Multivariate Geostatistics

An Introduction with Applications

By: Hans Wackernagel

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Hardcover | 12 February 2003 | Edition Number 3

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Hardcover
404 Pages

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Revised

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24.13 x 16.51 x 2.54

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This book presents an introduction to geostatistics stressing the multivariate aspects for scientists, engineers or statisticians. Geostatistics offers a variety of models, methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time. This book presents a brief review of statistical concepts, a detailed introduction to linear geostatistics and an account of three basic methods of multivariate analysis. The third edition of this very successful textbook contains an advanced presentation of linear models for multivariate spatial or temporal data, of nonlinear models and methods for selection problems with change of suppport as well as an introduction to non-stationary geostatistics with special focus on the external drift method. Applications from diverse areas of science, as well as exercises with solutions, are provided to help convey the concepts and techniques.

Industry Reviews

SOME PRAISE FOR PREVIOUS EDITIONS:

"If you do geostatistics, you certainly should own [this book], because there are no competitors..."
-TECHNOMETRICS

"This is an introductory book on geostatistics (spatial statistics) with an emphasis on multivariate analysis of spatially indexed data. Explanations are intuitive, with graphical interpretations included where possible. Additionally, mathematical relationships are explained with uncommon clarity.''
-JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"This book is an excellent modern introduction to geostatistics, which is one of the main branches of spatial statistics [...] this is a fine book for students of statistics, statisticians and well-informed engineers and geologists."
-BIOMETRICAL JOURNAL

"For a physical geodesist ... it is both informative and beneficial to learn about these marvelous techniques which have so much in common with the applied methods of our branch of science. What a great source of inspiration!"
-JOURNAL OF GEODESY

"The book is attractively finished and well printed ... the author's style is very readable. It should have an immediate appeal to geophysicists, hydrogeologists, engineering geologists and those mathematicians and physicists already engaged in stochastic modelling in the oil and gas industry."
-GEOSCIENTIST

"... This book is an insightful introduction to linear geostatistics in general and multivariate geostatistics in particular, and provides a springboard to further study and research in this very interesting area."
-METRIKA

"The text is well structured and easy to read; the style is plain and appealing. It moves from practical intuitive ideas to their mathematical formulation in a straightforward and natural way."
-COMPUTERS & GEOSCIENCES

``Without doubt the book will find an extensive readership including serious practitioners.''
-SHORT BOOK REVIEWS(INTERNATIONAL STATISTICAL INSTITUTE)

``Very often, comparisons are made between least squares prediction and collocation with kriging. [The book] is a must for all those scientists and engineers who want to know the similarities of both techniques applied to geosciences.''
-GIS GEO-INFORMATIONS-SYSTEME

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Non-Fiction Earth Sciences, Geography, Environment, Planning Earth Sciences Geology & The Lithosphere Mathematics Probability & Statistics Science Science in General Maths for Scientists Engineering & Technology Technology in General Maths for Engineers

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Published: 15th December 2010

