Geostatistics for Environmental Scientists

✍ Scribed by Richard Webster, Margaret A. Oliver

• Publisher: Wiley
• Year: 2007
• Tongue: English
• Leaves: 332
• Series: Statistics in Practice
• Edition: 2
• Category: Library

✦ Synopsis

Geostatistics is essential for environmental scientists. Weather and climate vary from place to place, soil varies at every scale at which it is examined, and even man-made attributes – such as the distribution of pollution – vary. The techniques used in geostatistics are ideally suited to the needs of environmental scientists, who use them to make the best of sparse data for prediction, and top plan future surveys when resources are limited.

Geostatistical technology has advanced much in the last few years and many of these developments are being incorporated into the practitioner’s repertoire. This second edition describes these techniques for environmental scientists. Topics such as stochastic simulation, sampling, data screening, spatial covariances, the variogram and its modeling, and spatial prediction by kriging are described in rich detail. At each stage the underlying theory is fully explained, and the rationale behind the choices given, allowing the reader to appreciate the assumptions and constraints involved.

✦ Table of Contents

Geostatistics for Environmental Scientists......Page 1
Contents......Page 7
Preface......Page 13
1.1 WHY GEOSTATISTICS?......Page 15
1.1.1 Generalizing......Page 16
1.1.4 Control......Page 19
1.2 A LITTLE HISTORY......Page 20
1.3 FINDING YOUR WAY......Page 22
2.1 MEASUREMENT AND SUMMARY......Page 25
2.1.1 Notation......Page 26
2.1.2 Representing variation......Page 27
2.1.3 The centre......Page 29
2.1.4 Dispersion......Page 30
2.2 THE NORMAL DISTRIBUTION......Page 32
2.3 COVARIANCE AND CORRELATION......Page 33
2.4 TRANSFORMATIONS......Page 34
2.4.2 Square root transformation......Page 35
2.5 EXPLORATORY DATA ANALYSIS AND DISPLAY......Page 36
2.5.1 Spatial aspects......Page 39
2.6 SAMPLING AND ESTIMATION......Page 40
2.6.2 Simple random sampling......Page 42
2.6.3 Confidence limits......Page 43
2.6.4 Student’s t......Page 44
2.6.5 The x2 distribution......Page 45
2.6.7 Increasing precision and efficiency......Page 46
2.6.8 Soil classification......Page 49
3.1 SPATIAL INTERPOLATION......Page 51
3.1.2 Triangulation......Page 52
3.1.3 Natural neighbour interpolation......Page 53
3.1.5 Trend surfaces......Page 54
3.2 SPATIAL CLASSIFICATION AND PREDICTING FROM SOIL MAPS......Page 56
3.2.1 Theory......Page 57
3.2.2 Summary......Page 59
4.1 INTRODUCTION......Page 61
4.2.1 Random variables......Page 62
4.2.2 Random functions......Page 63
4.3 SPATIAL COVARIANCE......Page 64
4.3.1 Stationarity......Page 66
4.4 THE COVARIANCE FUNCTION......Page 67
4.5.1 Equivalence with covariance......Page 68
4.6 CHARACTERISTICS OF THE SPATIAL CORRELATION FUNCTIONS......Page 69
4.8 SUPPORT AND KRIGE’S RELATION......Page 74
4.8.1 Regularization......Page 77
4.9.1 The variogram cloud......Page 79
4.9.2 h-Scattergrams......Page 80
4.9.3 Average semivariances......Page 81
4.9.4 The experimental covariance function......Page 87
5 Modelling the Variogram......Page 91
5.1.1 Mathematical constraints......Page 93
5.1.2 Behaviour near the origin......Page 94
5.2 AUTHORIZED MODELS......Page 96
5.2.1 Unbounded random variation......Page 97
5.2.2 Bounded models......Page 98
5.3 COMBINING MODELS......Page 109
5.4 PERIODICITY......Page 111
5.5 ANISOTROPY......Page 113
5.6 FITTING MODELS......Page 115
5.6.1 What weights?......Page 118
5.6.2 How complex?......Page 119
6.1.1 Statistical distribution......Page 123
6.1.2 Sample size and design......Page 133
6.1.3 Sample spacing......Page 140
6.2 THEORY OF NESTED SAMPLING AND ANALYSIS......Page 141
