FEASBELITY 0F COMPLETELY AUTOMATED MECROFOSSIL IDENTEFECA'HON 1N PETROLEUM . EXPLORATION Thesis fo: the Degree of M. S. Micmm STATE UNEVERSHY FREDERECK CHARLES EWALD 1975 lnEsns a? minimum av -? '\ ' mm: & suns' 800K BINDERY mc. 32; ”I LIBRARY g - “E98 1’ :‘ §Pfilh;9..; , 1H m ABSTRACT FEASIBILITY OF COMPLETELY AUTOMATED MICROFOSSIL IDENTIFICATION IN PETROLEUM EXPLORATION BY Frederick Charles Ewald The purpose of this study is to explore the possiblity of eliminating the time-consuming aSpect involved in conventional methods of identifying ostracodes. Using computerized methods, this work can be accomplished with greatly increased rapidity and productivity in identification. Initially, this study attempts to differ- entiate 91 species of Mesozoic and Cenozoic ostracodes that have been selected on the basis of their proven use— fulness in biostratigraphic correlation and identify them on the basis of shape using Fourier shape analysis. This method, develOped by Ehrlich and Weinberg (1970), exactly describes two—dimensional shape in a multivariate fashion. The Fourier series generated 55 shape variables for use in the identification process. The objective of this study was to find the Optimum combination of the variables generated by the Fourier series and the Optimum clustering methods for the identification of ostracode Frederick Charles Ewald guide fossils. Parks' (1970) program using simple distance based on principal component values with results illustrated in dendrogram form enables interpretation of specimen clustering. Twenty specimens (12 species) were added later for species—level identification. After 53 specimens associated with sampling design error were omitted, a final cluster analysis was run with the remaining 58 specimens. Of these 58 specimens, 9 were replicated at the species level. Using the most optimal clustering method, the results indicated that only one specimen, Bythocypris (?) gibsonensis, was misidentified at the species level. This specimen was doubtfully assigned to the species gibsonensis and may belong to some other Species. FEASIBILITY OF COMPLETELY AUTOMATED MICROFOSSIL IDENTIFICATION IN PETROLEUM EXPLORATION BY Frederick Charles Ewald A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1975 Dedicated to my wife, Sue, for her assistance and support throughout this study. ii AC KN OWLEDGME NT S Don Merit and Tom Campbell (Merit Enterprizes) are to be thanked for their assistance and use of a sonic digitizer. I would like to thank Dr. James Fisher and Dr. Chilton Prouty for their helpful suggestions and important information given to me in this study. My parents and family are respectfully acknowledged for their confidence and moral support given to me through- out my academic pursuits. And special thanks goes to my wife, Sue, for the typing of the rough (there were many) drafts of my thesis. I am indebted to the Geology Department for its support of the computer work done at the Michigan State University Computer Laboratory. And finally, I would like to thank my advisor, Dr. Robert L. Anstey, for help in writing and adapting additional programs for use in this study and for his patience and guidance throughout the study. iii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . v LIST OF FIGURES. . . . . . . . . . . . . Vi INTRODUCTION. . . . . . . . . . . . . . 1 METHOD. . . . . . . . . . . . . . . . 5 Material . . . . . . . . . . . . . . 5 Fourier Shape Analysis. . . . . . . . . . 6 Factor Analysis . . . . . . . . . . 12 Optimal Clustering Methods . . . . . . . . 15 SPECIES IDENTIFICATION . . . . . . . . . . 24 SUMMARY AND CONCLUSIONS . . . . . . . . . . 31 LIST OF REFERENCES. . . . . . . . . . . . 32 APPENDICES Appendix 1. Listing of Program Fourier. . . . . . . 34 II. Listing of Program Rough . . . . . . . 40 III. Listing of Program Redraw . . . . . . . 41 IV. Listing of Program Angle . . . . . . . 44 V. Listing of Program Convert. . . . . . . 45 VI. Listing of CLUSTG Program With Final Cluster Results. . . . . . . . . . 46 iv Table 1. LIST OF TABLES Classification of specimens used in shape analysis and the geologic horizons of which they are indices . . . . . . . . Results of analysis of variance in determination of significant harmonic amplitudes based on the original 91 specimens (Appendix III) . . Results of Program Angle (Appendix IV) with resultant vector lengths of phase angles for their reSpective harmonic amplitudes based on 91 specimens. Maximum vector length is 91.00 . . . . . . . . . . Eigenvalues of transformed and untransformed data I O O O O O O O O O O O O 0 Comparisons of various clustering methods via results at genus and family level using the original 91 specimens . . . . . . . Principal component loading of Fourier shape character set for initial R-mode analysis of Park's CLUST6 program. Character 1, RC-ALL; 2, RADIUS; 3-28, harmonic amplitudes 2-27. Total percent variance extracted by the seven components is 79.856. Fl-7 indicates principal components 1-7 . . . . Evaluation of final clustering results in terms of percent of pairwise comparisons and calculated chi-square results for same . Page 10 16 19 23 25 LIST OF FIGURES Figure 1. Flow chart of study methods illustrating sequence of computer programs used . . . . 2. Q-mode dendrogram illustrating phenetic affinites of 58 specimens of Mesozoic and Cenozoic ostracodes based on 7 principal components extracted from 28 shape variables. 3. Triangular plot indicating clustering of specimens at the generic level. (Computed from principal components 1, 2, and 3 of final cluster analysis). . . . . . . . vi Page 14 28 30 INTRODUCTION Microfossils are useful in petroleum exploration for three basic reasons: (1) biostratigraphic correlation; (2) environmental analysis in depositional basins; and (3) they are retrievable from the subsurface in well cuttings. Therefore, microfossils are economically useful. One major problem is that they have been difficult to use because conventional identification is tedious and time— consuming and the identifier must search through a prolific literature beset with some degree of taxonomic chaos. Even present practices by competent professionals do not insure complete accuracy in all taxonomic assignments. Greater efficiency and productivity in such work could be obtained by utilizing trained specialists in the development of highly automated identification systems that could be Operated by nonpaleontologists and still yield a signifi- cant prOportion of accurate identifications. The purpose of this study is to explore the possibility of eliminating the time-consuming aspect of identification by creating a completely automated system for the identification of microfossils. Through the automation of large portions of the identification process, such work can be accomplished by less highly skilled workers with extreme rapidity of identification and prodigiously increased output. Needless