually and logarithmically. However, when "phi" values are converted to geometric values based on the logarithmic scale to the base 10, a troublesome method of conversion must be employed. Although Krumbein (1938, p. 235) has provided conversion charts, these were not readable to the desired degree of accuracy. It was therefore found necessary to compute the So and Sk values in the following manner: In obtaining So from QDd, it was first necessary to find the log 50, the antilog then yields the 80 value. This means that QDp/ 10 one may use the relation J equals lOgZQDg, and to find logloQD loglon equals loglOZ logzn, where loglOZ equals 0.301. By substitut- ing QDg for n, and QDd for logZQDg, there results logloQDg equals 0.301 QDQK. Since loglOQDg equals loglOSo, the antilog of loglOQDg equals 50. In a manner similar to the above, the geometric skewness, or its square, which is Trask's skewness, Sk, may be found. The rela- .tionship used is loglOSk equals -0.602 Skgd. The antilog of loglOSk yields Sk. From Tables III and IV it may be noted that the sign be- fore Sk fl is opposite to that before loglOSk. This is a convention in g terms of the change of variables, and is consistent with the phi notation. 42 The curve, whether expressed in phi terms or in diameters, is), of course, skewed in the same direction; merely the Sign given to the direction is changed. When the curve is symmetrical, the skewness is equal to unity. The values obtained, therefore, range from less than one to greater than one. The significance of this depends on the fact that numbers less than one present a reciprocal relation to the numbers greater than one. Reciprocal values, however, are not easily visualized; therefore, Trask introduced loglOSk, which is posi- tive when Sk is greater than unity, and negative when Sk is less than unity. TABLE III ROUNDNESS CALCULATIONS FROM CUMULATIVE CURVES No. Qld IVIdyi Q37 QDd 1 1.97 2.37 2.97 0.500 2 2.13 2.76 3.48 _ 0.675 3 2.14 2.61 3.40 0.625 4 2.10 2.52 3.19 0.545 5 2.08 2.48 2.93 0.425 6 1.91 2.38 3.05 0.570 7 2.82 3.16 3.78 0.480 8 2.35 3.16 4.00 0.825 9 1.98 2.33 3.03 0.525 10 2.28 2.79 3.44 0.580 11 2.20 2.75 3.56 0.680 12 1.66 2.25 3.00 0.670 13 1.87 2.24 2.85 0.490 14 1.88 2.44 2.95 0.535 15 1.96 2.43 3.07 0.555 16 1.82 2.17 2.72 0.450 17 2.25 2.80 3.73 0.740 18 2.33 2.91 3.68 0.675 19 2.00 2.41 2.89 0.445 20 2.26 2.92 3.55 0.645 21 2.35 2.77 3.37 0.510 22 2.42 2.95 3.60 0.590 So So Skgd 1453f 0.151 .L416 +.200'.4120 0 204 1.600 + 090 —.054 0.188 1.542 + 320 -.193 0.164 1.459 +.250 -.150 0.128 1.343 + 050 -.030 0.172 1.486 +.200 -.120 0.144 1.393 +.280 -.169 (1248 1.770 -L030 -.018 0.158 1.439 +450 -.271 0.175 1.496 +.140 -.084 0.205 1.603 +.260 «.157 (L202 1.592 +.160 —.096 0.148 1.406 +240 -.144 (L161 1.449 -.050 + 030 0.167 1.469 +.170 -.102 0.136 1.368 +.200 -.120 0.223 1.671 +.380 -.229 0.204 1.600 +.190 -.114 0.134 1.361 + 070 -.042 (1194 1.563 .4030 +.018 0.154 1.426 +.180 -.108 (i178 1.507 -5120 -.072 0 OOOCOOOOOCOO [—5 00000 43 .759 .883 .642 .708 .934 .759 .678 .960 .563 .825 .696 .802 .718 .072 .791 .759 .514 .770 .908 .042 .780 .847 TABLE III (Continued) 0.4 w «2.7 23 2.17 2.65 3.20 24 2.25 2.77 3.40 25 2.07 2.58 3.18 26 2.47 2.87 3.78 27 2.18 2.53 3.07 28 2.23 2.77 3.59 29 2.25 2.85 3.80 30 1.95 2.53 3.00 31 2.14 2.59 3.06 32 2.07 2.55 3.13 33 2.19 2.80 3.68 34 2.55 3.05 3.62 35 2.10 2.58 3.26 36 1.44 1.77 2.30 37 2.37 2.85 3.30 38 2.32 2.85 3.71 39 2.33 2.93 3.50 40 2.46 3.03 3.48 (208 So So Skgd 5* 0.515 0.155 1.429 -.070 .042 0.575 0.173 1.489 .110 .066 0 555 0.167 1 469 .090 .054 0.655 0.197 1.574 .510 .307 0 445 0.134 1.361 .190 .114 0.680 0.205 1.603 .280 .169 0.775 0.234 1.714 .350 .211 0.525 0.158 1 439 .090 .054 0.460 0.138 1.374 .020 .012 0.530 0.155 1 429 .100 .060 0.745 0.224 1.675 .270 .163 0.535 0.161 1.449 .070 .042 0.580 0.175 1.496 .200 .120 0.430 0.130 1.349 .200 .120 0.465 0.140 1.380 .030 .018 0.695 0.210 1.622 .330 .199 0.585 0.176 1.500 .030 .018 0.510 0.154 1.426 .100 .060 O p— COCO 000000 44 Well TABLE IV SPHERICITY CALCULATIONS FROM CUMULATIVE CURVES NO. 018 M88 Q38 QDd 1 7.36 7.73 8.13 0.385 2 7.52 8.02 8.48 0.480 3 7.75 8.06 8.45 0.350 4 7.26 7.87 8.35 0 445 5 7.64 7.93 8.35 0.355 6 7.50 7.91 8.28 0.390 7 7.62 8.23 8.42 0.400 8 7.53 8.07 8.34 0.405 9 7.54 7.95 8.37 0.415 10 7.58 7.92 8.36 0.390 11 7.62 8.13 8.34 0.360 12 7.54 8.06 8.48 0.470 13 7.70 8.04 8.40 0.350 14 7.39 7.86 8.24 0 425 15 7.60 7.95 8.29 0 345 16 7.50 7.96 8.34 0.420 17 7.44 7.64 8.20 0.380 18 7.67 8.00 8:43 0 380 19 7.57 7.98 8.31 0.370 20 7.78 8.20 8.37 0.295 21 7.54 7.93 8.35 0 405 22 7.61 8.04 8.31 0.350 0 OOOOOOOOOOOOOOOOOOOOO .116 .145 .105 .134 .107 .118 .120 .122 .125 .117 .108 .142 .105 .128 .104 .126 .114 .114 .112 .089 .122 .105 1.306 1.396 1.274 1.361 1.279 1.312 1.318 1.324 1.334 1.309 1.282 1.387 1.274 1.343 1.271 1.337 1.300 1.300 1.294 1.227 1.324 1.274 45 Skgd 83$ Sk +.030 -.018 0.960 -.040 +.024 1.058 +.080 -.O48 0.895 -.130 +.078 1.197 +.13o -.078 0.836 - 040 +.024 1.057 -.420 + 253 1.791 -.270 + 163 1.457 +.010 -.006 0.986 +.100 -.060 0.871 .