6.2.1 Link with regionalized variable theory......Page 142
6.2.2 Case study: Youden and Mehlich’s survey......Page 143
6.2.3 Unequal sampling......Page 145
6.2.4 Case study: Wyre Forest survey......Page 148
6.2.5 Summary......Page 152
7.1 LINEAR SEQUENCES......Page 153
7.2 GILGAI TRANSECT......Page 154
7.3 POWER SPECTRA......Page 156
7.3.1 Estimating the spectrum......Page 158
7.3.2 Smoothing characteristics of windows......Page 162
7.3.3 Confidence......Page 163
7.4.1 Bandwidths and confidence intervals for Caragabal......Page 164
7.5 FURTHER READING ON SPECTRAL ANALYSIS......Page 166
8 Local Estimation or Prediction: Kriging......Page 167
8.1.1 Kinds of Kriging......Page 168
8.2 THEORY OF ORDINARY KRIGING......Page 169
8.3 WEIGHTS......Page 173
8.4 EXAMPLES......Page 174
8.4.1 Kriging at the centre of the lattice......Page 175
8.4.2 Kriging off-centre in the lattice and at a sampling point......Page 183
8.5 NEIGHBOURHOOD......Page 186
8.6 ORDINARY KRIGING FOR MAPPING......Page 188
8.7 CASE STUDY......Page 189
8.7.2 Summary......Page 194
8.8 REGIONAL ESTIMATION......Page 195
8.9 SIMPLE KRIGING......Page 197
8.10 LOGNORMAL KRIGING......Page 199
8.11 OPTIMAL SAMPLING FOR MAPPING......Page 200
8.11.1 Isotropic variation......Page 202
8.11.2 Anisotropic variation......Page 204
8.12 CROSS-VALIDATION......Page 205
8.12.1 Scatter and regression......Page 207
9.1 NON-STATIONARITY IN THE MEAN......Page 209
9.1.1 Some background......Page 210
9.2.1 Estimation of the variogram by REML......Page 214
9.2.3 Kriging with external drift......Page 217
9.3 CASE STUDY......Page 219
9.4.2 Theory......Page 226
9.4.3 Kriging analysis......Page 227
9.4.4 Illustration......Page 232
10.1 INTRODUCTION......Page 233
10.2 ESTIMATING AND MODELLING THE CROSS-CORRELATION......Page 236
10.2.1 Intrinsic coregionalization......Page 238
10.3 EXAMPLE: CEDAR FARM......Page 240
10.4 COKRIGING......Page 242
10.4.1 Is cokriging worth the trouble?......Page 245
10.4.2 Example of benefits of cokriging......Page 246
10.5 PRINCIPAL COMPONENTS OF COREGIONALIZATION MATRICES......Page 249
10.6 PSEUDO-CROSS-VARIOGRAM......Page 255
11.1 INTRODUCTION......Page 257
11.2.1 Indicator coding......Page 260
11.2.2 Indicator variograms......Page 261
11.3 INDICATOR KRIGING......Page 263
11.4.1 Assumptions of Gaussian disjunctive kriging......Page 265
11.4.2 Hermite polynomials......Page 266
11.4.3 Disjunctive kriging for a Hermite polynomial......Page 268
11.4.5 Conditional probability......Page 270
11.5 CASE STUDY......Page 271
11.6 OTHER CASE STUDIES......Page 277
11.7 SUMMARY......Page 280
12.1 INTRODUCTION......Page 281
12.2 SIMULATION FROM A RANDOM PROCESS......Page 282
12.2.2 Conditional simulation......Page 284
12.3 TECHNICALITIES......Page 285
12.3.1 Lower–upper decomposition......Page 286
12.3.2 Sequential Gaussian simulation......Page 287
12.3.3 Simulated annealing......Page 288
12.3.4 Simulation by turning bands......Page 290
12.4 USES OF SIMULATED FIELDS......Page 291
12.5 ILLUSTRATION......Page 292
A.3 SCREENING......Page 299
A.4 HISTOGRAM AND SUMMARY......Page 300
A.5 NORMALITY AND TRANSFORMATION......Page 301
A.7 SPATIAL ANALYSIS: THE VARIOGRAM......Page 302
A.8 MODELLING THE VARIOGRAM......Page 304
A.9 SPATIAL ESTIMATION OR PREDICTION: KRIGING......Page 305
A.10 MAPPING......Page 306
B.1 SUMMARY STATISTICS......Page 307
B.3 CUMULATIVE DISTRIBUTION......Page 308
B.5.1 Experimental variogram......Page 309
B.5.2 Fitting a model......Page 310
B.7.1 Auto- and cross-variograms......Page 311
B.8 CONTROL......Page 312
References......Page 313
Index......Page 323
Statistics in Practice......Page 331

✦ Subjects

Горно-геологическая отрасль;Матметоды и моделирование в геологии;Геостатистика;