to say, such an increase in productivity could be of great economic value. Fourier analysis has been proven successful in "automatically" identifying a wide range of different types of microfossils from both two-dimensional outlines and photographic images of the complete fossil. Developed in an Optimal way by Ehrlich and Weinberg (1970), who applied it successfully to inorganic forms, this shape analysis method exactly describes two-dimensional shape. In a controlled experiment, two Soviet workers, Mirkin and Bagdasaryan (1972), successfully identified unknown micro- paleontological objects, using an Optical Fourier series taken from photographed images of the entire microfosSil. Their samples included spore and pollen grains, diatoms, and phytoplankton. Successful results in ostracode identification using Ehrlich and Weinberg's method have been achieved by Younker (1971, 1974) and Kaesler and Waters (1972). ChristOpher and Waters (1975) demonstrate the utility of the same method for palynomorphs. These studies suggest that with the use of an optical scanner to obtain the two-dimensional outlines automatically, and a minicomputer programmed to calculate the Fourier series (and having memory capacity sufficient to store the Fourier amplitudes of a wide range of known forms), the identification process could be accomplished with extreme rapidity and productivity with a minimal loss of accuracy. As a means of seeking quantitative solutions to the mass identification of microfossils for use in petroleum exploration, this study attempts to differentiate 91 species of Mesozoic and Cenozoic ostracodes and identify them on the basis of shape using the Fourier series. These 91 species have been selected on the basis of their proven usefulness in biostratigraphic correlation. Thus this study, unlike previous studies, specifically emphasizes the machine identification of taxa having potential economic importance. Automated identification poses several problems in that a great variety of options are available to any investigator desirous of building such a system. It is known that the Fourier method is operational, but the precise combination of Options for Optimal machine- processing is not clearly defined. Thus, the objective of this study is to search for the Optimum combination of the variables generaged by the Fourier series and the Optimum clustering methods for the identification of ostracode guide fossils. Complete automation of this method is desired if it is to eliminate the time-consuming aspects. This study includes in its equipage a sonic digitizer interfaced to computers that contain the necessary programs for the ultimate clustering analysis. This thesis, however, introduces some degree of human error because the digitizing of the estracode outline is done semi-manually. A device made by Visicon, Inc., called the GC-3A, is a fast, accurate, compact, and inexpensive terminal for the completely automatic conversion of graphic data to digital data. The Visicon GC-3A uses a raster scan type of optical/electronic digitizing. The GC-3A automatically scans and digitizes the information. This device, coupled to the stage of a microsc0pe, such as the automatic coordinate recorder discussed by Scott (1975), would achieve great accuracy because the raster scan would more accurately depict the outline boundaries, the human error in digitizing would be eliminated. The only limitations in this process involve the (minimal) time factor necessary to present the prepared Specimens to the Optical scanner. Thus this study prOposes to test the usefulness of Fourier analysis in a wide variety of Mesozoic and Cenozoic ostracode species that have been proven to be successful index or guide fossils to petroliferous horizons. The results obtained will provide a direct test of the economic usefulness of these computer-based techniques, and will determine, as a first approximation, the feasibility of completely automated identification systems in industrial applications. METHODS Material Photographs of 91 different species of ostracodes, all guide fossils from the Cenozoic and Mesozoic, were collected from published literature for preliminary study at the family and generic levels. The majority of these are Cenozoic and are common to the Gulf Coast area of the United States and its petroliferous horizons. Illustrations of 20 additional specimens of 12 of the same species were obtained for comparison and identification at the Species level. Outlines were drawn from projections of published photographs (Shimer & Shrock, 1944; Ellis & Messina, 1952- 1971; McLean, 1957; Moore, 1961). The photographs of these 11 ostracode specimens were the experimental units for this study. When possible the right valve view was selected. Of these 111 photographs, 53 were later eliminated because they were known to be females (8), juvenile instars (7), and imprOper views (38). Improper views include left valve images and other views that were not right valves. The reason for their elimination is because these sources of potential error occurred in a majority of Specimens that were misidentified in the final clustering of the total 111 specimens. Of the remaining 58 specimens (51 Species), nine are of species that have multiple representatives for use in testing species-level identification (Table l). Fourier Shape Analysis The Fourier method of shape characterization (harmonic analysis) was first develOped and used in studies of closed forms in geology by Ehrlich and Weinberg (1970). Fourier descriptors are very good shape discriminators; the proof of the Optimality of Fourier series has been esta- blished (Zahn & Roskies, 1972). To obtain the Fourier series of each Shape, the origin of a set of polar coordinates was centered over the projected photograph such that the valve length corresponded to the 0°-180° axis, and the breadth to the 90°-270° axis. In this way, all shapes were orientated in a consistent manner. The radii of each shape (measured from the approximate center of gravity of each form to the valve periphery) were Spaced at 6° intervals yielding 60 radiating lines in a sunburst pattern. The intersection points of the traced outline and the sunburst grid were digitized in Cartesian coordinates. The punched coordinates of the 111 outlines were used as input to program Fourier (Appendix I). The measurements were used to compute a Fourier series including calculation of the mean radius (the mean radius is Table l.