-.300 +.180 1.515 -.100 +.060 1.149 +.020 -.012 0.974 -.090 +.054 1.132 -.010 + 006 1.014 -.080 + 048 1.117 +.360 -.217 0.606 + 100 -.060 0 871 -.080 +.048 1 117 -.250 ~L150 1 413 +.030 —.018 0.960 -.160 +.096 1.247 46 TA BLE IV (Continued) NO 1 Mdyf Q38 (:08 So So 51688 135:“ Sk 23 7.64 8.11 8.40 0.380 0.114 1.300 -.180 +.108 1.282 24 7.50 7.94 8.95 0.725 0.218 1.652 +370 -.223 0.599 25 7.58 8.02 8.30 0.360 0.108 1.282 -.160 + 096 1.247 26 7.50 7.95 8.36 0.400 0.120 1.318 -.040 +024 1.057 27 7.50 7.93 8.32 0.410 0.124 1.330 -.040 +024 1.057 28 7.62 8.13 8.37 0.375 0.113 1.297 -.270 +163 1.455 29 7.50 7.96 8.31 0.405 0.122 1.324 -.110 +066 1.164 30 7.37 8.00 8.43 0.530 0.160 1.445 -.200 +120 1.318 31 7.60 8.02 8.43 0.415 0.125 1.334 -.010 +.006 1.014 32 7.50 7.92 8.31 0.405 0.122 1.324 -.110 +.066 1.164 33 7.57 7.92 8.31 0.370 0.112 1.294 -.040 +024 1.057 34 7.37 8.00 8.27 0.450 0.136 1.368 —.460 +277 1.892 35 7.49 7.81 8.29 0.400 0.120 1.318 +.160 -.096 0.802 36 7.29 7.69 8.14 0.425 0.128 1.343 +050 -030 0.934 37 7.52 8.03 8.46 0.470 0.142 1.387 -.080 +.048 1.117 38 7.70 8.06 8.41 0.355 0.107 1.279 —.010 +.006 1.014 39 7.47 7.94 8.36 0.445 0.134 1.361 -.050 +030 1072 40 7.55 8.00 8.43 0.440 0.132 1.355 —.020 +012 1.028 - -_.._.-‘.__.—__—.__~_'—.__.- .——. -fiw— 47 A WELL #1, Sec. Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm) Diam. a . a a H a n . . 4.... e s 1 . _ 3 1 w” a 0 2x 9. m AN: 4 1. 11 Au m a m ll 1 I g a k 0 q I“ MW; 3 S K 1' — — IJIIIITIIL'Illvlu'Lv'IArl'll'lI'lé'Ill'l'II'LIIIA18I” " _ j] H _ " Z n 9 — / "‘-II.III'LWII-fil"""'Ll-'lli'lI." hw _ WI] . 1 .il _ _ -JI! 1 L n l // m _ _ m m _ . - 1- -- 1-“ l _ a I .1 9w _ _ _ _ 1 _ _ a l _ i1“ 4 / 1 .o(/ . _ n _ (Li-m 1| b l 9m 4 _ _ L .1317 n _ _ n _ _ _ n O _ _ H 2 ._- 8&1 n _ H _ 1n O_ 42. O 0% O/ 71 5 2 l _ _ m r _ mom-111 41-1-14-.. - . - . - - . o _ H 11.- fl 0 O O O O 0 do 6 w 2 l mwwpcmopom copmfldeso mo. No. me. C“ O OH. ON. 0 M ~92 8. R. O 9 P 3 Q d M) m. m w 1 an m m pas L Cumuleted Percentage 48 WELL-#2, Soc. A Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm) Diem. .. . 20 559 ’4 .2197 .810 .an9 -}05 .9711L 100 . ' /’ O r 80 1/ 5 /I 1 I 1 /1 60 / i y . l 50 _ _ 1 /l. E ' 1 110 /i l I i : Eflq; 0.949 H I 1 30 1.86 T I -1 _2§ _,_"___ __ __/f i : KQe 0.277 1 ' ' 20 1 1 1 / : 1 1 4 : 1 10 1 I. i 1 i I i “" 4 f i I OEMM‘EJ) 11111 1111 11.11 111111111 QIIJLLJ 111 Mmmmt 5: 3. “r 3. 9: 3’: S 88 s ‘8 L03 Diameter (mm) Cumulated Percentage 49 WELL #3, Sec. A Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mvaDiam. .569 .920 .297 .810 .149 .105 .074 100 90 / .2.“ __- ._ _ -__ . 1 : 80 f I _ _ __ ___ ___ __/ i lull. . /1' I ' I I I 11 1 i '4 ————I————— 4I-—-— I —I I—a» l . 60 J/, 1 7 | I f 50 - ' 1 I ! I I l 1 r | Ir 1 ‘1 40 h L I i ' 3kg 0.937 I ___- 1-1-- ....._. 11 '- 9 I I 1 80 1.47 _ 25 _ j 1-_ 1 K93 0'28} 1 i ' 20 I I I - _/ I I ' / I 1 1 .10 l. 1 i I I . I I l , I I T l i l 1 0mm 1111:1111'1111 11111 1111 111111111 1111111111 mmnuun 1111 O O i O 3 O O O O\ 760 N \O (\- \0 Ln M N H O O O 0 P10 91 Md 95 P90 Log Diameter (mm.) 50 A WELL #4, Sec. Cumulative Curve of Sieve Analysis Weights Tyler 'Sieve Sizes (mm) Diam. mwdpcmosmm cmpefideso ,4. .. s m w” 9, 9. mw mwo 0V0! 0 .1. o mWO. a... a a. 8. w, 1 S. 1.. H . 1 O 'J'Jl-lllllsl'll'lmnlirlnlfil'lTII‘ll-LrlulullllfnlLII'TIi'IIII-11 P9 _ 1 9 _ H \I w- _ VT - m. e jflll'TlleI'I-llfille" I+III'T'LI'IIII|Ill-m %/ m - I1 _ _ Iljlll - m r O _ _ [I n . d W a - - - 1 -- - -1-- om M e I _ 1 m . u [I] U m I I _ ijl-JIIIIIIIM H“:- D W M _ . H . we 2.! + mom 0 L /-/..-.-. p1 0 [m o 2 l. .41 0.: 0 r1 0 . w J 5 2 1 om 9 _ i4 1 $.21 W8. mos. 0 w m w w .2 0 1 51 WELL #5, See. A Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. .589 .1120 .297 ‘510 .1119 .105 .0711 100 : v‘fl 90 _ _ _ __ / I i l I 80 //r I ' I - /I . I 1 E? L ' I I I I; 60 , . 0 j/ I I 0 4 ‘4 I I :1. 80 f I I I '8 A 1 1 ‘3 1 1 1 I; no 1 1 1 I I s ' ' 3kg 1.010 U Tr T 1—-( [I I I 80 1.40 -25 _ / '- 1 («111 0.261 fl : 1 - 20 3 I I § I I ' I 1 1 ' I T I I 10 jg I 1 l I I I .I I I I I I . i 1 I 1 Ow “11111111111111 1111 111111111 1111111141 ' (11111111111111 0 i. 8 8 8 a 8 E?- 88 s 8 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumuleted Percentage 52 VELL #6, See. A Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diem. .?9 .II-ZO 2?? ,q10 .1349 .1'.05 .07“ 100 ' 1 9o _ i _ _ _ I /1_ _ . 80 / l I 5 ’{ I f I E 1 ' I /: 1 60 I] I I / I ' 4 l I 50 1‘ ' I I 71 : . I I l 110 /I 2 2 I : 1 1 3kg 0.971 | T I ; I i 3° 1-3‘3 .1 ' I 25_ j/ : I : Kq. 0.270 — 1 I | | 20 711 . . i ' ! 1 l I 1 I ' 10 1 J 1 I I I I I I I I I l I I f i i i UNI-“h“ 111111I11111I11111I1 111111111!11111111|1 111111 \0 as s 3 a a 9.33:3 1; 9 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage WELL#7, Sec. B Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. 53 .