Geostatistics for environmental scientists

Geostatistics for Environmental Scientists......Page 2
Contents......Page 8
Preface......Page 14
1.1 WHY GEOSTATISTICS?......Page 16
1.1.1 Generalizing......Page 17
1.1.4 Control......Page 20
1.2 A LITTLE HISTORY......Page 21
1.3 FINDING YOUR WAY......Page 23
2.1 MEASUREMENT AND SUMMARY......Page 26
2.1.1 Notation......Page 27
2.1.2 Representing variation......Page 28
2.1.3 The centre......Page 30
2.1.4 Dispersion......Page 31
2.2 THE NORMAL DISTRIBUTION......Page 33
2.3 COVARIANCE AND CORRELATION......Page 34
2.4 TRANSFORMATIONS......Page 35
2.4.2 Square root transformation......Page 36
2.5 EXPLORATORY DATA ANALYSIS AND DISPLAY......Page 37
2.5.1 Spatial aspects......Page 40
2.6 SAMPLING AND ESTIMATION......Page 41
2.6.2 Simple random sampling......Page 43
2.6.3 Confidence limits......Page 44
2.6.4 Student’s t......Page 45
2.6.5 The x2 distribution......Page 46
2.6.7 Increasing precision and efficiency......Page 47
2.6.8 Soil classification......Page 50
3.1 SPATIAL INTERPOLATION......Page 52
3.1.2 Triangulation......Page 53
3.1.3 Natural neighbour interpolation......Page 54
3.1.5 Trend surfaces......Page 55
3.2 SPATIAL CLASSIFICATION AND PREDICTING FROM SOIL MAPS......Page 57
3.2.1 Theory......Page 58
3.2.2 Summary......Page 60
4.1 INTRODUCTION......Page 62
4.2.1 Random variables......Page 63
4.2.2 Random functions......Page 64
4.3 SPATIAL COVARIANCE......Page 65
4.3.1 Stationarity......Page 67
4.4 THE COVARIANCE FUNCTION......Page 68
4.5.1 Equivalence with covariance......Page 69
4.6 CHARACTERISTICS OF THE SPATIAL CORRELATION FUNCTIONS......Page 70
4.8 SUPPORT AND KRIGE’S RELATION......Page 75
4.8.1 Regularization......Page 78
4.9.1 The variogram cloud......Page 80
4.9.2 h-Scattergrams......Page 81
4.9.3 Average semivariances......Page 82
4.9.4 The experimental covariance function......Page 88
5 Modelling the Variogram......Page 92
5.1.1 Mathematical constraints......Page 94
5.1.2 Behaviour near the origin......Page 95
5.2 AUTHORIZED MODELS......Page 97
5.2.1 Unbounded random variation......Page 98
5.2.2 Bounded models......Page 99
5.3 COMBINING MODELS......Page 110
5.4 PERIODICITY......Page 112
5.5 ANISOTROPY......Page 114
5.6 FITTING MODELS......Page 116
5.6.1 What weights?......Page 119
5.6.2 How complex?......Page 120
6.1.1 Statistical distribution......Page 124
6.1.2 Sample size and design......Page 134
6.1.3 Sample spacing......Page 141
6.2 THEORY OF NESTED SAMPLING AND ANALYSIS......Page 142
6.2.1 Link with regionalized variable theory......Page 143
6.2.2 Case study: Youden and Mehlich’s survey......Page 144
6.2.3 Unequal sampling......Page 146
6.2.4 Case study: Wyre Forest survey......Page 149
6.2.5 Summary......Page 153
7.1 LINEAR SEQUENCES......Page 154
7.2 GILGAI TRANSECT......Page 155
7.3 POWER SPECTRA......Page 157
7.3.1 Estimating the spectrum......Page 159
7.3.2 Smoothing characteristics of windows......Page 163
7.3.3 Confidence......Page 164
7.4.1 Bandwidths and confidence intervals for Caragabal......Page 165