--Clessificetion of specimens used in shape enelysis end the geologic horizons of which they ere indices. I. Order Podocopide A. C. Suborder Metecopine 8uper£eeily Heeldiecee I-ily leirdiocyprididee leirdiocnrie norrieoneneie Math, 1933 Inhorder Pletycopine Fellily Cytherellidee Cytherelle nerlboroeneie Ulrich, 1901 Cytherelle ovate (leaner, 1840) Suborder Podocopine Superfeeily Ieirdiecee III-11y hirdiidee [ythocmrie gibeonensie Hove end Che-here, 1935 ychocyprie goodlendenlie Alexender, 1929 athocxprie eubeeguete Ulrich, 1901 Superf-ily Cypridecee Fe-ily Perecyprididee Perecyprie perepiculete Almnder, 1934 Superf-i 1y Cytherecee hilly Brechycytherldee grechycythere interreeilie Alexender, 1934 Brechycythere ledeforee (Iereeleky, 1929) Brechycythere ledeforu erogete Crane, 1965 Brechycythere ephemldee (Reuse, 1854) Dimcythere ruuelli (Rowe end 1., 1936) Eerygocythercu cornute “rig Ulrich end leeeler, 1904 I‘ll, lythocytheridee fimceretine Eden (Mereeon, 1880) ”sweeten! roeeee Alexender, 1934 Feeily Cytherideidee Subtletily Cyrherideinee W M (Hove m lloulh. 1935) Clithrocychuidee erretti love end Che-here, 1935 Eglocytheridee m Stepheneon, 1936 Ueplocyrheridee non-outheneig lorry, 1925 Gobi-11y Eucyrherinee lucythere brighteeeteneie (Berry, 1925) Qcythere brounuoveneie Alexender, 1936 flcythere chickeeevhezeneig More, 193‘ lucythere wooduerdensis Hove, 1936 Subfunily Neocytherideidinee leocyrherideie eeherneni Ulrich end heeler, 1904 Phil)! Cytheruridee gytheropteron glericulu “one end Lev, 1936 Cytherogteron nidveyensie Alexender, 193‘ Cxtheropteron eont‘oneryeneie More end Ch-bere, 1935 Cytherogceron neverroenee Alexender, 1929 Cytherure ban-emu Hove end Lee, 1936 Cxtherure cretecee Alexender, 1936 Cztherure urdeneie Hove end Bron, 1935 Eocfiheropteron bilobetu- Alezender, 1929 Eocytheropteron grinitieneie (Venderpool, 1928) Bucxtherure nurdercreekeneig love end Lew, 1936 Orthonotecnhere criatete Alexender, 1934 Orthonotecythere hennei (Iereelehy, 1929) Philly Loxoconchidee Exoconche cleiborneneie Denney, 1938 Loxoconche fletcheri lereeleky, 1929 [exoconche gerdecoge Alexender, 193‘ r-ily Schizocytheridee Ehicytherure dubie (Mereeon, 1880) 1‘11 'rrechyleberididee grimcyrhereie ”enthuse (Ulrich end heeler, 1904) Actinocythereie exentheeece neglendice More end w, 1935 cmereie heuleri Ulrich, 1901 chereie heuleri Le_t_e Jenninu, 1936 chereie beee1eri reticulolire Sch-1dr, 1m Exchereie bee-leri vecuitetie Schulz, 1958 Qflereie co-unie retiveece Grene, 1965 gxflercie aetulosiuiee Alexender, 1929 tahereie eniplicete house, 1846 §1t_hereie veuflni (Ulrich end heeler, 190‘) W m1 (love and locum. 1935) W 12mm Glove and Pratt. 1935) Lower Morrleon Fe. Aquie Pm, Peeporenee Mb. Ileverro Group 1.. Jeckeonul. (hickeeeuhey Merl Frederick-bur; Group, Goodleod h. Aquie I'm, Peepotenee Mb. Miduy Group, Uille Point end 1.. Kinceid he. Mibey Group, Kinceid end Uille Point Pee. leverro Grcaup 1.. Teylor Herb-Austin Ghelh Teylor hrluAuerin (belt Cleiboroe-Wichehur; he. Colbert P... 1.. P1:- Point hrl IO. U. Gret. Glide lease) Mihey Group, U. Uille Polo: Pe. Chocteuhetchee h. Lover-u: Jecheon h. Vichhur; Group Flo-sud! PI. bunch Pb. Upper-oer Austin Ghelh, 1.. Irwnetovn Merl Vickebur; Group-4.. (fluctuate); Merl Upper-oer Vickehuu Group, ”r- Merl Gelverr h., 1.. '1‘- Point Merl lb. Upper-oer Vick-bur; Group, tyre- hrl Mikey Group, lover-oer Uille Point h. 1.. Jeckeon PI. leverro Group Upper-oer Vickehun Group, lyr- Merl Upper-oer ‘reylor mrluleverro Group Choctuherchee h. Heal-nice Group, Reno lquivelent Trinity Sends Uppemoet Vichbur; Group, tyr- Merl Midwey Group, linceid end Ville Point he. Oeen Pea-Lowers”: hurro Group Cleihorne h. Teylor Merlo-lleverro Grasp Mihey Group Teylor hrl-erro Group Gelvert h., 1.. Flu. Point um Mb. Gelvert I... 1.. Ph- Point hrl Mb. Wilcox h.--Cleiborne Group Upper Momth Group, leveeink in. Lower PM Group, lover-net Aquie h. Upper lumen Group, Dar-helluva h. hverro Group, Goreieene Ihrl Ueehite Group Auetin Chelknhylor thrl uplin Merl lover-oer atocteuherchee ll. Jecheon h. end Vichhur; Group calculated as the average of the 60 measured radii drawn from the exact center of gravity of each Specimen), 29 harmonic amplitudes, and 29 harmonic phase angles. The maximum number of harmonics that may be computed is one less than the Nyquist frequency, n/2, where n is the number of measured data points (Gevirtz, 1975). In addition, the normalized roughness coefficient was calculated from selected harmonic amplitudes (Program Rough, Appendix II). The roughness coefficient is the average squared deviation of the grain perimeter from a circle of equal area or Simply the square root of one-half the sum of the squared normalized harmonic amplitudes (Ehrlich & Weinberg, 1970). A root mean square error comparison of harmonics (Program Redraw, Appendix III), combined with a modified analysis of variance design and Snedecor's F-test (Table 2), permits identification of significant harmonic amplitudes (Gevirtz, 1975). The harmonic amplitudes insignificant at a = .002 level were tabulated for the entire data set. The F-test indicates that harmonics l, 28, and 29 make Significant contributions to the total shape in less than 50 percent of all the Specimens Studied. Because phase angles are expressed as angular rather than linear variables, the stability of each angle can be determined by letting each individual phase angle represent a vector of unit length (Table 3), and calculating (Program Angle, Appendix IV) the length of the vector which is formed from the sum of all unit vectors for that Table 2.--Results of analysis of variance in determination of Significant harmonic amplitudes based on the original 91 specimens (Appendix III). Percent Specimens Having Harmonic Number Insignificant F—ratios at a = .002 l 100 2-24 0 25 l 26 2 27 13 28 53 29 100 harmonic (Christopher & Waters, 1975). The median value of 12.12 was used as the cutoff value reflecting the stability of the phase relationship within the total sample. Angles with resultant vector values below the median have highly variable phase relationships. These variable angles might reflect lack of homology among species. Evolution might represent change in either the magnitude (amplitudes) of a structure or in its angular position (phase angles). Changes in angular position should not generally be great in homologous structures; therefore, very highly variable phase angles probably reflect non- homologous structures that are contributing to the same harmonic amplitude. All phase angles are calculated from the position of the second harmonic. The results of 10 Table 3.-—Results of Program Angle (Appendix IV) with resultant vector lengths of phase angles for their respective harmonic amplitudes based on 91 specimens. Maximum vector length is 91.00. Harmonic Resultant Vector Average Phase Number Length Angle in Degrees l 25.04* 53.16 2 91.00* .00 3 52.07* 246.95 4 70.37* .89 5 56.09 249.90 6 16.47* 164.86 7 32.04* 344.70 8 29.64* 135.44 9 7.23 285.32 10 16.72* 102.19 11 5.33 4.96 12 6.79 296.89 13 13.95* 161.82 14 8.87 359.93 15 8.56 114.11 16 13.93* 301.81 17 14.05* 185.98 18 12.79* 303.26 19 9.19 108.55 20 2.89 3.46 21 9.67 114.96 22 7.16 289.64 11 Table 3.--Continued. Harmonic Resultant Vector Average Phase Number Length Angle in Degrees 23 8.30 77.01 24 4.54 352.08 25 8.93 216.39 26 12.12* 197.28 27 9.95 76.60 28 23.24* 185.98 29 14.78* 8.79 *Values greater than the median. 