$9 .I'I'zo .297 .210 Olug .105 .072; 100 I I I I I I _ 0 _ __ __ _ __ __ _____ I I I SO I _ 5' _ _ _ __ __ _‘_ __/ l ' I 1 I /' ' +-V———-11— I I v.1», I l 60 l I I : l ‘T ._ 50 _ __._ __ .0. _/l I I I - 1L ! I : : 1 i 1 40 I I l / I 1 3kg 1.011 11 -1_. I I—J I I So 1.I+S 1 T __ _ 25 _ _ l I an 0.276 . i I r I I I I 20 I I r I I I I I r T ' 1 _lo //I I I 1 I T I I | | _L I 1— I I If ' I I I O 111111111111 11LL 1111 111111LL1 1111111111 111111111111111 1‘3 8 1% .9. R 8 3 8‘00 '5 ‘8 P Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage 54 WELL #8, Sec. B Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (111111.) Diam. . 9 .I20 . es 297 .230 .1119 .105 .0711 100 I 1% O __ _ _ _ / ‘//1 I 80 f I _ _ _ f 1 I 1 /1 1 I I _ /: 1 ' I 60 l/ 1 : - l / 1 I I _So _ _ f , 1 fl ' I /I i i I I “0 1 f 1 1 l 1 1 I 3kg 0.96"- I ' ~"r ”-1 t I ; l/ g i I 80 1.37 M I 25 1 1 1 mm 0.273 . ' ' 20 I: I I I /' _1 I :‘ / I 1 I I 10 I J I I I | I I /1' I 1 I I I 1 I I I 0911101511] 0 ’1‘1111I1111I11111I1 11111111I11111111I1 1 111111111111111 O O I: I0. “3 5'. I) “1 3 3‘3 '5 ‘3 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage WELL #9, Sec. B Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. 55 12° 2.97 410 .119 .105 .071 100 , / 0 fl I I 80 i 5 — — ——— — 1 I I I i /1 I i I 60 1 1 I I 1 ~1 ' I O I . 1 /. 1 1 I i 1‘ 110 3 ' ' i IL 3 3113 0.9235 1 I j I 30 1.33 I ' . — 25 _ ! l l KQa 0.256 . : . 1 20 . i I / : . 1 I / I i 'L ' I I I __;O a” 1 i I 1 *4 I l I '1 ,/ I | I I I 0m 1111 111111111111k111 1111 111111111 ILLIII 1 11111111111111 :9- 9x .3 9x 3 8‘8 '5 ‘8 P10 Q1 Md Q3 P9o Log Diameter (mm.) 56 Umflo, 880. B Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.)Diam. $89 .II20 .297 .1110 .JIII9 .IOS .07II 100 ’1" O I /II 1 '1 r 80 I 75 1 l I I I o 1 l 3’ I I +’ 60 I G I o I 2 I I o 0 j/ I I p' 'f I '3 1 I I +2 I I a! “.0 / I I l I I 3kg 1.163 15 //7 I I, a I/ I I 30 1.42 IT I ~ 21 j 1 I Kg? 0.300 I l 20 [E 1 TL ' I I I I I ' I 1 10 _ _ _ 1 I I I I .I I I 1 1 I 1 I I l <- I QMM 1111111 11111 IIII 11114111111111111111 my 1111111 I; e a .sg a a 2 es '5 13 P10 Q1 ”‘1 “3 P90 Log Diameter (mm.) Cumulated Percentage 57 WELL #11, Sec. B Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. .?89 .II20 .2197 .2'10 .1‘LI9 JI-O‘i .974 100 2 _1__ 0 V I I I I so / I I _, 5 _ _ __ _ ‘__ i I I I i / I I I1. 1-.. ' l L / ' . 60 I I l I ' 1 O I I 1 ' I I I I /: 1 I 110 I 1 f I I I 1 3kg 0-95° I I 1 So 1.I11 I re' H 25 I I qua 0.275 ‘ _ I I I I 1 I 20 , I , I I 1 I r I ' ' I 10 _// I 4 I 1 1 . I ' I I l 1 v v I 1 1 I I I I Oil-WWW 111111111111 1l111 11111 111111111 111111141 mmmnm 111 2.883. a a 2888‘s P10 Q1 Md Q3 P90 Log Diameter (mm.), Cumulated Percentage 58 WELL #12, Sec. B Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes (111111.) Diam. ,, .1120 , , 10 .1II .10 .0 II- 100 $9 I 2I97 a I 9 I 5 17 .4 90 _ I / 80 l :1 f ]I 1 / I I I so / , . / . 1 5o 1 I ‘— 1 I I I I I I10 ' I ' I l I I I 3kg 0.957 __ I I / I 1 | 30 1.26 ’— 25 _ I I 1 ma 0.230 I I I 1 20 1 I 4 1 I I | l I 1.0 1 I I I 1 I I e/! 1 ' I I ' | 1 l 0 1111111111111111 111111I1111!1111 11I11 111111111111111111 1111111111111 .2 e a 3 a a s; as e ‘8 P10 Q1 “‘1 Q3 P90 Log Diameter (mm.) Cumulated Percentage 59 WELL #1}, Sec. C Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.)Diam. .?59 .II20 '2197 '2110 JIM-9 .3105 .0711 100 0 ,f I I “ /// ‘ “ 80 I i _ 1 _ 1 I l I . I / I I % _IL_.__ 4 I _ 6o / I ' / ' I I Iwr I O J. I I I '1 1 1 r— I I 110 I I I 1 3kg 0.929 I So 1.39 I ' M I K 0.26 ‘_2 I g] _1*____ (hi 5 z. . . 20 I f i I I I I f e I 10 l I I 1 .4] I 14 1' ' ' / I I , I I 0 w [III IIII Ill! lJJl lllllllll IIIIIJJIII ' lUlIIIIIII III] 0 O a. w. a .9, a e 2 ea '5 ‘8 P10 Q1 Md Q3 P90 Log Diameter (mm.) WELL #lu, Sec. C Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm) Diam. 60 .( .uzo 10 . 4 100 l$99 I .297 .q Jr 9 ios .971I I Q _ _ _ _ ___ _____ I I 80 f I I Z I I I I //. I g) I I l E 60 I ' o I I 34 I. I 3 .50 I I I s /E I I .p I I 340 [I I . g 1/ : i 3kg 1.057“4 | L 30 1.146 I ' “i _2 I I 15%. 0.255 I T g 20 ' I g . I l I i | I I 10 l I I I I : I L ' I I | T I 0 ~ “(1111 .1111 Jill IIII LiLLililli Lfil lllldli mjmuuml e e s e a a 2 8‘8 '5 ‘8 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage 61 WELL #15, Sec. C Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes hmn) Diam. .§89 .IIBO .297 .210 .‘1II9 .105 .071I 100 I I I I I I ”I 90 _ __ _f __ ___ 1,0k‘ Z— _J ——~+——- .. .g ___. f h I. I 80 // I 75 ‘_, _ _ : A I ' I L JL—__.r____-IL—__ ll 1 | I 50 I L / ' ' 1r 1 50 / J L i I I k #1 / ' ' ' LLO 1 4' 1 I I |L : 3kg 0.932 I g I I So 1.37 I I I F“ _2 _j/ 1 l I KQa (3.273 I I I 20 I J L ' I ' : I I I + 1 I I I 10 l .1 g l I I ' I j J 1 L y/ I ' I I 0 11111 llll llll 11H lJll I‘lL 111! L 111 Illlll Ill [1111 Ill 1] III III [III III a e s 3 a s 2 9; s a ‘8 P10 Q1 ”‘1 Q3 P90 Log Diameter (mm.) Cumulated Percentage WELL #16, Sec. C 62 Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.)Diam. 0' euao . 