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Introduction	p. 1
From Statistics to Geostatistics	p. 7
Mean, Variance, Covariance	p. 9
The mean: center of mass	p. 9
Distribution function	p. 11
Expectation	p. 12
Variance	p. 13
Covariance	p. 14
Linear Regression and Simple Kriging	p. 15
Experimental covariance	p. 15
Linear regression	p. 16
Variance-covariance matrix	p. 20
Multiple linear regression	p. 21
Simple kriging	p. 24
Kriging the Mean	p. 27
Arithmetic mean and its estimation variance	p. 27
Estimating the mean with spatial correlation	p. 28
No systematic bias	p. 29
Variance of the estimation error	p. 30
Minimal estimation variance	p. 30
Kriging equations	p. 31
Case of no correlation	p. 32
Geostatistics	p. 35
Regionalized Variable and Random Function	p. 39
Multivariate time/space data	p. 39
Regionalized variable	p. 40
Random variable and regionalized value	p. 41
Random function	p. 41
Probability distributions	p. 42
Strict stationarity	p. 43
Stationarity of first two moments	p. 44
Variogram Cloud	p. 45
Dissimilarity versus separation	p. 45
Experimental variogram	p. 47
Replacing the experimental by a theoretical variogram	p. 48
Variogram and Covariance Function	p. 50
Regional variogram	p. 50
Theoretical variogram	p. 50
Covariance function	p. 52
Positive definite function	p. 53
Conditionally negative definite function	p. 53
Fitting the variogram with a covariance function	p. 55
Examples of Covariance Functions	p. 57
Nugget-effect model	p. 57
Exponential covariance function	p. 57
Spherical model	p. 58
Derivation of the spherical covariance	p. 58
Anisotropy	p. 62
Geometric Anisotropy	p. 62
Rotating and dilating an ellipsoid	p. 62
Exploring 3D space for anisotropy	p. 64
Zonal anisotropy	p. 65
Nonlinear deformations of space	p. 65
Extension and Dispersion Variance	p. 66
Support	p. 66
Extension variance	p. 67
Dispersion variance	p. 68
Krige's relation	p. 69
Change of support effect	p. 70
Change of support: affine model	p. 71
Application: acoustic data	p. 73
Comparison of sampling designs	p. 76
Ordinary Kriging	p. 79
Ordinary kriging problem	p. 79
Simple kriging of increments	p. 81
Block kriging	p. 82
Simple kriging with an estimated mean	p. 84
Kriging the residual	p. 85
Cross validation	p. 87
Kriging with known measurement error variance	p. 88
Kriging Weights	p. 89
Geometry	p. 89
Geometric anisotropy	p. 91
Relative position of samples	p. 91
Screen effect	p. 92
Factorizable covariance functions	p. 93
Negative kriging weights	p. 94
Mapping with Kriging	p. 96
Kriging for spatial interpolation	p. 96
Neighborhood	p. 97
Linear Model of Regionalization	p. 101
Spatial anomalies	p. 101
Nested variogram model	p. 102
Decomposition of the random function	p. 103
Second-order stationary regionalization	p. 104
Intrinsic regionalization	p. 105
Intrinsic regionalization with mostly stationary components	p. 105
Locally stationary regionalization	p. 106
Kriging Spatial Components	p. 107
Kriging of the intrinsic component	p. 107
Kriging of a second-order stationary component	p. 108
Filtering	p. 110
Application: kriging spatial components of arsenic data	p. 111
The Smoothness of Kriging	p. 113
Kriging with irregularly spaced data	p. 113
Sensitivity to choice of variogram model	p. 115
Application: kriging topographic data	p. 117
Multivariate Analysis	p. 121
Principal Component Analysis	p. 123
Uses of PCA	p. 123
Transformation into factors	p. 123
Maximization of the variance of a factor	p. 125
Interpretation of the factor variances	p. 126
Correlation of the variables with the factors	p. 127
Canonical Analysis	p. 137
Factors in two groups of variables	p. 137
Intermezzo: singular value decomposition	p. 138
Maximization of the correlation	p. 138
Correspondence Analysis	p. 140
Disjunctive table	p. 140
Contingency table	p. 140
Canonical analysis of disjunctive tables	p. 141
Coding of a quantitative variable	p. 141
Contingencies between two quantitative variables	p. 141
Continuous correspondence analysis	p. 142
Multivariate Geostatistics	p. 143
Direct and Cross Covariances	p. 145
Cross covariance function	p. 145
Delay effect	p. 145
Cross variogram	p. 146
Pseudo cross variogram	p. 149
Difficult characterization of the cross covariance function	p. 150
Covariance Function Matrices	p. 151
Covariance function matrix	p. 151
Cramer's theorem	p. 151
Spectral densities	p. 152
Phase shift	p. 153
Intrinsic Multivariate Correlation	p. 154
Intrinsic correlation model	p. 154
Linear model	p. 155
Codispersion coefficients	p. 156
Heterotopic Cokriging	p. 158
Isotopy and heterotopy	p. 158
Ordinary cokriging	p. 159
Simple cokriging	p. 161