12 PrOgram Angle were used as input to Program Rough. Roughness coefficients were calculated for harmonic amplitudes having stable phase angles (stable RC) and for harmonic amplitudes having unstable phase angles (unstable RC); RC-ALL refers to roughness coefficients calculated from all harmonic amplitudes. A flow chart (Figure 1) illustrates the methods and sequence of computer programs used in this study. Factor Analysis The phase angles, on, greater than 180° were con- verted (Program Convert, Appendix V) to 360°-On in order to represent the absolute magnitude of a phase shift irrespective of direction (referred to as "upper quadrants conversion" hereafter). Also all other variables were converted (Program Convert, Appendix V) to logarithms to represent better possible logarithmic growth relationships. The total data set generated consisted of 26 harmonic amplitudes, 25 phase angles, three roughness coefficients, and the mean radius. All 55 original variables and their log-transforms (except for phase angles) were subjected to separate R—mode principal components analyses. This analysis was carried out by means of program FACTOR using the PAl and VARIMAX rotation Options (Nie, Bent, & Hull, 1970). Examination reveals that 50 of the 55 variables in the transformed data have their highest loadings in the first 10 factors 13 Figure 1. Flow chart of study methods illustrating sequence of computer programs used. 14 Ieleer lies of guide been Convert veriehlee by ell-gin. oetreeodeerobeueedinrhie bleeerid-e end! (hue eqlee ere not converted ) no burirhe-eee rat) 1 1 run»: mar Iuhjecr origieel to end eeevertedn dete to en I-eode priecipel “81““ M 9' 9“" one-en” eeelyeie no deter-lee 0091-“ ’ hear lendin- of ell veriehlee 8 2 PM” FACTOR Gluener epeeieeee eeiu lelee W0“... Celculete heroeeic qlieudee cdieerie. e! creator-Clone :u ”2,“. mrsrrr: O‘M‘Ifl- ’9'.“ .dcleeeerin option “h lrueeleerioeproeehree epecinen elneeer e-lyeie netted need in file only 3 9 runs mm m m 12 Gelculete root seen «are oe e11 I ehepee end nee Fun: to deter-lee Gnu-e cluurin reeulre no 311-1.“ "CW 81'“ m '01"! euniuceet her-nice to he need treetiee cleeeilieetioe o! M“. m cw'“ ee veriehlee Q..- 4 m I” 10 hm Mill. ~10 50' “unity specie-e eei. ellheueieqliudee-dreec rack-“WWI!“ tor “011“! 0! “I“ 3! fie heer reeelte ‘- enered with amulet!” the reeelrnr veneer 5. mg“. “gunner“. he eeeh 9 13 rm All! ' PM we Wee nor-1 undue-e eeerrieieet verieble tor e11 e1.- ‘ nuke-t helmets -litudee, M eiptfleeet hemeiu in eeehle positions, ad for eieeifloeer M in eeeuhle peekin- 8 m 15 as compared to 43 of the 55 untransformed variables that load on the first 10 factors (Table 4). This result indicates that the transformed data shows higher inter- correlations than the untransformed data. This result indicates nonlinear or allometric relationships among the variables studied. Optimal Clustering Methods Parks' (1970) CLUST6 program, designed for use with either qualitative and/or quantitative data, which uses simple distance as a measure of Q-mode association, was used to cluster and identify the original 91 specimens at the family and genus level. It performs an R-mode principal components analysis on the data, using either Simple distance or the correlation coefficient, and extracts the principal components which explain 80 percent or more of the variation in the data unless otherwise specified. Principal component loadinds are calculated from the original data to produce orthogonal coordinate values that are normalized to a 1.0 scale. A final Q-mode cluster analysis based on the principal components is diSplayed as a line printed dendrogram. The following clustering methods are used to determine which Options available from the cluster program when used with combinations of Fourier shape variables give the most Optimal clustering result when comparing the line printed dendrogram with the Treatise (Moore, 1961) classification at the various taxonomic levels. 16 Table 4.--Eigenva1ues of transformed and untransformed data. Variable Eigenvalues of Eigenvalues of Number Transformed Data Untransformed Data 1 13.15547 11.79944 2 4.90825 4.81495 3 3.87711 3.64735 4 3.19030 3.08630 5 2.64294 2.80417 6 2.43407 2.45225 7 2.00441 2.25828 8 1.71222 1.98235 9 1.52071 1.65244 10 1.43024 1.52393 11 1.33053 1.34448 12 1.18217 1.21724 13 1.14911 1.17134 14 1.08280 1.12514 15 1.01988 1.01836 16 .91185 .95694 17 .82179 .89009 18 .80150 .84799 19 .73487 .77741 20 .70612 .75604 21 .64459 .70645 22 .64142 .66545 23 .61181 .62150 24 .52450 .60003 25 .50122 .53275 26 .48557 .50152 27 .42351 .46047 28 .41048 .39386 29 .39136 .36749 30 .35792 .36120 31 .33056 .35221 32 .32281 .31108 33 .29705 .30032 34 .25150 .27942 35 .24381 .24908 36 .21248 .22594 37 .19504 .21725 38 .17796 .21287 39 .16800 .19227 40 .15349 .17067 41 .14380 .15815 42 .13746 .14564 43 .12007 .13828 44 .10464 .12842 17 Table 4.--Continued. Variable Eigenvalues of Eigenvalues of Number Transformed Data Untransformed Data 45 .09053 .11215 46 .08092 .10063 47 .07275 .08509 48 .06666 .07783 49 .05296 .06550 50 .05067 .05924 51 .03884 .04978 52 .03137 .04026 53 .02048 .03799 54 .01857 .03150 55 .00974 .00925 18 Clustering options include varying the number of principal components used in the computation and weighting of the principal components in prOportion to the amount of the variance they explain. Results of the various com- binations of analytical Options are given in Table 5. In the comparison of the results of the 20 com— binations of variables used for clustering, two methods were used in calculating the similarity to the Treatise classification. One method used is to compare the total perceht of pairwise comparisons that match the conventional (Treatise) taxonomy in the observed clustering results at the family and genus levels. The other method is to take the percent of all specimens that do not fall within the main cluster, irreSpective of small clusters outside the main cluster. The results of pairwise comparisons were calculated only if the latter method produced results of 41 percent misidentification or less at the generic level (Table 5). All combinations incorporating harmonic phase angles gave the worst clustering results (all combinations except 2 and 11). Of the combinations using harmonic phase angles, the ones incorporating unstable harmonic phase angles (1 and 4-9) gave significantly more mis- identifications at the generic level than did combinations containing only stable angles (3, 10). Therefore, it may be concluded that phase information is not generally taxonomically useful in ostracodes. The combinations 19 Table 5.