10 . n 100 If9 I 297 .g 1,9 .Jl.05 .9711 o ,W/ /I T I 80 l/r i I —— _ _ — _— i I I I I /. . j l l I 60 / I I I I r I o I I I 1 l I I I | 1+0 - I I l / L + 1 3kg 0.9634 I : i 30 1.31 H .25 _ j I I i ms 0.239 I I I I 20 V J, i I i I , I I I ' I l _1 I I I I I I I ”/41 I I I I I OLlIIuIIIIIun 11 11:11111111111111 111i11111 IIIIILlII MW 11 g e a g a a 2 as '5 ‘8 Log Diameter (mm.) Cumulated Percentage m#l7, Sec. D Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizee (mmw) Diam. 63 .. , 20 , , 1 . II- . . 100 I39 II 2197 II" I9 I05 97“ 90 /‘I / I 80 75 I I I I I r 60 // I? I I 60 fl / g I I 7II I I f 5 no /; J I j 1 1 8kg 0.966 / I 1' 80 1.51 __ 25. .. _ m/, I I IS: 0-255 ' I I I , 20 1 I I 1 I ' I l 1 I I l I ' 4T— I r I I I I I I I I I 0Lu111111111111111111nl 11111I111111 111111111111111111 MM 111 I; . a g. a a ass '5 ‘8 P10 Q1 IIId Q3 1’90 Log Diameter (mn.) Cumulated Percentage 64 WELL #18, Sec. D Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. -319 .1120 .297 gm .1119 .105 .0711 100 ' ' /‘ _ 9Q _ _ _ __ 1 _ I I 80 I 7 1 _ _ __ __ ___ 5% | i ' I I I l l 60 / I I / ' 'I ' I SO ___; g I I I l I 1 I l I 1+0 /l 1 I l I Skg 0.983 1 I; P. I I 30 1.27 1 i l 2 ' ! KQa 0.290 ._ _ 1__ _ l I I I l I 20 // I I I I f I l i I I I 1Q. 14/ l i 1 fl I I ' | I I . 1 I I 1 0 fi111111:111111|1111111|111111111111111141 ' mmLLLHl .2 s a 3 a a 2. 8‘8 '5 :3 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage UELL #19, Sec, D Tyler Sieve Sizes (mm.) Diam. 65 Cumulative Curve of Sieve Analysis Weights .1359 .1120 .297 .210 .1119 .105 .0711 100 I I I I ‘I I QO._ _ _ __ __ I 80 J5 _ V/ / / I 60 / ' 50 1/ ' I I I no I 3kg 0.771 _1 l ' So 1.95 _ 25 4f ' file 0.336 20 l: ' I I ' I 10 I ' I I I I | 1 I I V’ I l I 0L1 1111111111 111 I111 111|11111111111 111111111 111111141 mm 111 g e s .5; a a 21 8‘3 '5 23 Log Diameter (mm.) Cumulated Percentage 66 WELL #20, Sec. D Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.)D1am, .359 ,IIIao '2197 .2IlO .JI’+9 $05 .974 100 I _90 __ . g l I 80 1‘ I I 5 _ __ __/ I I fl '_ l I ‘ L - 4 L : -11.- 50 I i I - / | ‘ I 1 I 50 71% ' ' | 1 . +__...1 : I I 40 ' : 1 1 I | ,___ L 3kg 0.932 .1 j [I I I 30 1.60 I I . P1 25_ __ I __I”_ KQa 0.29 1 TI l I l I 20 I 4 I / l I I II I i I 10 I l I I I l I I I I I I I l I I I OMfiuu 11 1111111 1111 1111 111111111 1111111111 m 11111111111 111 1‘3: 8 1% 3 R 8 2 8‘8 '5 ‘8 P10 Q1 M Q} P90 Log Diameter (mm.) Cumulated Percentage 11m, #21, Sec. D 6? Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes (mm.)Diam. .. .1120 , 10 . 11 I89 1 2.97 -% I9 105 .111 VJ I/ _90 1/ fr | 80 / i _ _ 1 l I ' 1 1 | 1 1 6o 1 / 1 1 I I So _ / I 7 ' ' L 1 1 I I 40 1 1 4' l 3158 1.010 r I— [I : I 30 1.39 _ I I _25 _ _ _ _ I 1 11% 0.227 1 ' I I 20 1. i I ‘i 10 / ' I 1 I T’ 1 . l l '1 I I : all 1 0h 11111171111111111111|1111 111 l1111 111111111 111l11111 IIIIIIIIIIIIIIIIIIIIMIIIU 1111 "3. fr”: ~53, 9» 8 2 es s ‘8 P10 Q1 Md Q; P Log Diameter (mm.) 68 11 III III! 1111 1H 1 b4 KQa 0.255 I/VI’ D 1111111111 1 11 ”MIMI l WELL #22, Sec. 11__ .297 "'l Tyler Sieve Sizes (mm.) Diam. T l I .1120 25 50 Cumulative Curve of Sieve Analysis Weights / 11 “1111111111111 [‘11 111111111 11 80 100 . $9 mwSpCmOAmm umpMHSESU 01:11 P90 Md Log Diameter (mm.) P10 Q1 Cumulated Percentage 69 WELL #23, Sec. D Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mvaDiam. .319 .5120 .297 .2310 .1I119 .JI.05 .0711 100 I pa 90 _ V / l _ I w I so I S J// 1 ‘ ‘ __ ‘ __ 1 1 1 1 I I 1 I I 60 / 1 I l 1 I I O ___‘ I I 1 l I 11 f I I 110 I I 1 I / I I 3kg 0.9% l : So 1.49 T I H ._2 __ __ _/I I l an 0.422 . . 1 I 1 I 1 20 I I I I r I I I 10 / 1 I I | I I I . I I I L I I ' I I ' Chara—11,111” 1111 III 1111 11‘1 1111 I|I1111111 11111l1111 11111111111111 0 O O 3 O O O @150 N \o N \0 Ln M N H O O O 0 P10 Q1 "d Q3 P9o Log Diameter (mm.) Cumulated Percentage .359 .1120 .297 .210 $19 .105 .0711 100 I I I I I I—d —— O— : — —— :— ——— ‘——— w— I I 80 i I I 1 I J/r : 1 I 60 /r I 1 I I 1 i ' U _ 0_ _ _ _ I I I I I I I . % I'I’O I 3 : I I l I I 1 3kg 0,921+ I I ¥ So 1.35 H I 211 _f I ' . 111,,1 0.2116 _ — — —' I I I | I ' 20 ' 4 I 1 I I I I I ' 1 l i i ' _10 ' I I I 1 I I 1 i I l ! I 1 I I l l I I l I uu1111111111111111111111111111 11111 1111 111111111 1111111441 1111111111111 .2 e a .52 a s :3 es '5 ‘8 P10 Q1 Md Q3 P90 WELL #2M3 Sec. D Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes (mm) Diam. 70 Log Diameter (mm.) WELL #25, 800. E 71 Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes (mm.)Diam. "$39 .1120 3'97 ,2‘10 .1119 .105 .0711 100 - ' ' _90 _ _ _ _ __ ___ _____ A“ 1 1 l 80 [/l I 5 I " " “ " "‘“‘ i ' 1 / ' ' l 1 O I I 3:60 / I ‘ 8 / 1 ! ‘h V l a 50 — : : '8 1 1 t’ 1 1 I; 11.0 / '1 l 5 . 