Holdings: Statistics of earth science data

Statistics of earth science data: their distribution in time, space and orientation ; with 52 tables

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Bibliographic Details
Main Author:	Borradaile, Graham J. (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2003
Subjects:	Geostatistik Earth sciences > Statistical methods
Online Access:	Inhaltsverzeichnis
Physical Description:	XXVII, 351 S. Ill., graph. Darst.
ISBN:	3540436030

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245	1	0	\|a Statistics of earth science data \|b their distribution in time, space and orientation ; with 52 tables \|c Graham Borradaile
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300			\|a XXVII, 351 S. \|b Ill., graph. Darst.
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Record in the Search Index

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adam_text	CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIII THE GOALS OF DATA COLLECTION AND ITS STATISTICAL TREATMENT IN THE EARTH SCIENCES . . . . . . . . . . . . . . . . . . . . . . . . . . XIII ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . XVI ABBREVIATED GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . XVII 1 SAMPLING SCHEMES . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 SAMPLING VERSUS SPATIAL SAMPLING . . . . . . . . . . . . . . 1 1.2 INTRODUCTORY CONCEPTS . . . . . . . . . . . . . . . . . . . . 2 1.3 EXAMPLES OF SPATIAL DISTRIBUTIONS . . . . . . . . . . . . . . 3 1.4 SAMPLING SCALES AND THE PERIODICITY OF GEOLOGICAL FEATURES 3 1.5 GEOLOGICAL EXAMPLES OF SPATIAL VARIATION . . . . . . . . . . 5 1.6 SITE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . 8 1.7 SITE SPACING . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.8 LOCALLY PLANNED SAMPLING SCHEMES . . . . . . . . . . . . . 12 1.9 MONTE-CARLO SAMPLING . . . . . . . . . . . . . . . . . . . 16 1.10 GEOMETRICAL LIMITATIONS TO SAMPLING IMPOSED BY GEOLOGICAL STRUCTURE . . . . . . . . . . . . . . . . . . . . 17 1.11 FABRIC INFLUENCES ON OBSERVATIONS: THE CUT-EFFECT . . . . . 17 1.12 INTERPRETING SPATIAL VARIATION OF SCALAR VALUES FROM SAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.12.1 CONTOURING . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.12.2 TREND-SURFACE ANALYSIS . . . . . . . . . . . . . . . . . . . . 29 2 CENTRAL TENDENCY AND DISPERSION . . . . . . . . . . . . . . 33 2.1 CENTRAL TENDENCY: MEAN, MEDIAN AND MODE . . . . . . . . 33 2.1.1 ARITHMETIC MEAN . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1.2 MEDIAN AND MODE . . . . . . . . . . . . . . . . . . . . . . . 37 2.1.3 WEIGHTED MEAN . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 OTHER AVERAGES . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3 HISTOGRAMS AND FREQUENCY DISTRIBUTIONS . . . . . . . . . . 39 2.4 HISTOGRAMS AND THEIR RELATION TO CONTINUOUS FREQUENCY DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5 DISPERSION: INTER-QUARTILE RANGE, HALF-WIDTH AND STANDARD DEVIATION . . . . . . . . . . . . . . . . . . . . 42 2.6 REVIEW OF SOME STATISTICS FOR FREQUENCY DISTRIBUTIONS . . . 45 2.7 DETECTION LIMITS AND PRECISION WITH ANALYTICAL DATA . . . . 45 2.8 SAMPLE SIZE . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.9 MEAN AND VARIANCE OF SPATIALLY DISTRIBUTED SAMPLES: KRIGING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3 THEORETICAL DISTRIBUTIONS: BINOMIAL, POISSON AND NORMAL DISTRIBUTIONS . . . . . . . . . . . . . . . . . . 