--Comparisons of various clustering methods via results at genus and family level using the original 91 specimens. m m c: c: O O -H -H u O O O m 'o O o D O -H m -H c u 1H O m O o -H'H -H m c .4 o O O v.4 u H 8. m H O m C-H c O E O.u .4 -H O 5 O c E -H a .Q E<9.4 vo -o O s o o o o O -a m -H U c m U c -a -a m > m m 0 a m -H m H O c 3 ~d.4 -H.4 «4 u g H up «u 0.0 2H 2H O u .H m'o m c > m d d .4 m H O u Q.O O U-H o u u .o c m g B -a u Iu c 1H c H-H c c c c M-H .4 0.2 o o o O m u O-H O-H -H.g -H m m c U) o. O 0.0 0.: O.C so 58 x :3 58 5 :8“ 88 89 >0 m: 0 O3 20 2 9:08 0.3 0.3 1 CC** L,U** 10 55 60.67 50.52 2 CC L 6 28 92.70 47.92 36.71 3 CC L,U 6 15 51.58 43.57 4 CC L,U 4 15 49.00 47.47 5 CC U 9 25 57.42 46.67 6 CC U 6 13 66.25 56.10 7 CC L,U 10 28 57.92 49.05 8 CC L,U 10 41 53.50 49.57 9 CC L,U 10 28 60.33 55.14 10 CC L,U 9 40 90.35 45.75 40.10 2 CC L 7 28 93.24 51.35 35.86 2 DF** L l 28 49.08 44.98 2 CC NL** 5 28 89.72 44.25 37.49 2 DF ML 1 28 49.75 45.44 2 CC L X 10 28 86.64 44.42 40.85 2 DFf L X 10 28 54.25 48.06 2 CC NL X 10 28 54.58 41.41 20 Table 5.--Continued. U) : m 0 : -H o u -H O u m p 0 O p O -a m -a a u ‘H O 0 O 0 .H-a -H O c .4 O O O 0.4 u H O O H O O c- c O E a. o.u H -H O O c H E -H x .0 E m m o x m -H m H O c O -H.q -a.4 -H u : F! H O O m 0 A 2.4 2.4 O4.) -.-I O Of!) 0.: :> a: a: a: .4 O H O H 0.0 O .u-H 0 u p .Q : O H B -a u tn : m : H-H : c : : M-H .4 s 0.: O 8. o O g4u O-H O-H -a -H O O c 01 0 O 0.: 0.: Oo 58 a as as a :55 :2 39 >0 m2 0 D43 20 z {3.00 0.3 0.3 2 DP NL X 10 28 51.00 41.85 11 CC NL 7 26 48.17 45.47 12 CC L 7 28 51.83 45.79 **L = Logarithmic; NL = nonlogarithmic; CC = correlation coefficient; DF = distance function; U = upper quadrants conversion. *Variable combinations list (HAR = harmonic; RC = roughness coefficient). 1 HARZ-HAR27, all phase angles and amplitudes; RC-ALL; stable RC; unstable RC; and RADIUS. 2 HARZ-HARZ? amplitudes; RC-ALL; and RADIUS. 3 Harmonic amplitudes with stable angles, stable RC, and RADIUS. Harmonic amplitudes with unstable angles, unstable RC, and RADIUS. Phase angles (HARB-HAR27). A11 unstable phase angles. Harmonic amplitudes with stable angles, stable RC, unstable-_ phase angles, and RADIUS. HARZ-HAR27, all unstable phase angles, RC-ALL, and RADIUS. Harmonic amplitudes with unstable angles, unstable RC, and RADIUS . 10 HARZ-HAR27, all stable phase angles, RC-ALL, and RADIUS. 11 Same as 2 without HAR2 and RADIUS. 12 Same as 2 deleting first factor score variable. 21 using the correlation matrix computation to produce principal components appear to give slightly better clustering results than does the distance function matrix. Weighting the principal components used in variable com- bination 2 did not significantly improve results of the clustering. Choosing the proper number of principal com— ponents to be computed for the cluster analysis is critical. Using seven principal components computed from principal component loading results of combination 1 (all 55 variables) produced better results than when six com— ponents were used. The combination 2 using seven principal components gave a 93.24 percent pairwise comparison com- pared with combination 2 using Six principal components which gave a 92.70 percent pairwise comparison at the generic level. Combination ll deletes harmonic amplitude 2 and the mean radius (size) in hOpes of eliminating the possible effects of ontogeny. Younker (1971) found that a continuous increase in the second harmonic through molt stage eight in CypridOpsis vidua. The deletion of these variables in this cluster analysis increased the number of misidentifications in the clustering. Therefore, it can be stated that the second harmonic and the carapace Size, although partially reflecting ontogeny, also carry valuable taxonomic information. Another combination eliminating the first factor score variable from the analysis was run. This was done in an attempt to eliminate noise caused by the 22 intercorrelation of the variables loading on the first component. AS this clustering result also gave a large number of misidentifications, the noise was not eliminated. The best result is combination 2 using unweighted, logarithmic variables, a correlation coefficient matrix, and computing seven principal components. The 28 variables used were harmonic amplitudes two through twenty-seven, the radius, and the roughness coefficient computed from all harmonic amplitudes. For this combination of 28 Fourier shape variables (Table 6) the total percent variance extracted by the seven principal components is 79.856. All characters loaded highest on the first five components. The results of this optimal clustering method yielded a 93.24 percent pairwise comparison at the generic level. Biologically, the results indicate that these Specimens can be identified quite successfully at the generic level using only these 28 shape variables. 23 Table 6.--Principal component loading of Fourier shape character set for initial R-mode analysis of Parks' CLUST6 program. Character 1, RC-ALL; 2, RADIUS; 3-28, harmonic amplitudes 2-27. Total percent of variance extracted by the seven components is 79.856. F1-7 indicates principal components 1-7. F1 F2 F3 F4 F5 F6 F7 1 .240 -.313 -.O77 -.355 .518 .082 -.332 2 —.205 -.024 .582 .625 .374 -.025 -.013 3 .425 .225 .446 -.l34 -.374 -.088 .139 4 .156 .442 .585 -.277 .294 .035 .087 5 .430 .529 -.045 .219 -.258 .105 -.051 6 .441 .544 .598 -.055 -.018 -.l33 -.050 7 .516 .487 -.231 .126 .041 .470 -.155 8 .629 .458 .016 -.153 .105 -.024 -.295 9 .702 .495 .012 .007 .135 -.154 .013 10 .760 .297 -.139 -.022 .360 .066 .057 11 .776 .268 -.169 -.021 -.294 .125 -.037 12 .710 .281 .045 .211 -.115 .073 .188 13 .705 .106 -.202 .124 .028 .297 .078 14 .780 .169 -.O97 -.202 .055 -.140 .001 15 .735 -.023 -.157 -.087 .030 -.343 .301 16 .846 .093 -.l9l .015 -.006 —.099 .055 17 .826 -.050 -.129 .084 .174 -.154 .091 18 .799 -.292 —.125 .115 .122 -.203 -.020 19 .726 -.271 -.223 .055 .119 -.017 .092 20 .760 .012 -.241 .021 .091 .058 -.O43 21 .775 -.347 .047 .024 -.O48 -.225 .016 22 .699 -.234 .213 .105 -.095 -.244 -.315 23 .559 -.455 .155 .041 -.152 .107 -.302 24 .675 -.365 .123 -.l93 -.273 -.015 -.302 25 .725 -.440 .077 -.034 -.120 .063 .052 26 .611 —.397 .381 -.134 -.034 .441 .018 27 .599 -.391 .200 .473 .065 .088 .085 28 .468 -.434 .218 -.295 .068 .263 .475 Eigenvalues 11.643 3.388 2.098 1.218 1.173 1.016 .930 Percent of Variance 41.583 12.100 7.492 4.350 4.191 3.629 3.323 Explained SPECIES IDENTIFICATION For species—level identification 20 replicates (12 Species) were added to the cluster analysis. After the sources of sampling design error were detected 53 specimens (40 species) were eliminated and a final cluster analysis (Appendix VI) using Parks' CLUST6 program was run using the remaining 58 specimens (51 species), including 9 replicates at the Species level. Results of the percent pairwise comparisons at the specific, generic, and family levels are given in Table 7 for the Optimal combination of Options. These results Show that this method of identifi- cation works best at the Specific level. The only mis- identified specimen, Bythocypris (?) gibsonensis, was doubtfully assigned to the Species gibsonensis, and may belong to some other Species. The generated dendrogram (Figure 2) illustrates the clustering of the 58 specimens. A triangular plot (Figure 3) computed from components 1, 2, and 3 shows clustering of the specimens at the generic level. These figures show that sources of biological noise such as sexual dimorphism and ontogenetic variation are causing these misidentifications in the clustering results, especially at the higher levels. 