8kg 0.9811 :3 I H 1 30 1.117 25_ . g } an 0.232 '_ " i 20 /' I ' 1 1 i/1 1 : I 1 1 10 1/ 1 ' 1 Z | .l l 1 1 l 1 I I ,I I O 111111111I11111l1111111 1111111111111111111 m 1111111 2,- 8, 5’: .53 $3 8 2 8:3 '5 ‘8 P10 Q1 Md Q} P90 Log Diameter (mm.) Cumulated Percentage Cumulative Curve of Sieve Analysis Weights ‘UELL #26, Sec. E Tyler Sieve Sizes (mm.) Diam. .1119 .105 .0711 100 I I I ’1’“ _30 ____ 1 so 1‘ 1 __J ; 7i . / ' ' , 1 ‘ 1 60 J : I I I 1 50 J I 2% 1 1 L 1 I 1+0 /1 1 , 1 3kg 1.0114 1' i 1.43 I 25 J_ 1 an 0.214 4 1 I ‘ 20 7 I r 1 f I I T I 10 I l l T I I 1 1 I 1 I I 1 O I l11111114 mu 1111111 33% 23% Q3 0 Log Diameter (mm.) 73 WELL #27, Sec. E Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.IDiam. .359 .1120 .2'97 .aglo #9 .105 .97I1 Cumulated Percentage 100 , "" 190 _1 I I 80 I 7 _ I I I I I I 60 i I 1 ! U ' l 50 / 1 . 1 I | I ' I I10 ' I 1 : ' 3kg 0.95“» __1 : 1 30 1.57 ' I'" I _25 _ _ j/ 1 j an[0.298 ' 1' . I I I I 20 I , 1 | I 1 I I I I I I 10 AJ/ 1 1 1 I I I I {‘(}1 1 1 I I I 1 I I I 0 11111111111111111111111111 11111111111111L111 . 111111111111111 .2 e a g a s 2 e123 '5 ‘8 P10 Q1 ”C1 Q} P90 Log Diameter (mm.) WELL #28, Sec. E Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. 74 .1359 .1120 .297 .210 .1I19 .105 .0711 100 I I I I I I -L- /h_I 9o 1 / I ~—« I so I 7 _ _ __ __ _ I Z’ . I I m 1 [/I : l I 3: 6O / : i 3 / 1 I L1 I I 33 .50 ._ __ ___ ___. 1 I U /1 I II 0 f '1 I I p as I I I '3 40 i i ‘ g 1 l 3kg 0.956 ' 1 I I 30 1.6”» I 1 I ~ _25 _ _ _ _ _L _. l an O .4129 u I I I 20 I I i ' I I 1 ' 1 I 1 ' 1 10 I L : I 1 I 1 1 "r! 1_ I 1 1 1 1 I 1 O 111111111111111111111111111l1111 1111 4111111 1111111‘1 “AIM 1111111 2 e 12 .9. .2 s .2 e s s ‘8 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage WELL #29, See. E 75 Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes hum.) Diam. .§89 .1120 .297 .210 .1119 .105 .0711 100 I I I l 1 I I .4 90 I“ / 1 80 I 7 _ _ ____ ___ _/ [I I l I 1 1 l l l 60 / 1 1 1 » 1 50 __ / 1 ' I I I I I 110 I ' / I I 3kg 1.000 // | 1 So 1.u4 21 _ I I Mia 0.250 . I ' 1 l 20 I T I 1 l, I 31 10 / I I 1 I / . . s . 1 1 I I l 1 | T I 0m “11$ 11 1‘ 1111 11h 1111 L‘IJIIIII 111IL1L11 “11111113111111 1111 <3 68 <3 :3 <3 <3 <3 oxao r~ \o h~ u\ ~\ «1 .4 c><3 <3 <3 P10 Q1 Md. Q3 P90 Log Diameter (mm.) Cumulated Percentage . 9 $5 80 O‘\ O .p O 20 .70 60 76 WELL #30, Sec. E Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. .II20 .297 .230 . I19 .105 .0711 3kg 0.986 80 1.31 KQa 0.118 5% E? 5% E3 53 EFE9 2? P10 Q1 Md Q3 P90 Log Diameter (mm.) .06 Cumulated Percentage 77 MIMI, Sec. F Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm) Diam. ?69 ,1I20 .297 ,qio 4,119 .105 .0711 100 I 50 K i I 80 I ‘i __ _ _A/ 1 /4 1 I 1‘ 1 I I I 1 60 1 1 I I 1‘ . I I 50 j 1 I 7' 1 l : 1 1 I I10 I I 1 : / i L I 3kg 0.986 1 1 "‘ / I 1 1 80 1.36 ' I j _ 21_ _ I 1 1 mm 0.261 I i 1 l 20 /I I 1 I 1 1 L I T I 10 I I I I 1* fl 1 1 I . 1 7&1 I I L I 1 1 I * OLA 11flu111l11111l11111I1L111111111 IIIIIILII m1u11111111 1 O O O O OO\’60I\\O fig It? .3 M N HOOO 0 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage 78 mm#32, Sec. r Cumulative Curve 0f Sieve Analysis weights Tyler Sieve Sizes (mm.) Dian. .359 .I120 .2197 ,2'10 .JTI19 4.105 .0711 100 f 90_ _f __ _ __ __ __ ' I . 1 so / ' 1 i — — ——— 1 1 /1 ' l 60 / I 1 / 1 I30 I I I I l 1 l I I 1 I10 {/1 I l . l _1 8kg 1.030 1 / 1 I I So 1.43 1 , 25 _ . I mm 0.259 1 20 //I 4 I I j 1 I i 1 1 1 1 ' I . I I 1 1 I I I OLD 111111111111111 11L 1111 11 I1111 111‘ 111111111 1111111111 W111111111111111 Fl. 8 1% 3 1% 8 3 8‘8 '5 ‘8 P10 . Q1 Md Q3 ‘ P90 Log Diameter (mm.) Cumulated Percentage WELL #3}, Sec. F Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes (mm) Diam. 7 9 .339 .1120 .297 .210 .1149 .105 .0711 100 I I I I l 1 I’— _11__1L—1 / 30 i j I 1 80 I I _ 1 1111 /I I I I / 1 1 1 _1 1 1 60 l 1 / ' 1 I I u 80 /’ I | 1 I | 1‘ ' 1 -1 1 I | I I E 110 1 1' I 1 JI 1 8kg 0.956 1— ~~—---—1——- _4 / I I I SO I.“ l I 1 fi 25 __ anL _4 KQa 0.274 I I I I 20 I i / 1 1 1 1 T 1 10 I I 1 I 1 1 I ' 1 1 1 1 1 1 1 I“ 0L“ 1111111 1111111111111111114 111111141 1111111111 1111111111 11.111111.ou 1111111 1‘3 8 1% .53 R 8 S 8‘ “8 '5 ‘8 P10 Q1 Md Q3 P9o Log Diameter (mm.) Cumulated Percentage WELL #34, Sec. F Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. 80 .§89 .1120 .297 .210 .1119 .105 .0711 100 I I I I I 1 (I _90 __ __ __ 11-- 2F / 1 I I 80 1 i _ _ _ _: == __/ I a. . /1 I | l 60 1 ' / ' I { - 0 j 1 I g. _, I] 1, . 1 1 : I 1 10 /. 1 . / l 1 3kg IWOOS , ' _ 4: ! 80 1.113 _ 21; _ _ _ 1 : an 0.2111 l i 20 /I1 I l I I 1 ' I I 1 I l I l 3 l9 __ ‘g 1 | 1 i 1// l I l | l 1 1 r ' I V I OiIJJI 111111111111 1111l11 111111.114 1441’111 1111111111111 (3 c: c: :3 <3 <3 <3 oxeo P~ \o N \0 1.0 M N H O O O 0 P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage 81 WELL #35, Sec. F‘ Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes hmnj Diam. °?89 .I'IZO $2.97 '2110 .1149 .}05 .974 100 30 _ _ w __ __ 1//. a I 4 I I' so // I 5 _ = g 1 1 l I I T TW 1. I I 1 1 I 1 1 60 I 1 I I I I i t; 0 j l I . l l I I I l l_ 40 I 1 4 I 1 I 1 1 8kg 0.913 I I ‘ "j r “* H / 1: 1 1 1 1 80 1.35 H l I 25 j I I 1 an 0.245 I 20 71 : 1 1 1 I I I K | I L I I 10/ 1 I I I l l I I I 1 I I 1 l 1 I l 1 0L111111111111111 111111 11111111111! 111111111 1111111111 11111111111111111111 O O ,1. e a .9, a a .2 as '5 2% P10 Q1 Md Q5 P90 Log Diameter (mm.) Cumulated Percentage WEIJ..