61 3.1 THE BINOMIAL DISTRIBUTION . . . . . . . . . . . . . . . . . . 61 3.2 THE POISSON DISTRIBUTION . . . . . . . . . . . . . . . . . . . 68 3.3 THE NORMAL DISTRIBUTION . . . . . . . . . . . . . . . . . . . 70 3.4 THE LINKS BETWEEN CERTAIN THEORETICAL PROBABILITY DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4 STATISTICAL INFERENCE: ESTIMATION AND HYPOTHESIS TESTS . . 77 4.1 THE CENTRAL LIMIT THEOREM . . . . . . . . . . . . . . . . . . 77 4.2 ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.1 STANDARD ERROR OF THE SAMPLE MEAN . . . . . . . . . . . . . 79 4.2.2 CONFIDENCE INTERVAL THAT CONTAINS THE POPULATION MEAN . 79 4.2.3 CONFIDENCE INTERVALS BY THE BOOTSTRAP METHOD . . . . . . . 80 4.2.4 ESTIMATION AND BAYESIAN STATISTICS . . . . . . . . . . . . . . 81 4.2.5 ERROR BARS AND CONFIDENCE REGIONS ON GRAPHS . . . . . . . 82 4.3 HYPOTHESIS TESTING . . . . . . . . . . . . . . . . . . . . . . . 89 4.4 MECHANICS OF HYPOTHESIS TESTING . . . . . . . . . . . . . . . 91 4.5 FURTHER CONSIDERATIONS IN HYPOTHESIS TESTING . . . . . . . 92 4.5.1 SELECTING H0; ONE- AND TWO-TAILED TESTS . . . . . . . . . . . 92 4.5.2 SELECTING A . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.5.3 CHOOSING A TEST STATISTIC AND A SAMPLING DISTRIBUTION . . . 93 4.5.4 INTERPRETING THE DECISION . . . . . . . . . . . . . . . . . . . 94 4.5.5 COMMUNICATING THE RESULT . . . . . . . . . . . . . . . . . . 96 4.6 SAMPLING DISTRIBUTIONS USED IN HYPOTHESIS TESTS . . . . . 98 4.6.1 THE T-DISTRIBUTION (COMPARING MEANS) . . . . . . . . . . . 98 4.6.2 THE F-DISTRIBUTION (COMPARING VARIANCES S1,S2) . . . . . . 99 4.7 MULTIPLE INDEPENDENT VARIABLES: PAIRED SAMPLES AND RANDOMISED BLOCK DESIGN . . . . . . . . . . . . . . . . 101 4.8 COMPARING MULTIPLE SAMPLES: ANALYSIS OF VARIANCE (ANOVA) . . . . . . . . . . . . . . . 103 4.9 ANOVA: IDENTIFYING IMPORTANT VARIABLES IN A MULTI-VARIABLE SYSTEM . . . . . . . . . . . . . . . . . . 106 4.10 INFORMAL USES OF PROBABILITY TO ASSESS IMPORTANCE . . . . 109 5 COMPARING FREQUENCY-DISTRIBUTION CURVES . . . . . . . . 111 5.1 THE EMPIRICAL RULE TO COMPARE WITH THE NORMAL DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2 LINEARISATION USING NORMAL-PROBABILITY PAPER TO COMPARE WITH THE NORMAL DISTRIBUTION . . . . . . . . . . . . . . . . . 111 5.3 NORMAL SCORES TO COMPARE WITH THE NORMAL DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . 113 VIII CONTENTS 5.4 STANDARDISATION OF OBSERVATIONS TO COMPARE WITH THE NORMAL DISTRIBUTION . . . . . . . . . . . . . . . . . 113 5.5 CUMULATIVE FREQUENCY DISTRIBUTIONS . . . . . . . . . . . . . 115 5.5.1 APPLICATION OF CUMULATIVE FREQUENCY PLOTS IN SEDIMENTOLOGY . . . . . . . . . . . . . . . . . . . . . . . 116 5.5.2 INTERPRETING NATURAL PROCESSES FROM FREQUENCY DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.6 LOG-FREQUENCY DISTRIBUTIONS; THE LOGARITHMIC AND OTHER TRANSFORMATIONS . . . . . . . . . . . . . . . . . . 120 5.7 QUANTIFIED COMPARISON OF FREQUENCY DISTRIBUTIONS: NON-PARAMETRIC STATISTICS . . . . . . . . . . . . . . . . . . . 123 5.7.1 C 2-DISTRIBUTION AND GOODNESS-OF-FIT . . . . . . . . . . . . 123 5.7.2 C 2-DISTRIBUTION AND CONTINGENCY TABLES . . . . . . . . . . . 126 5.7.3 C 2-DISTRIBUTION AND SINGLE-SAMPLE VARIANCE . . . . . . . . 129 5.8 KOLMOGOROV-SMIRNOV TWO-SAMPLE TEST . . . . . . . . . . . 129 6 REGRESSION: LINEAR, CURVILINEAR AND MULTILINEAR . . . . . . 