24 25 Table 7.-—Eva1uation of final clustering results in terms of percent of pairwise comparisons and calculated chi-square results for same. Percent Calculated Taxonomic Sample Pairwise Chi-Square Level Size Comparison Results Specific 9 94.44 22.49* Generic 49 91.33 77.97* Family 56 86.95 132.08* *Values exceed critical chi-square value of 10.83 at a = 0.001. One way to test the degree of association between the conventional classification (Treatise) and the generated dedrogram of the cluster analysis used in this study is by use of the chi-square method. This test is designed to reveal a degree of association statistically greater than is likely to occur by chance. A two by two contingency table is used wherein the conventional classification is compared to that generated by cluster analysis. Contingency tables were set up for Specific, generic, and familial taxa. The null hypothesis is that no association exists between the two methods of classification. If the selected level is .001, a Significant chi-square result indicates the interaction observed between the two types of classifi— cation will occur only once in a thousand times if they are not in some way associated. Results of the pairwise 26 comparisons and their corresponding chi-square calculations are given in Table 7. Significant chi-square results indicate association between the dendrogram generated by the cluster method and the Treatise classification is greater than would be expected by chance. All three (specific, generic, and family) taxonomic levels yielded significant chi-square results; each calculated chi-square value exceeds the critical value of 10.83 set prior to construction of the tables at the .001 level. 27 Figure 2. Q-mode dendrogram illustrating phenetic affinities of 58 Specimens of Mesozoic and Cenozoic ostracodes based on 7 principal components extracted from 28 shape variables. 28 TAXON Lueconcne puma Alexeodev.)934 Lancet-die pereecere Ale:onder.l934 Cytberefle norm uIrIcIIJQOI Monocflherldee Haldane (Howe a Houeh. I 9 3 3) lelrev'eeypm eeemeeenele Ron. . I 9 33 Cyihuele ”Helm Reoee.l846 CyMereie bees/"i vecunefie schmIdI,I8e. Cyfhereie pululeduine Alelondev,l929 CyIIIerele 0088!.” reticulalire SchnIeI.I948 CyMerwe brew: Have 8 Love, I938 CyMeIopleron pelerIcuIeeI Home 8 Law, I936 CyMueIe veep-l IUIrIchIBenIev,I904) Cynnereu werdeaeie Hoe-e 8 Bro-n. I933 . CyMUQIeIoI unique-men's How. 8 Chambers. I933 Orwell Deeded Iele JeanInqe,I936 runway...» mm (Vendevpool,l9281 Leroeendae cleleemeeue Huvroy.l938 EuyMenre mterueeteeeie Home Loe.l936 Cynenwe reelecee elenoneer. I936 Eocylnerepreron Dileoeluel Alexendev.I929 Cymerepleton neveneenee Meander, I929 CWWOH end-enema eleaeedev.l934 Amphcythwwe m (Mouton. I880) Orlhenorecymae ensure Mound", I934 arrow-oracymre enelen Alexander, I 934 armrecymere bonnet (measly. I929) Acrrnecytnereu eunmumte neryleedlca (Ho-e a Hooch, I933) Pinnacnrmeoe cornure emenceee UIvIch 8 Bottle: . I904 Cymerels commums reheeece Crone. I963 Adinocnnenie uenmenme (much 8 Bower. I904) Wherry": “800000“ Ulvich.I90I amen": Melendeneie Aleleedev,l929 Luecenche flucheri Iuogluy,l929 Hwecere flee teuee Muendev. I934 Digmcyrhere rueulh I More 8 Leo, I936) annocypns 9188000081: None 8 Chenhen . I9 33 Brechycyrhere Iedelerme IIueeIuy, I929) Cylherelle were (Roemv,I84OI Echimymereie iecueneneie IHweGPyeooI.l935) Heplocymeridee blanpieli SIODann. I936 Eucnhere briplneeateneis (Bere,.I923) Who‘wfl'fl'l plasmneie More 8 Che-ten. I935 Brochycy'here rphenoides I Reuse, I854) Noplocylhendeo monmowhensis 8eny,l925 Eucymere chicken-nanny: Houe,l938 Eucfllere bro-uneven!!! Alexander, I936 furnace mdeordenu‘: Howe . l936 Brocnycymere Iedelerme erupere Crone.l965 Cyrherelloieee don sullen su None . I928 Neecyflten‘deie eehermnl UIvicIIG 8oesler.|904 CHI/very” gene!” More 8 Cheeeete.I935 Echlnecyrherele pattern (More 8 IcGeIrI.I93SI Brochycyrhere inierrallie AIuonder,I934 Uenocerefine pedete (Manson . I880) CyflIerele boulen' UIrIch.I9OI Perocyprle perepiculoro llenonder.l934 Parocypris perdpiculofl Hannah's” Pencyprle perepo‘culele AIeuendev.I934 DISTANCE FUNCTION Figure 3. 29 Triangular plot indicating clustering of specimens at the generic level. (Computed from principal components 1, 2, and 3 of final cluster analysis). Genus Cythereis Bythocypris Brachycythere Eucythere Loxoconcha Cytheropteron Paracypris EOWMUOWP Orthonotacythere SUMMARY AND CONCLUS IONS The method used in this study is highly successful for Species-level identification. The method only works with partial success for identification purposes at higher taxonomic levels. The differences in ontogeny and sexual dimorphism must be more fully known and studied by a competent investigator. The effects of these differences could be filtered from the cluster analysis using the Fourier series. The method works somewhat successfully for classification purposes at the higher taxonomic levels. Additional work is required due to the morphological convergence at the higher taxonomic levels. When the work in this area and the work in ontogeny and sexual dimorphism is complete, the optimal clustering method discussed in this study will represent a technique for identification and classification of specimens at the higher levels as well as at the Species level. 31 LI ST OF REFERENCES LIST OF REFERENCES Christopher, R. A., & Waters, J. A. 1974. Fourier series as a quantitative descriptor of miospore shape. Jour. Paleontology 48:697-709. Ehrlich, R., & Weinberg, B. 1970. An exact method for characterization of grain shape. J. Sed. Petrology 40:205-212. Ellis, B. F., & Messina, A. R. Catalogue of ostracoda. Supplements 1-35, American Museum of Natural History. Gevirtz, J. L. 1975?. Fourier analysis of heterodont bivalve outlines: implications on evolution and autecology. In press. Kaesler, R. L., & Waters, J. A. 1972. Fourier analysis of the ostracode margin. Geol. Soc. Amer. Bull. 83:1169-1178. McLean, J. D. 1957. McLean card catalogue of ostracoda, cumulative index, Vols. I-XIII. J. D. McLean, Jr. Alexandria, Virginia. U.S.A. Mirkin, G. R., & Bagdasaryan, L. L. 1972. The feasibility of identifying paleontological objects with the aid of Optical analyzing systems. Paleont. Zhurn. 