#36, See. I“ 82 Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (111111.) Diam. .- . 20 . 10 . 11 .10 . 11 100 $9 lI, .2I97 % 1I 9 I 5 97 I so / I 1 / 1 so . J5 1 I / I / 1 ' 6o \ I . 1 50 // ' I I I 1 ; 1 11,0 - . I 1 8kg 0.975 l - "‘ / I 1 So 1.58 _ _25 __/ I :an 0.262 fl I 1 I 1 - 20 1 1 j I 1 I / 1 1 1 10 1 , I I I 1 1 I 1 1 I I 0w111111111111111111111111 1111 1111 L111 1111111 111111111' 1111111 1‘3 8 Ex .3 R 8 3 8‘8 '5 ‘8 P10, Q1 “‘1 ~ Q3 P90 Log Diameter (mm.) Cumulated Percentage 83 WELL #37, Sec. G Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. .?89 .II'~20 .2'97 .290 .1lI-I'9 $05 .97II 100 ’1 a) -1 9o )4 /.' "“ I so / I _75 __ ___. I 1 : 1 | _ / 1 ._ 1 1 60 / I / 1 . o 1 I /I 1 / ' ' I 110 1 l I l I 3kg 1.012 / 1 1 So 1.112 1. i l 25 _/ I...i_. I 1 Ma 0.270 | I I I 20 f I I I j | I I I F I I 10 I J 1 1 1 T 1/ 1 _ I 1 If I I Oh11111111111111111111111111111111 111I1 111111111 1111111111 “11111111111111111 2. s 521 .92 a s 2 es s- 2% P10 Q1 Md Q3 P90 Log Diameter (mm.) Cumulated Percentage WELL #38, Sec. G Cumulative Curve of Sieve Analysis Weights Tyler Sieve Sizes (mm.) Diam. .1?89 .IIBO ’2197 .8110 -}II9 -}05 .QYII 100 f _90 .1 _///;P l | I so 11 5 1 T Z 1 /' ' I 1 60 I, 1 I / I 1 I I 50 1 I . 1 I /J . 1 40 I 1* . 8k 1 I I g 1.010“4 1 I ' , 4 g! I So 1.32 _1 25__‘ _‘ j] I I I an 0.247 I I l 20 L I I I 1 ' I I l, 1 i 1 : l 10 _j’ 1 I I | Z i T i . I 1 1 I I 1 / I I I I I O 111111111111111111 1k1111111 1111111111 111111111 111111111111111 <3 .7 s s s a s 2 as s- 8 P10 Q1 Md Q5 P90 Log Diameter (mm.) Cumulated Percentage 85 WELL #39, Sec. G Cumulative Curve of Sieve Analysis weights Tyler Sieve Sizes (mm.) Diam. .359 .1120 .297 .210 .1119 .105 .0711 100 I I I I I 1 FA!‘ 0 ,K . —-4». I so / I 7 / I I I I I I_ 1 ' 1 6O / I f / ! I I 1 o / 1 I 1 I I 1 1 I 1 40 I 1 I I T I 8k 1 g 1.017 L— 'T r- A / I I1 I 30 1.37 I | I — . ' ' I 1 I ' I 1 1 ‘r I 10 1 I I I I | I I I 1 I I I l ; I 1 1 O‘U-I-I 111111111111 111.1 1111 1|1111111 1111111111 111111111111111 O O O .3 O O 0 mm N \D P- U) UN ~\ Q1 .4 c>H~.0 H0.H 0m~.0 NHN.0 >0N.0 000.0 0hvu0 0H mwN.0 Hm0.1 Nm0.0 50H.0 hm.~ NHH.0 mh~.0 0mN.0 0mm.0 000.0 0H mmm.0 wmo.+ wm0.H 00H.0 0¢.H 000.0 0HH.0 NOH.0 0vN.0 $00.0 0H m0m.0 Nmo. 0N0.0 m¢~.0 0m.~ N00.0 00H.0 000.0 0mm.0 0Nm.0 0H 00m.0 0H0. nm0.0 00H.0 0N.H 000.0 vNN.0 ¢0N.0 vmm.0 $00.0 NH mn1.0 0N0. 0m0.0 0vfi.o Hw.H 500.0 00H.0 MHN.0 FON.0 000.0 HH 00m.0 0m0.1 m0H.H vm~.0 N0.H 000.0 00H.0 00H.0 0HN.0 mnm.0 0H 0mN.c >00.1 000.0 vNH.0 mm.H 0Na.0 00H.0 MNN.0 NON.0 0wm.0 0 mFN.0 0~0.1 000.0 nmfi.0 um.~ 00H.0 mm~.0 ONN.0 00N.0 000.0 0 050.0 000.+ HHO.H mn~.0 0¢.H 000.0 ¢NH.0 NOH.0 0>N.0 000.0 N 0nN.0 0H0.1 Hn0.0 HmH.0 mm.H 00~.0 wmfi.o mHN.0 NON.0 000.0 0 HON.0 000.+ 0H0.H 0vfi.o 00.H >00.0 NmH.0 v0fi.0 00N.0 Nvm.0 m 0m~.0 N00.1 000.0 HHH.0 0N.~ 0NH.0 Nm~.0 NON.0 th.0 000.0 0 000.0 0N0.1 000.0 >0~.0 nv.H 000.0 NNH.0 00N.0 0n~.0 000.0 m pnm.0 000.1 000.0 w0fi.0 0¢.H 000.0 00H.0 m0H.0 0NN.0 Nom.0 N 0mN.0 0N0.+ 000.H 00H.0 0m.~ m00.0 00H.0 mmH.0 00H.0 0>N.0 H my 0 o 0 I. I m -m m 0 m a 0H .02 0 M 004 #0 004 om m G 32 O Am So? mHm>A 0.01:0 <0. 91 Analysis of Size Distribution The material summarised in Table II was used in preparing the cumulative calculations presented in Table V. From Table V the values of median size, Md; sorting, So; skewness, Sk ; and kurtosis, an, were taken and plotted at their reSpective well locations to produce isopleth maps (Maps 4, 5, 6, 7). An isopleth map has been defined by Krumbein (1939, p. 587) as a map in which “lines of equal abundance (contours) are drawn through sets of numbers, such that each number is located at the point of sampling and corresponds to the magnitude of the character- istic being mapped." Trask (1930) first suggested the use of such maps, and it is recognized that any characteristic of a sediment which may be eXpressed as a number in a continuous range of values may be used as the basis of an isopleth map. From the isopleth maps presented for size distribution, a def- inite similarity may be noted, showing that relationships between the median size, sorting, skewness, and kurtosis do exist and may be compared quantitatively. Certain relationships are believed to pre- vail in normal water-laid sediments. For example, it may be seen from Well No. 19 (Map 3) that the So value of 1.95 (Map 5) is higher or more poorly sorted, whereas the median size, 0.253 (Map 4), is 92 MAP No. 4 MEDIAN SIZE DISTRIBUTION SIEVE ANALYSIS 0 .2I3 J80 . .32” I“ 134 '99 .7 J8 O 0.203 190 / -Legend-* Size Decrease Size Increase Well IBOpIeth Interval .020 mm. Scale 1 ‘ O 10 PO Miles 93 HAP No. 5 SORTING (So) DISTRIBUTION . SIEVE mums we L402 0 L32 L43 "3 .l.44 O :57 .m7 . L43 Ml 1.40 o :35 / 155 0L5}, R O m / / / -Legend- Sorting .37 ”.2 W Increase BS 0 0 Que "‘ . \.