7.5 FURTHER READING ON SPECTRAL ANALYSIS......Page 167
8 Local Estimation or Prediction: Kriging......Page 168
8.1.1 Kinds of Kriging......Page 169
8.2 THEORY OF ORDINARY KRIGING......Page 170
8.3 WEIGHTS......Page 174
8.4 EXAMPLES......Page 175
8.4.1 Kriging at the centre of the lattice......Page 176
8.4.2 Kriging off-centre in the lattice and at a sampling point......Page 184
8.5 NEIGHBOURHOOD......Page 187
8.6 ORDINARY KRIGING FOR MAPPING......Page 189
8.7 CASE STUDY......Page 190
8.7.2 Summary......Page 195
8.8 REGIONAL ESTIMATION......Page 196
8.9 SIMPLE KRIGING......Page 198
8.10 LOGNORMAL KRIGING......Page 200
8.11 OPTIMAL SAMPLING FOR MAPPING......Page 201
8.11.1 Isotropic variation......Page 203
8.11.2 Anisotropic variation......Page 205
8.12 CROSS-VALIDATION......Page 206
8.12.1 Scatter and regression......Page 208
9.1 NON-STATIONARITY IN THE MEAN......Page 210
9.1.1 Some background......Page 211
9.2.1 Estimation of the variogram by REML......Page 215
9.2.3 Kriging with external drift......Page 218
9.3 CASE STUDY......Page 220
9.4.2 Theory......Page 227
9.4.3 Kriging analysis......Page 228
9.4.4 Illustration......Page 233
10.1 INTRODUCTION......Page 234
10.2 ESTIMATING AND MODELLING THE CROSS-CORRELATION......Page 237
10.2.1 Intrinsic coregionalization......Page 239
10.3 EXAMPLE: CEDAR FARM......Page 241
10.4 COKRIGING......Page 243
10.4.1 Is cokriging worth the trouble?......Page 246
10.4.2 Example of benefits of cokriging......Page 247
10.5 PRINCIPAL COMPONENTS OF COREGIONALIZATION MATRICES......Page 250
10.6 PSEUDO-CROSS-VARIOGRAM......Page 256
11.1 INTRODUCTION......Page 258
11.2.1 Indicator coding......Page 261
11.2.2 Indicator variograms......Page 262
11.3 INDICATOR KRIGING......Page 264
11.4.1 Assumptions of Gaussian disjunctive kriging......Page 266
11.4.2 Hermite polynomials......Page 267
11.4.3 Disjunctive kriging for a Hermite polynomial......Page 269
11.4.5 Conditional probability......Page 271
11.5 CASE STUDY......Page 272
11.6 OTHER CASE STUDIES......Page 278
11.7 SUMMARY......Page 281
12.1 INTRODUCTION......Page 282
12.2 SIMULATION FROM A RANDOM PROCESS......Page 283
12.2.2 Conditional simulation......Page 285
12.3 TECHNICALITIES......Page 286
12.3.1 Lower–upper decomposition......Page 287
12.3.2 Sequential Gaussian simulation......Page 288
12.3.3 Simulated annealing......Page 289
12.3.4 Simulation by turning bands......Page 291
12.4 USES OF SIMULATED FIELDS......Page 292
12.5 ILLUSTRATION......Page 293
A.3 SCREENING......Page 300
A.4 HISTOGRAM AND SUMMARY......Page 301
A.5 NORMALITY AND TRANSFORMATION......Page 302
A.7 SPATIAL ANALYSIS: THE VARIOGRAM......Page 303
A.8 MODELLING THE VARIOGRAM......Page 305
A.9 SPATIAL ESTIMATION OR PREDICTION: KRIGING......Page 306
A.10 MAPPING......Page 307
B.1 SUMMARY STATISTICS......Page 308
B.3 CUMULATIVE DISTRIBUTION......Page 309
B.5.1 Experimental variogram......Page 310
B.5.2 Fitting a model......Page 311
B.7.1 Auto- and cross-variograms......Page 312
B.8 CONTROL......Page 313
References......Page 314
Index......Page 324
Statistics in Practice......Page 332