133 6.1 CONTROL AND RESPONSE VARIABLES . . . . . . . . . . . . . . . 133 6.2 ASSOCIATED VARIABLES WITHOUT CLEAR CONTROL . . . . . . . . . 135 6.3 LURKING VARIABLES . . . . . . . . . . . . . . . . . . . . . . . 136 6.4 BASIS OF LINEAR REGRESSION . . . . . . . . . . . . . . . . . . 138 6.5 AN INTRODUCTION TO THE CORRELATION COEFFICIENT . . . . . . . 140 6.6 CONFIDENCE INTERVAL ABOUT THE REGRESSION LINE . . . . . . . 140 6.7 THE MAJOR-AXIS LINE AND THE REDUCED MAJOR-AXIS LINE . . 141 6.8 LINEARISATION TO FACILITATE REGRESSION ANALYSIS . . . . . . . 141 6.9 DIRECTLY FITTING CURVES TO THE DATA . . . . . . . . . . . . . . 144 6.10 MULTIPLE REGRESSION . . . . . . . . . . . . . . . . . . . . . . 152 7 CORRELATION AND COMPARISON OF VARIABLES . . . . . . . . . . 157 7.1 COVARIANCE AND THE CORRELATION COEFFICIENT (R) . . . . . . . 159 7.2 SPEARMAN*S RANK-CORRELATION COEFFICIENT (RS) . . . . . . . 159 7.3 COEFFICIENT OF DETERMINATION, R 2 . . . . . . . . . . . . . . . 161 7.4 SIGNIFICANCE OF CORRELATION . . . . . . . . . . . . . . . . . . 161 7.5 CONFIDENCE IN THE REGRESSION LINE . . . . . . . . . . . . . . 162 7.6 PROGRESS, PROBLEMS AND PITFALLS WITH SIMPLE LINEAR REGRESSION . . . . . . . . . . . . . . . . 164 7.7 SPECIAL CASES IN CORRELATION . . . . . . . . . . . . . . . . . 172 7.7.1 CO-LINEAR VARIABLES . . . . . . . . . . . . . . . . . . . . . . . 172 7.7.2 THE BIVARIATE NORMAL DISTRIBUTION . . . . . . . . . . . . . . 174 7.7.3 CONSTANT SUMS, RATIOS AND THE CLOSURE RESTRAINT . . . . . . 175 7.7.4 PEARCE ELEMENT RATIOS . . . . . . . . . . . . . . . . . . . . . 178 7.7.5 TRIANGULAR DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . 178 7.7.6 MULTIPLE AND PARTIAL CORRELATION . . . . . . . . . . . . . . . 179 7.8 MULTIVARIATE SITUATIONS . . . . . . . . . . . . . . . . . . . . 181 7.9 LINEAR DISCRIMINANT FUNCTION ANALYSIS (LDFA) . . . . . . . 183 7.10 CLUSTER ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . 184 CONTENTS IX 8 SEQUENCES, CYCLES AND TIME SERIES . . . . . . . . . . . . . . 187 8.1 RUNS ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.2 RANK CORRELATION . . . . . . . . . . . . . . . . . . . . . . . . 191 8.3 MARKOV CHAIN ANALYSIS: IDENTIFYING CYCLICITY . . . . . . . . 192 8.4 TIME SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 8.5 STATIONARY AND NON-STATIONARY BEHAVIOUR . . . . . . . . . . 197 8.6 CUMULATIVE SUM PLOT ( CUSUM ) . . . . . . . . . . . . . . . 200 8.7 MOVING AVERAGES . . . . . . . . . . . . . . . . . . . . . . . . 201 8.8 REGRESSION LINES AND CURVE FITTING . . . . . . . . . . . . . 203 8.9 DATA STACKING WHERE THE CONTROL PERIOD IS PREDICTABLE . . 204 8.10 AUTOCORRELATION TO REVEAL PERIODICITY . . . . . . . . . . . . 204 8.11 ISOLATING FIXED WAVEFORMS BY FOURIER ANALYSIS . . . . . . . 207 8.12 DECONVOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . 209 8.13 POWER SPECTRA OF GEOMAGNETIC SECULAR VARIATION . . . . . . 212 8.14 TIME-SERIES ANALYSIS OF GEOMAGNETIC POLARITY . . . . . . . 219 8.15 PRECISE, TIME-PROXIED SERIES . . . . . . . . . . . . . . . . . 219 9 CIRCULAR ORIENTATION DATA . . . . . . . . . . . . . . . . . . . 221 9.1 AXES, DIRECTIONS OR UNIT VECTORS AND VECTORS . . . . . . . . 222 9.2 ROSE DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . 228 9.3 IDIOSYNCRASIES OF ORIENTATION DATA . . . . . . . . . . . . . . 233 9.3.1 AXES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 9.3.2 UNIT VECTORS . . . . . . . . . . . . . . . . . . . . . . . . . . 