Collocated Cokriging	p. 165
Cokriging neighborhood	p. 165
Collocated simple cokriging	p. 166
Collocated ordinary cokriging	p. 167
Simplification with a particular covariance model	p. 168
Isotopic Cokriging	p. 170
Cokriging with isotopic data	p. 170
Autokrigeability	p. 171
Bivariate ordinary cokriging	p. 173
Multivariate Nested Variogram	p. 175
Linear model of coregionalization	p. 175
Bivariate fit of the experimental variograms	p. 177
Multivariate fit	p. 178
The need for an analysis of the coregionalization	p. 181
Case Study: Ebro Estuary	p. 183
Kriging conductivity	p. 183
Cokriging of chlorophyll	p. 185
Conditional simulation of chlorophyll	p. 187
Coregionalization Analysis	p. 194
Regionalized principal component analysis	p. 194
Generalizing the analysis	p. 195
Regionalized canonical and redundancy analysis	p. 196
Cokriging regionalized factors	p. 196
Regionalized multivariate analysis	p. 197
Kriging a Complex Variable	p. 200
Coding directional data as a complex variable	p. 200
Complex covariance function	p. 200
Complex kriging	p. 201
Cokriging of the real and imaginary parts	p. 202
Complex kriging and cokriging versus a separate kriging	p. 203
Complex covariance function modeling	p. 205
Bilinear Coregionalization Model	p. 207
Complex linear model of coregionalization	p. 207
Bilinear model of coregionalization	p. 208
Selective Geostatistics	p. 211
Thresholds and Selectivity Curves	p. 213
Threshold and proportion	p. 213
Tonnage, recovered quantity, investment and profit	p. 213
Selectivity	p. 216
Recovered quantity as a function of tonnage	p. 217
Time series in environmental monitoring	p. 219
Lognormal Estimation	p. 221
Information effect and quality of estimators	p. 221
Logarithmic Gaussian model	p. 223
Moments of the lognormal variable	p. 224
Lognormal simple kriging	p. 226
Proportional effect	p. 228
Permanence of lognormality	p. 228
Stable variogram model	p. 233
Lognormal point and block ordinary kriging	p. 233
Gaussian Anamorphosis with Hermite Polynomials	p. 238
Gaussian anamorphosis	p. 238
Hermite polynomials	p. 239
Expanding a function into Hermite polynomials	p. 240
Probabilistic interpretation	p. 240
Moments of a function of a Gaussian variable	p. 241
Conditional expectation of a function of a Gaussian variable	p. 243
Empirical Gaussian anamorphosis	p. 244
Smoothing the empirical anamorphosis	p. 245
Bijectivity of Gaussian anamorphosis	p. 247
Isofactorial Models	p. 250
Isofactorial bivariate distribution	p. 250
Isofactorial decomposition	p. 251
Isofactorial models	p. 252
Choice of marginal and of isofactorial bivariate distribution	p. 253
Hermitian and Laguerre isofactorial distributions	p. 254
Intermediate types between diffusion and mosaic models	p. 258
Isofactorial Change of Support	p. 262
The point-block-panel problem	p. 262
Carrier's relation and point-block correlation	p. 262
Discrete Gaussian point-block model	p. 266
General structure of isofactorial change-of-support	p. 267
Kriging with Discrete Point-Bloc Models	p. 273
Non-linear function of a block variable	p. 273
Conditional expectation and disjunctive kriging of a bloc	p. 274
Disjunctive kriging of a panel	p. 275
Uniform conditioning	p. 277
Non-Stationary Geostatistics	p. 281
External Drift	p. 283
Depth measured with drillholes and seismic	p. 283
Estimating with a shape function	p. 284
Estimating external drift coefficients	p. 285
Cross validation with external drift	p. 290
Regularity of the external drift function	p. 294
Cokriging with multiple external drift	p. 296
Ebro estuary: numerical model output as external drift	p. 297
Comparing results of conditional simulations and kriging	p. 297
Universal Kriging	p. 300
Universal kriging system	p. 300
Estimation of the drift	p. 302
Underlying variogram and estimated residuals	p. 303
From universal to intrinsic kriging	p. 306
Translation Invariant Drift	p. 308
Exponential-polynomial basis functions	p. 308
Intrinsic random functions of order ?	p. 309
Generalized covariance function	p. 310
Intrinsic kriging	p. 311
Trigonometric temporal drift	p. 312
Filtering trigonometric temporal drift	p. 312
Dual kriging	p. 313
Splines	p. 314
Appendix	p. 317
Matrix Algebra	p. 319
Linear Regression Theory	p. 329
Covariance and Variogram Models	p. 334
Additional Exercices	p. 337
Solutions to Exercises	p. 339
References	p. 353
Bibliography	p. 358
Index	p. 381
Table of Contents provided by Publisher. All Rights Reserved.

Multivariate Geostatistics

An Introduction with Applications

At a Glance

Hardcover

Industry Reviews

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