*6 L4 7 Que 4, Sorting I q Decrease 0 Hell L30 /—T‘35\: leapleth Interval 0.05 unit “0 Scale E:::l!!!5:i===:=l!!!!!!: 10 5 O 10 20 Miles 94 HAP No. 6 SKEWNESS (S ) DISTRIBUTION SIEVE ISIS I -Legend- 1‘ W Coarseness Increase l I q Fineness Increase 9‘ .96 0» well '0' \ I l l l 9 Q‘ 97 leapleth Interval 2.5 units '33 Scale EEEEIEEEFEIEEEEEIEEEEEES 10 5 O 10 a: Miles 95 MAP No. 7 KURTOSIS (an) DISTRIBUTION e 311m: ANALYSIS 26 .270 ’\ ‘lr .26 ' .270 - Lege nd- /, Peakedness 113° If Increase Peakedness Decrease 0 ‘Well ¢¢> o I 130p1eth Interval . ‘1'. ' e010 unit 236 “$ . .26l 0 Scale GE=EEEESEEEZEEEEEEEEEES IL) 5 O 10 20 Miles 96 larger than at adjacent wells. Also, the Sk value, 0.77 (Map 6) of 8 ) Well No. 19 is considerably less than one, indicating that the curve is skewed toward the smaller sizes; that is, smaller than the median. In the case of the an value of 0.336 (Map 7), peakedness of the curve is much less than in other parts of the area. As the sediment becomes better sorted, these relationships are reversed. In this same manner, comparison of other sections throughout the area of investi- gation may be studied, A second method by which the size distributions may be com- pared is through the use of the logarithmic values of both So and 5kg expressed in Table V. As explained on page 38, logarithmic values may be compared. mathematically. For example, Well No. 12 may be said to be 2.9 times better sorted than Well No. 19, because 0.290/0.100 equals 2.9, where the logarithmic value of sorting, "So," for Well No. 19 equals 0.290, and for Well No. 12, equals 0.100. In the case of skewness, it may be said that the curve for Well No. 19 is skewed 5.9 times farther toward the smaller sizes than is the curve for Well No. 12, because 0.113/0.019 equals 5.9, where the logarithmic value of skewness, Sk , for the curve repre- senting Well No. 19 equals 0.113, and for that representing Well No. 12 equals 0.019. 97 Still another method of comparison may be found in examining the Cumulative curve from which the above numerical values have been obtained (pp. 58, 65). It will be noted by examining the curves for Well NO. 19, and Well NO. 12, that in the case of Well N0. 19, a definite polymorphic curve is present, suggesting more than one period of deposition such as an intermittent stream might deposit. In the case of Well No. 12, on the other hand, a smooth, even curve persists, showing a continuous grading of sediments. Another notable feature is that the areas of most prominent expression in Maps 4, 5, 6, and 7 are found around the locations of Well Nos. 3, 7, 10, 19, 20, 27, and 28. If these well numbers are also compared with their cumulative curves, it will be seen that in all cases the curves are not smooth, but show polymorphic shapes. By comparing the weight percentages listed in Table II with these curves, the exact weight percentage in each sieve size may be ob- tained and the resulting effect on the curves noted. If the above three methods of comparison are now interrelated, it is possible to discover many interesting relationships which may be used in obtaining the final results. For illustration, it may be observed from the cumulative curves for Well Nos. 35 and 36 on pages 81 and. 82 that the closer together the Q and Q3 lines are, 1 98 the smaller the sorting value is, or the better the sample is sorted. If these wells are then compared on the sorting map (Map 5), it will be noted that the sorting increases toward the northwest, suggesting that the material was derived from the southeast in that particular area. If the lOgarithmic values of sorting are now compared as on page 96, the relationship is both visible and mathematical. Analysis of Roundness Distribution In the analysis of roundness distributions, four methods of comparing the data secured in measuring the quarz grains are pre- sented. The first method is by directly comparing the arithmetic averages as summarized in Table VI. In this method, however, the averages are so nearly alike that a visual comparison is of little value. The second method of comparison may be illustrated by the histogram analysis on pages 108-117. To obtain these figures, the number of quartz grains measured between each 0.05 interval of roundness, beginning with those having a roundness of 0.100 to 0.149 and from 0.150 to 0.199, et cetera, through 0.500, were plotted in arithmetic form. Because one hundred grains of sand were measured from each well sample, each grain was equivalent to 1 per cent of 99 TABLE VI ARITHMETIC AVERAGES OF ROUNDNESS AND SPHERICITY -_.. -fi_- _-—._——.-__—H_._—-_—_~.——.__ -—-.— ._--.—~—~—F-r-—.—--‘V. -—~—_._..~_--.—— - -.. -fl.‘_*~ -—. -—-.——-._.. Well Round - Sphe - Well Round - Sphe - No. ness ricity No. ness ricity 1 0.256 0 775 21 0.288 0.791 2 0.285 0 793 22 0.301 0 793 3 0.277 0 802 23 0.247 0.800 4 0.266 0.783 24 0.286 0.793 5 0.252 0.796 25 0.271 0 791 6 0.252 0 790 26 0.308 0 791 7 0.328 0.796 27 0 264 0.791 8 0.324 0 791 28 0.293 0.789 9 0 252 0.793 29 0.301 0.788 10 0.292 0.794 30 0.257 0.790 11 0.286 0.796 31 0.270.. 