233 9.3.3 VECTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 9.3.4 SPECIAL CHARACTERISTICS OF ORIENTATION DATA . . . . . . . . . 233 9.4 CIRCULAR STATISTICS: NO THEORETICAL MODEL ASSUMED . . . . . 236 9.4.1 THE MEAN ORIENTATION . . . . . . . . . . . . . . . . . . . . . 236 9.4.2 MODE AND MEDIAN . . . . . . . . . . . . . . . . . . . . . . . 239 9.4.3 DESCRIPTORS OF ANGULAR DISPERSION . . . . . . . . . . . . . . 239 9.5 THEORETICAL ORIENTATION DISTRIBUTIONS . . . . . . . . . . . . 241 9.5.1 ESTIMATION AND SIGNIFICANCE WITH VON MISES 1 MODEL . . . . 243 9.5.2 ESTIMATION WITH SMALL OR DISPERSED SAMPLES . . . . . . . . 245 10 SPHERICAL ORIENTATION DATA . . . . . . . . . . . . . . . . . . 247 10.1 VISUALISING ORIENTATIONS IN THREE-DIMENSIONS: THE STEREOGRAM . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.2 RECORDING AND REPORTING THREE-DIMENSIONAL ORIENTATIONS 252 10.3 FIELD MEASUREMENTS, ORIENTED SAMPLES AND ASSOCIATED ERRORS . . . . . . . . . . . . . . . . . . . . . 255 10.4 STEREOGRAM DENSITY CONTOURS . . . . . . . . . . . . . . . . 258 10.5 THE MEAN ORIENTATION OF AN AXIS, DIRECTION OR VECTOR . . . 262 10.6 THEORETICAL ORIENTATION DISTRIBUTIONS IN THREE DIMENSIONS . . . . . . . . . . . . . . . . . . . . . 264 10.6.1 CIRCULAR CONCENTRATION: FISHER MODEL . . . . . . . . . . . . 269 10.6.2 ELLIPTICAL CONCENTRATION: BINGHAM MODEL . . . . . . . . . . 273 10.6.3 ELLIPTICAL CONCENTRATION: HENRY-LE GOFF BIVARIATE NORMAL APPROXIMATION . . . . . . . . . . . . . . . . . . . . 275 10.7 STATISTICAL MODELS: CIRCULAR OR ELLIPTICAL CLUSTERS? . . . . . 276 X CONTENTS 10.8 TESTS FOR PREFERRED ORIENTATION AND CONFIDENCE LIMITS FOR THE MEAN ORIENTATION . . . . . . . . . . . . . . . . . . . 282 10.8.1 TESTS FOR PREFERRED ORIENTATION . . . . . . . . . . . . . . . . 283 10.8.2 APPROXIMATE COMPARISON OF MEAN ORIENTATIONS WITH CONFIDENCE CONES . . . . . . . . . . . . . . . . . . . . 285 10.9 SYMMETRY COMPATIBILITY OF ORIENTATION DISTRIBUTIONS AND THEIR CAUSATIVE PROCESSES . . . . . . . . . . . . . . . . 285 10.10 THE FABRIC ELLIPSOID . . . . . . . . . . . . . . . . . . . . . . 289 10.11 SHAPE OF THE ORIENTATION DISTRIBUTION ELLIPSOID . . . . . . 290 11 SPHERICAL ORIENTATION DATA: TENSORS . . . . . . . . . . . . . 293 11.1 SECOND-RANK TENSORS IN GEOLOGY . . . . . . . . . . . . . . 294 11.2 MEASUREMENT OF SECOND-RANK TENSOR ANISOTROPY . . . . . 297 11.3 MEASUREMENT PROCEDURES FOR ANISOTROPY . . . . . . . . . . 299 11.4 INTERPRETATIONS OF ANISOTROPY USING SECOND-RANK TENSORS IN ROCKS AND MINERALS . . . . . . . . . . . . . . . . . . . . . 302 11.5 CRYSTALLOGRAPHIC CONTROL OF AMS . . . . . . . . . . . . . . . 303 11.6 PROPERTY ANISOTROPY OF A POLYCRYSTALLINE AGGREGATE . . . . 307 11.7 MEAN TENSOR AND ITS UNCERTAINTY FOR MULTIPLE SPECIMENS . 308 11.8 THE MEAN TENSOR: HEXT-JELINEK STATISTICS . . . . . . . . . . 309 11.9 EXAMPLES OF TENSOR ORIENTATION DISTRIBUTIONS AND THE CONFIDENCE CONES OF THEIR PRINCIPAL AXES . . . . . 310 11.10 ORIENTATION DISTRIBUTIONS INVOLVING MULTIPLE FABRICS AND FABRIC HETEROGENEITY . . . . . . . . . . . . . . . . . . . 316 11.11 HETEROGENEOUS OR MULTIPLE FABRICS AND THE MEAN ORIENTATION OF SAMPLE TENSORS . . . . . . . . . . . . . . . . 317 11.12 SPECIMEN-LEVEL UNCERTAINTY AND ITS CONTRIBUTION TO SAMPLE-MEAN-TENSOR CONFIDENCE LIMITS . . . . . . . . . 320 11.12.1 JELINEK STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . 320 11.12.2 LE GOFF-HENRY BIVARIATE FISHER STATISTICS . . . . . . . . . . 324 12 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 APPENDIX I: ERRORS IN COMPOUND QUANTITIES . . . . . . . . . . . . 327 APPENDIX II: NOTES ON THE MANUAL USE OF STEREOGRAMS . . . . . . . 328 PLOTTING LINES, PLANES AND POLES TO PLANES . . . . . . . . . . 328 GREAT CIRCLES, SMALL CIRCLES; DIP PLUNGE AND RAKE . . . . . 331 ROTATIONS: FOR CONVENIENT VIEWING OR FOR TECTONIC RESTORATIONS . . . . . . . . . . . . . . . . . . . 332 CONTOURING . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 CONTENTS XI
any_adam_object	1
author	Borradaile, Graham J.
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discipline	Geologie / Paläontologie Mathematik Geographie
format	Book
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id	DE-604.BV014694176
illustrated	Illustrated
indexdate	2024-07-09T19:05:11Z
institution	BVB
isbn	3540436030
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009966250
oclc_num	52653737
open_access_boolean
owner	DE-20 DE-824 DE-703 DE-521 DE-634 DE-83 DE-11 DE-188 DE-B16 DE-B768
owner_facet	DE-20 DE-824 DE-703 DE-521 DE-634 DE-83 DE-11 DE-188 DE-B16 DE-B768
physical	XXVII, 351 S. Ill., graph. Darst.
publishDate	2003
publishDateSearch	2003
publishDateSort	2003
publisher	Springer
record_format	marc
spelling	Borradaile, Graham J. Verfasser aut Statistics of earth science data their distribution in time, space and orientation ; with 52 tables Graham Borradaile Berlin [u.a.] Springer 2003 XXVII, 351 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geostatistik gtt Earth sciences -- Statistical methods Geostatistik (DE-588)4020279-3 gnd rswk-swf Geostatistik (DE-588)4020279-3 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009966250&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Borradaile, Graham J. Statistics of earth science data their distribution in time, space and orientation ; with 52 tables Geostatistik gtt Earth sciences -- Statistical methods Geostatistik (DE-588)4020279-3 gnd
subject_GND	(DE-588)4020279-3
title	Statistics of earth science data their distribution in time, space and orientation ; with 52 tables
title_auth	Statistics of earth science data their distribution in time, space and orientation ; with 52 tables
title_exact_search	Statistics of earth science data their distribution in time, space and orientation ; with 52 tables
title_full	Statistics of earth science data their distribution in time, space and orientation ; with 52 tables Graham Borradaile
title_fullStr	Statistics of earth science data their distribution in time, space and orientation ; with 52 tables Graham Borradaile
title_full_unstemmed	Statistics of earth science data their distribution in time, space and orientation ; with 52 tables Graham Borradaile
title_short	Statistics of earth science data
title_sort	statistics of earth science data their distribution in time space and orientation with 52 tables
title_sub	their distribution in time, space and orientation ; with 52 tables
topic	Geostatistik gtt Earth sciences -- Statistical methods Geostatistik (DE-588)4020279-3 gnd
topic_facet	Geostatistik Earth sciences -- Statistical methods
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009966250&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT borradailegrahamj statisticsofearthsciencedatatheirdistributionintimespaceandorientationwith52tables

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