6:103-108. Moore, R. C. 1961. Treatise on Invertebrate Paleontology Part Q, ArthrOpoda 3, Geological Society of America and University of Kansas Press. Nie, N. H., Bent, D. H., & Hull, C. H. 1970. SPSS: Statistical Package for the Social Sciences. McGraw-Hill Book Company; New York. 343 P. 32 33 Parks, J. M. 1970. FORTRAN IV program for Qnmode cluster analysis on distance function with printed dendrogram. Computer Contribution 46., Kansas Geological Survey, 32 p. Scott, G. H. 1975. An automated coordinate recorder for biometry. Lethaia, Vol. 8, 49-51. Shimer, H. W., & Shrock, R. R. 1944. Index fossils of North America. The Massachusetts Institute of Technology. 660-693. Younker, J. R. 1971. Evaluation of the utility of two- dimensional Fourier shape analysis for the study of ostracode carapaces. Mich. State Univ., MS Thesis, 62 p. . 1974. Fourier shape analysis: a method for mathematical description of two-dimensional form. Geol. Soc. Amer., Abstr. w. programs 6 (7). Zahn, C. T., & Roskies, R. Z. 1972. Fourier descriptors for plane closed curves. IEEE Transactions on Computers, Vol. C-21, no. 3. 269-281. APPENDICES APPENDIX I LISTING OF PROGRAM FOURIER 0 N e 9 T. I R E z “s Y E 0 L 7 9 L 0 Y NV P e 9 n... 90 Z 9 Ala K N R 1 ELB X 9 H" N A U 3.0”. 9 x T N s o 9 ICVI SS..- 0 L J o S S QANS EL 83" . 2 EN E IAe RU Dc 9 DIG 800 x 00 EE‘ 0 e I NEPUA NN BTE 7 v 51R U0 E" s R 9 o T E NREDX E TEF 1 N NH" 0H2: VX 550 ECU QCTOX A UN 9 9 INN EE 3 HF ”ID 5 T CUM GRNET o N R E IDN E ORN 0 SEE E T F P TER I LE L8 3 s F9L NBFEO UU P s N N EEO I BP 0L "IL I N 0V T5 HA ASA E CRT TSNT? 5V SUN N ee UN IUISH N5 L5 COM GHTUI IO N I 9 7 I I R" eTN 3cos I] NN. 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I P S F x 9 9 I 6 N E 5 N 6 3 A A N & 6 A 9 9 R N I9 I 6 3 A c G I ’s 6 F I 9 I "I NE E 9 9 I I I N DAN oDI N x R I N N O RI7 9U, N 5 E 1 R RI N 93 FTI 6 9 6 o A AN R 65’ 9IX 9 6 N 6 I N NR A EII “L“ x 9 U F 2 N NA N z 9 9 9 9 6 N 6 6 9 9H IEN 6 Z 9 F 1 O 1 1N 6 L21 FAI N 9 c 9 I m 3 9 F AII 6 I I A x I x I N N1 6 2 N36 166 s E 3 N 7 s 9 9 9.. 6 I R 1. I1. CIN 9 O 5 E N66 IN 6 L OE 9 VAN 9 IS" 6 "6’ L ION N9 9 A N16 70x NC“ 9 R51 6 '29 9I 6 N PA 6N7 019 6 AI. N A’N NN 2 R NN6 IRS NNX F N96 A RII I9 9 6 AA1 6A, R6“ 9 HRF PNY Y" 6 N ES 9 oHI AN 9 X R59 5 AIA AI 6 N N I 6Nx NR6 7 161 s IDR I RV 6 6 N69 F96 AI 9 9N9 A OAR N RA A 3 6L" 919 NH" 2 qu N IQA I N AR NI 9 “61 192I A 0 I QNZ P NAI 6 N OR PA x 9AI 9XI6 INN 9 NN9IN II9 NA C NIA LI 2 X56 I33Io DAR X 16322 DIN NRNR N96 AE A ZU1 6I597IEEA 2 IoIo1 AR 9AN 9NI 6 9 9 9 I991F6NNN 9II3X979 96 9 1.9/ 961. 9 9 9. 6 6H1. 6 6 96AHH6 6.92 91. F6 A56 :NN56:Z3 6A N HZH ZHNXICGAH HAIX2H6N : 8 6 E 0 N H H 7 0 N 7 7 E 1 H E 1 1 2 1 I116I1119 1I21I111 99,9” 9 0°62 OBUOPUI IIII III IIII I II III HH N07RR 1 N1LNTIITTDIITITTTTT)TTITTITT IITI:5::IT7INI AIAQAAAEAAAAAAAAAoAAAAAAAA RRROCOCCRRORUOEFOOROOO 000000000900000000N AAPCRDRRPPDPPCRICF9FFFWFFFFFFFFFNFFFFFFFFE A 3 7 15 66 566 666666123 66666236 5 5 5 75 67 70b 567090000 01365770 6 6 6 66 66 699 999996666 66666666 1111 11111 2 38 E H E T H T- 9R 00 T F 0? OS nu C SI FLT 0E5 VI HF?! 19 ULA 6 L 9.9 2 9073 1 EV?- 0 R 1c T. UVLI 9 GOIR \9 ’ INBT 6 0 FRAE $6 6 IBN K1 1 THOA F 9 9 NSRR 96 1 Au . PA N2 = CV P 61 J IORN ET: 9 FRED HS ‘- IOHN F! J "Carl 0 9H 9 500 9LDK I I" (OLE 9 It SL951", T 009HF6 s “KP-91. 92 \l .1 H91 2 H RE 0 9AA?» 9 K OHFLRVS 1 9 1 F'CEGFI 9 0 I9 3 9 "SC 9H1: 0 J 0 6 6 UYAEHVN' u! I. I 1 I IBCI K 9S I Q 6 6 9 5 9| L Is 9 99.91 9| 6 6 8 I- " 6 2 6 '9 09F SNUH H h 6 N 9 U 1 6 1 Q5 VEIFENUK U 9 9 T 9 .1 N 9 1 9 I 9 TNOC 96 9 N 6 6 6 N1 ‘9 1 . 6 o 9 6 H6 656 N16" 1. 3 5 6 9...! I R N 1N6 2 6 9 0N1 TRFIEE61U6 R6 9 0 9 X 9 1 9’ 9‘ Y3 A 106 o o o 6 1 N o 6 91 AATS IOCNO B60 0 0 A ,6 9FT T AN E 9E0666 6 1 9 1 9 6' 009 T £00916 N03 6 5 N 16 11NN S N. H ’0H6660oo 66H6 6 : H 0N6616 SSSFLSZB 0 N36 6 9 I9 1991 I oIN N(H R1/106660 21121 0 1K1 OIZOF1 N109 (N61 N11! 1 1 N (5 3TH] LH N1N NIH A19/00666?99:91 1 69: 6F91 1 EO 6L”. C 9 9.! 91. 9 I. N I1R6 UNI'O 9N IO/ 99/ V 6N11166. 119.1199 6199 1 91’ 9 NIYLTAUN N1 1119.. 1IJ I HOB ZIHN .. H: HHH 1RRRFIOA/l/009 : : J: (I) 1..J (6..)61 IYTE RNOE:6=(=(E :.CE N :1N1E [1:11 39E :UU :AAACN1EDNX11SIJ91T16 9J9ETbIIS5 TAIVTO ILI=T IRU I1RU . IZIHU POHNITNJIU Iss1 IVVVThturIA/IK I STD I TUN1 (13 ULLELINSA 1 EN UBN X /+.N KN .(N: (N0 NN.0 KKKRES:HHNRSF111ZIS1 (6(NI 70 . DUALUVONVOIUNONIIDONIJl 5NNN II‘I7HT11671 =6: : N :6 = = = OH KN = = : KK .. 669.0 HI . T.6.lT.:T6.1TN RC" SIN—P.9119‘2‘31vl :56"! :NnuobNHuu.I : z H615916S'N7NNNR9RRR511ADNX : .. R1151NHK951S'TN1: NN BLRSNHHHU R R MN 1 NX:: (slNDW: (IN! INU UAMA AAA: =EEIARSA I (N191 INNI 01‘ UIO0OEOIOOBOBOFOIO FO‘RNO HFOENFO=H800HOSOSE VOVVVSF'HNNHKKVOOHOFzF=HOH01WWIRF SCNoCBCDEDNDNDICND ICNKND HICNINDINLIDNCNDNNNKDKKFKIKFFFFFFFDDKDIKIKKDKCF FF! 6 0 00 00 56 67 6 6 0 1 3 5 662 7 1 Z 36 56 66 66 7 9 6 6 0 6 000 0 1 1 1 1 111 1 666°C 39 s V . E1 0 V s N 0 55 Q R AS I 0 LA H 5 :L s 3 c c H E V L IE 0 o 12 . R K SI 0 s G H L O k ‘ H 2 U L 9 Q" 0 o 55 K N z o o, H I 2E “ T U z u "L i B 1‘ o I v N R s o T E" I S I” , ‘ t I O" ‘l , U o "I N N 3 Ex N N I L UA I! I I R ‘ a" ‘I \l , t In E 2 0 0 S 3‘ RE .3 0 0 I 0 PH 8 1 1 D N t 20 O O A 02 ’ - L ‘ 7° 6’ 1 I g ‘1 ‘l (1 ( ’( " t D 1 '2‘?! Idol R I H ‘ ROFS (s o F F0.“ 00.... TI N OH 0 5’." SH 7 I 1 .53" IN 3 ‘ 0 "N 9 JSKC‘ ’H‘ v ’7 N “I x .KII‘ JN‘ 3 N 9 T .(H 2.! '0‘; o (I. o 9 "7 I o G ‘ T.," 0’ R’, n‘ F O F O’OE 5. "In-21 81.... ‘5 3?." IN 10F.“ N" ’ O Y. ‘ ‘ 059', i CUHOR *TR ’ o R’ T 751 “‘( I1 :18 .158 I no OTX X I A.» H" o .0 ‘C’IN I!" t 1 SSA ‘ O D! 0560 oififr"o (Ht’oo’ I IE" N SHRFF1 ZONN‘RSZ RNSIZII X 6'0 0 H’HIIF’QO o’IIHBB! 3:8(9.‘ A 30 o 0 239 0 SK! 12H‘UN52 N’ADZXDEH c.1196 303015131 :I::N:I: :IllleUU 1X8191 (5‘ 'N (( IT’,":I ’(=IIH:NIN8‘ N1FTVTIL‘1 ‘ 0 Q. 5 1 2 ‘3 6 7' a 9 . 0. 1 ~ 56 1 1 11 APPENDIX II LISTING OF PROGRAM ROUGH E L a A .l s N .U . av 2 H 1 1 , x 1 ’ . 3 E 1 L 0| 3 H A fl 9 S \l . 3 C 1 R 1 H N 9 , 0 x ’1 3 H6 0 g I. N1 I. 00 6 it A P 2 I.» . Q 9 6.. 7 o c 9|, 1) 2 \l \I 7 9 U1 :32: .l. T. Iv, F H P9 ’11, I. 9 33 7 '0 cl I 01:3 1 1 9 9 Io 9 U3 1N)... K K 11 u x 0‘ 1 1 31 1 1 = .. o 3 98 6 "‘1‘ \a N Mu JJ 7’ 0 ol 2 N I 0| 1| 9 I. F“ 0 U a. 9 O B. Q 9 R N I!" c 03 p, 1 Q! 18 J O l .11 10" I! ".1 .. J .x... .5 It 1 ‘1 09 ’1" I... .19 J 1 1111 I 1 I 1 I ‘1 JJ “F3 0 0| 9 9 Av: .. 21.. . In 9 n 9 In ‘1 03 Q. o 6 I! \v / 11...! \a U I: . U ‘l U 88 7 0.x 1 ”2 T. I ‘7 ‘11,; 7!. O) K .5 K S l!" P. 1". F n11 9 o 7.. (V2... 9 C 3‘ 1 3.! 1 1 v 9 91 9 3 UA1J 8 1J 119 N (”2 1 5J T 1N T 1” T 911 9'1 I . O 9... 2 9C 99... 7 t." 1 Q. 2... cos 9! on ( .oo‘ o XXH .4 9s“ 9‘ 0. 1‘ I 91 9 s R. 9 1 1A .(0 1‘ 20 1A 20 1 v a. 711 1 01(51 1%: .fi1lEE1 7O 6 1 1§r./S :OE/S :OE/SEB:3G.E(I( C U T. .. 9U : 0:0 UU 2 .. U : .21 .Q .. _.fl :9 4 U" .. nLKVIUU. :OKHUM. ..U1T..11U ASIZNJ QIUNSI’ NKK1891KKI oJUNU’ 0 UN”) 0 UNU’N NTTT .l D N .l P. .31: III : :1: .. 2 0 .315T0031510131311T2T HTARA A GE1DT3:“:.I)5 1T811111916..7="2 0213...... 921:7... OTN1NCTIHMH’H ON AN My “NJ JNN K311“ K "- H" "11. NNHZU.MHNH1NI INNRQR’R” PDDRCOSDSCC.DRCCH.NNNH.H0"OSDSCSBSUSCSBSDSCSBCPDPPCS-FF 'FE 1 Id. 823 a 9 7 o 1 6 2231.! 