0.798 12 0.258 0 798 32 0,264 0.790 13 0.242 0.804 33 0.305 0.790 14 0.243 0.780 34 0.306 0.785 15 0.264 0.800 35 0.264 0.780 16 0.296 0.788 36 0.192 0§771 17 0.298 0.775 37 0 292 0.794 18 0.309 0.802 38 0.298 0.793 19 0 252 0.791 39 0.301 0 790 ' 20 0.289 0.806 40 0.311 0 794 - .——-—. 100 the sample. The histograms, therefore, are direct representatives of the data obtained. From these, it is possible to visualize graph— ically the sorting, skewness, and distribution of the sand measure- ments which are obtained from the quartile calculation of the cumu- lative curves. Features to be noted from these figures are: the interval containing; the largest percentage of grains, that is, the modal class, does not, in most cases, contain the arithmetic average (Table VI), nor in many cases does it correspond to the median cal- culations (Table III). This represents the skewness values derived from the cumulative curves, and the modal class represents the sorting values. The writer feels that when these histograms are compared with the results obtained from the cumulative curves, the reader will gain a better understanding of these results. , Table III is a summary of the roundness calculations taken from the cumulative curves. These curves were drawn using the phi notation as the independent variable (Figure 3), from the same data used in making the histograms. In studying the cumulative quartile calculations, important information may be obtained by com- paring the quartile deviation, QDpi, values. These values are taken directly from the graphs plotted according to Krumbein's phi scale, whereas the "So" values are calculated as described on page 41, 101 which is the same as the values obtained when the curves are plotted on semilogarithmic paper, The iSOpleth maps (Maps 10 and 11) plotted with QDpi and 50 values will illustrate the similarity. The same relationships exist between skewness, Skgyzi, and skewness, Sk. The logarithmic data presented for So and Sk are to be compared in the same manner as the logarithmic values explained in the size analysis on page 96. In the fourth method of comparing roundness measurements, isopleth maps have been used to represent the values derived from calculating the arithmetic averages (Map 8) and to represent the Md, QDd, So, and Sk values (Maps 9, 10, 11, 12) obtained from the cumu- lative curves. It should be noted that in all cases these iSOpleth maps show the same general pattern. For example, it may be seen that Well Nos. 8 and 17 (Map 3) represent areas of sediment having a comparatively high degree of rounding (Maps 8 and 9). These same locations should now be examined on the maps representing roundness sorting (Maps 10 and 11). The same trends may be observed, and it will be seen that the sands in these areas are rather poorly sorted, in comparison to the sands in other areas such as those around Well Nos. 19 and 36. The skewness (Map 12) values should also be examined for Well NOS. 8 and 17, and the area around these 102 AVERAGE ROUNDNESS DISTRIBUTION -Legend- Roundness Increase Roundness Decrease Sell ‘2? Isopleth Interval § .010 unit 3:2 Scale F:=:E!!!§;::====£!!!!!!! 10 5 o 10 20 Niles 103 MEDIAN (mas) Rosannmss DISTRIBUTION .1285 Roundness Increase Roundness i Decrease O> Well IsOpleth Interval .010 unit '2.“ Scale i:::2!!!§§i:::::!!!!!!!§ lO 6 O 10 20 Miles 104 SORTING (QD¢) DISTRIBUTION ROUNDNESS - Legend— W Sorting Increase v Sorting Decrease .1 well IsOpleth Interval .OHO unit 460 493 Scale \m 10 5 o 10 20 Miles 105 HAP No . 11 SORTING (So) DISTRIBUTION 0'5 ROUNDNESS \ 1.55 0 LG 0 -' Lege nd- W Sorting Increase q Sorting ."59 I1— Decrease e Hell 1.44 4 o 1.40 [.45 0149 | IBOpéSSISl ::Egrval 0: «5° 1:4 W Scale m I” \ 10 5 o 10 20 L60 Niles 106 MAP No. 12 SKEWNESS (Sk) DISTRIBUTION ROUNDNESS -Legend-' / _ / W Increase toward I less rd,grains I Increase toward ° 8° more rd. grains I : I. well I I IsOpleth Interval 0.05 unit Scale 0 ' 5 O 10 20 Miles 107 locations compared with the other isopleth maps mentioned above. From these exampleS, it may be seen that the average and median roundness, sorting and quartile deviation, and skewness appear, in general, to illustrate similar trends of deposition. The relationships, however, existing between these values are _not, in all places, those expected in normal stream deposits. That is, many geologists take for granted that as a sand grain is tranSported it becomes more rounded, the sorting increases, and a graph, such as a histogram, will show the skewness of a sediment to be toward the less rounded grains as the tranSportation distance increases. The relationship skewness has to the histogram may be seen when the modal class is compared with the median roundness (Table III and pages 108-117). Those cases including the example given above which appear to differ from the expected results will be considered in the section on inter- pretation. 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