5 1 1 1 11 1 4O APPENDIX III LISTING OF PROGRAM REDRAW o 5 7 I 1 1 I z 1 ) N X o N I ( s V. R o E \I V X . u... a. H E 1 on. v. 9‘ . U 2 O o F 1. ,) "1 x1 ‘1. "X 9.7 (H 6‘ \I Y‘ 0A 0 .rvu 3.91 1 1+ p6. 1| x x1 H 2. a "X F... N 1 M. M H O A U x (H 1 1 N J I Y1 .1011 I“ I xx 1'. "in ’ Luv... 1 “a 4 l\ PH? 1 ’ J8 2 "H 10‘ 9101‘"... v o. I. 3 VIVI 1. U DN31I .Jn. 3 6 8 5 .11 X1 USA 1..... 9 N 1 7 7 2 7. 1.... N1 ‘5 067'. .r. 16 Q. 1 0 1 11 (x fl A (ll 3. J 1 3 .9 6 O 11 n VAN“. a U... 1 1 1V- 0 (a 7 7 5 7 11 .1. . (a 3 D. M13751 O M. v.5 D 1 1 1 II 6 1X5 .b N11. 1.» 1 I an. 2 ad 5 N 9 (1 9 X . 9 D 157"... 195 D 1 6 7 7 7 N T. 7 xx r. "1... .1» 1| (".111 H ’G \l ’ l. I H (I! 9 Hx1 2 .CYANJ 1 3...: .r. J“ Kfv 1 1 1 H x 1 SN I. 5 (N6 6 NR H 7x AH N (I. (7 7 1 1 x I 1 01 .9 9 van: 1 9 “U 9..... 9(( HQ A XFUY 9 I I I I . I CS L n. ((1 .U pT1/1x L "N N OIIJIJJ 1 l| l! o 1 l\ 0 ¥ “In an. .xa 3 0.9.Inofiénttzufo .11! . 95.6 71Lx1 1|.x1 val-T. 1LY1 L11 1.1 9 N 6 A121. 6 EUTIs CO N9 0. 9 1 S 1L1 1 1.... 1 1.... A 9111 11 9.1.1 1.0111 NE 6.0 .- F (Du‘M N703...) .J L 1LJK1 112 . l. (2 . 0| «4139117. . l\ 1‘... 3.. .. JJ M. 3R1 1 3.u..11 1 quflo... .vOJstqJ 1. 0* QOJslurltrl-g N‘sXX...X:NX.:X 8.117 =XV....:VY ...LJ(I\ OUIAI. I. AOLI. L NS .7 ILLHQ. . .. .. 8 9 F.3(KXIU11E. :.IIfl.IU. .111UIV.‘YII£IUI(( 5 : Xv. Y. QHXVX1 . YM . V1 . I NPNSAIL:11O(L 09X IHNOO P: H=Nz HzN: (I: M:N :: ILIII HCY::M+X :YXHOY .VTOOONNCSG 0:1. cl .5: .1....KT.LUC1OX3XXINK¢XNIVA~€2 ..xa6V-XI1111..‘7.. .. x1": ..AQNXN1A~..NNYN1 GUNH H. 1115‘ 3000754N11L01611T .JJT. . N‘7IATI7IITA7 1117133131.... . QT.911rsu.. .. : Manufzz .. N1: ...Ml\ .. N1 .. OF ”HM HUGTL‘AG...O 2T... .. 38. T. N .. .. Kl.“- (NNH (HNN II” ("N ((LEO JJ .. =YXO0F; X : XQO Y : V .« N000100..Ir.L:.OSTNDHLUP...FOHFO.LUC .. FXOFXOXOFXOXC‘l‘YOFv-GOXY .. STO‘IJAYHM Nu. 3AM. XFH an”... MVP.” FICCCCELFI‘FPILHFJJIFID.KEJJGlIIGIICICT.ICIDXYIn..IICD.JILILUXYNRHVYXYXF VIM YVT.V MIN 0 .U Pa 0.. 4.. no 2 3.3 65 7 93 1 1 1. a. I 1 E. 3 z 3 N 5 6 7 7 77 77 7 77 a 7 7 a 9.... 1 Z .9 .5 56 e 6 41 42 I O B S C t O .l 1 1 o .1 .l. N T. I N 1 1 A D D c A A 1 R R s 1 t! It C. m t . L A \l P l. N N H X F F A O O o S 1 N N I. .r. F G N o C N H E F. T. 1 L I. H X G G 0 . N N L a A A L . , ( 1 o 16 2 I I F 11 O 1 \l '1 O ’ \l .5. "VI 1 1 1 I... H (H 1 N S N .l X1 N ..... o .I. 1 0X E C c s “H 1+ C X . . 0 I7 v.1 X . 2 2 A 26 NV- . 1 s N I s, "H 1 I o I O I1 (N .1 pl C S A. .9 X1 1 X l. 1 o EH (x x l‘ 7 ‘ Q 1 21 4 l\ 1 + \I 1 1 1 \I .1." 11 In... 2 T. 1 1 1 2 mu 5.... 1. 1594 .... ( I T. N 0 .b 1 Y) "6.5.. 1 2 o l\ (I l‘ O a up. 9 "1 E 1’ I 7 A O O A 1 \I 1 L8 (Y COAN 1." 9 R 1 1 A A I 5 N P. PA Yuud '34.; r. ‘1 8; + 1111a D. 1 Q. l\ 2 Mano. .1111 . 6 AI: 9 T7 2 1 I111. . N 91+ 8 9 A1 1'6 0 o 1 937 9 .r. ‘7 T. 1.11.11 1 1 06 0 r; S 1 Y . 933 7.1.0 . 6 H9...) 0. I (1((ININ 7 33 1 2 15 Z 6 1 H1. 0 o (511 q. T619 1. AAAAIFIF 3 (3 3 [#3 o 6 E+ MYQAA YGIIH .U .783 03H TTTT‘I‘I 3 n. 9 N c. o. 15 9 H. . LH (H.653... ( ((9 .0 1 .27 AAR ...Ec..t0101 51:. «.6 A3 1 H2 5 R1 A1 81 Yu. 1. J. (1AYA 6 .10 o 7c.A HHHHA1A1 7....) 9.3 .13 o 3 0 R113 0 0 AN HA A... ((.:AA NHT‘H o. .1351 1H .ITTTRNRS 90... A o. A an... in. AC 0 I.» 9 H(3 PT Ss 1 +71YXLAEE‘N o L J (7+J C. M... s. . _. i (1‘0 90 H7 0 28 “6 H. 325 6 NA5 NLE U1 41 A(5(( 1..-unfit )0 9 9 A SA 0 6... 9 NNNN‘S‘C 70 0. N3 631 33 NN663 .5 91.6 NAB o. 7.81 3+ I/1AXTc 1.. 1 6 T1L . r. 7L1 FFFF I. + o 761... 9 . 9 + + 9 . 3 . + 1T5 o. 9 . H1 0AA gin-1“.” .- .. o .. All 8 1 l.- .. ...En0...JJ G .. (1(1),), 05 1) ‘51) 11 1) a 1’ o. 3. 0 .74‘ adv 23A AOLOOI111SII FT. 1 HLN 1.3.51NN «DSNNNIVI...1N..J»J .. 1 03 01‘11N..... N11N3N“...Nfi42 SnarL1H? .21 (11 X H . NH .11... 8 1 I L ISAruT? LA 031.1(1‘1UL .. 13NN .t37N‘...N(UN(N\u(6(5U 511330.. .FU(:\1 ( :er YXC‘111‘5 .11. stl 0 8+1 CCSSADFPNFD (9 SCC (Cu. C‘(rv C "Int/+9“ 1LNTTOTTT As": :SAXAI7: 0 5.30.1 EAEA :0_~.05 .. z .. : ..A..AI.~01.01A:0:A:OB:15:CC..0:019:0N 01 AIAAEAAA EH (N157. 1T‘.O11.L27I(1L(Ll. L71A7N21211P1D .IT.0173111111....(1T31111T1.1T.71A NLTfnJl..Iu..uuQ,u.Hu. 2.0 r z: .p. ED .12.... .. :G G 3 (.- =SSN NN.N.N(GI N N N NN N N N N: ..L IA NF..r.USF.R AMFCC HF4A910LJ073PINFNF:.0F00N031112(20F0t 007(01F‘0F(001FF10U000(0NA0?.1F 030 090 777.er 71.1.; .LAAFA D1IAIAIIGIACFCCSSAND.$CIN.FGDICGCEEICCTJCIICGCCCDAALCGFFICFFEFFF 1 1 .9 ... 3.1.0 .0 0...... 330 «Vt-.1... a .J 5 6 7 z 3“... 3 Q1 2 5 .... :5 no»... 3.00. 3 on 56 7 09 C12 3‘ 5 6 7 8 3 3 3 333 666 6 3 9 15 65:» 551 .P 6 .56 6 65 7? 7 77 7 7 7 7 . 7 88 899 99.". 11 43 ’6HNUNRER’IS) ,15(16,2X)) .0) XO 1...? ’5 9 R1 0 E 9 3 8x (- "1. a U/ F N“ o co 9 9 IE Q 9 NE 0 0 OR 5 9 la "Pu—r o ‘ R 5 7 N AF 9.. ‘99? H0 9 A16 H x .91. SS 1. .C( 9 1.8” “2., 9:523 TI" .- 9 VAR 9E A3 5 268R 9N‘ a) Est-A 9 F 2 7.9. 9 ZOSU ..L 9 a 1H2 P. I 10 79 9 5 up! )D\\I) 9R 9A) ”(.09 9! 0‘5. 0 HAHN" 00x N035 O 05) l 9 RHRROTIN 9. (3 N . O9 I 5 AN&.ANA/A absent o )CJ 9 91.99“. 9H” NS...— A R 9 .14 l‘ 9 5 éNSNNC.IOH 9 9 9 .I. (’0 9 11.1.1. 91. 9 9LMII L99 9 9 CIA 1. 9.. 9 96 : 650.071?! 999) 9 (CR 0 . 11111I11HNAO H73... A .A . 1. L a 9.. z .. 9.. :AERO Di§(7 Pu .90) . l‘.l’f$£1)f¥ibo . AYB‘ 1| :JH 9 I 99... 991-. 99HHFH SH N 9 H JJI‘U O \I H I"\III\)\IJN.H7 H" 9 9O H Ox ((NS 2 T. U (UII‘DIIlsoei. R1319A U ARV IHRU. o .(ZQ. 1P(l.lr((:9999 ".JQLQ 5 HA , .TD‘H- I 001‘ NDFP.”DF.KJ.J~MJ .EITia.L0n?ku No .Enflpflu (?PLQI NI)!£Nl;3AHHHHn "51“" 9n 0 L 9|: 9H.\I\S . ’0’! 11.1.1 IMIX‘DAL .. 3.10.5.1... 1.7 .. 90...L2/ .3... 9 9 9 9 9 9 9 91““ 7/ :I:9::=U:(.=QIHLU=U.HPSU95675567 UNN NSJJPIHNIA oJIJUON)UUX(N TTTT OOOCN (U UT. .. .v ((5 31.155 .. .. ITTV'TTITAARA .w "H um...3msas.|19 .. z s N 3 27!. 8 .. 997V NVNNNNNHHHH nPunH nvnuN .1" 0.1053nNnTéZT¥£N13£IT$£IT¥AMFbLED UOCCIOA— LOLOOI. HfiwwOFNH ((09.9 .19. P. RRROOOON SCCCUDFODOCDA OFF SXXFRCF FPF‘PPFFFFFE 3 a 2 .1 . 3567 APPENDIX IV LISTING OF PROGRAM ANGLE . ’ a“ o a \I 1 cl F U 3 P 5 Q cl ‘0 b 0‘ U 9 7‘, 56 T. o 2 1” 99 Q Q. 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(A NGLE Jin:1:Zg; ¥ORHNU T (7X.F7: 4 a2710. 4:711. 3/7X. 977.471cF7i4/7E7. 4) FORMAT (14X08'7.2/10F7o2/7F712) FORHAT (IOaOXoBFO. 3/10F8.3110FB.3/2FI.3) FORMAT (10F7,2) END 45 APPENDIX VI LISTING OF CLUST6 PROGRAM WITH FINAL CLUSTER RESULTS V Y T. 9 LP. 7 NF. p. Tu. r a T II A4 ,2.‘ flu) v‘ I )3)... I 9 u. H 9:“ 9‘ 6 c.NI 3:. T n. 2. NA 3.. s A n. 0 3L 9. r. I. 0* Q L L “A L 6 T ANT. C BNN 9 RAN E A00 .a T. T?\ T:\ f..1 .J .J Novel “A 3‘37: C 3 s 2.0.... E ‘50 .l .r 3.1 H... VHN U L OT- d'.‘ In) .J 3 J 1.... VT... .. N pup—d CH 0... 1% Q 10 I E N 3..) 9 0 T o)oc 0 9 ST.) RI ISM. I I n. STE U SIR I T 0 IL 93 TN... 9 9 2 V39 r LFQ. N I 003 T O ANT. U U PT. flu. NOn ... i 9 -)Q, «.5 A, .l 5 NC. I! HO. .. J c. ..J V 3... .333 n. n. L O 9 V3 T... N 9 fl. so ID‘ N x A T..I Hfldu :t..?.I 1: U vs anC c nuUNAo S P 0 PI DVD OPT I N A 53' ADA DIQ D I V 0N6» LC ‘9‘ .. or So Ox! N .5 nu 9N.) FFT CIT O .t 0 IF. 3V" 0" P 1 FOL Na)... LOE P l. L. D. A H A T. r T .1 sun." “Hay P)... 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