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Preface and Acknowledgments.............................................................. vii

1.   Introduction.......................................................................................... 1

1.1   Plan of this Book, 2

1.2   The Premise of Geostatistics, 4

1.3   Nomenclature, 6

2.   Getting Comfortable with Probabilities............................................. 7

2.1   Parametric Probability Distributions, 7

2.2   Variance of Linear Combinations, 13

2.3   Standardization and Probability Intervals, 16

3.   Obtaining Representative Distributions........................................... 21

3.1   Basic Declustering, 22

3.2   Debiasing with Bivariate Gaussian Distribution, 28

3.3   Comparison of Declustering Methods, 35

4.   Monte Carlo Simulation.................................................................... 41

4.1   Impact of the Central Limit Theorem, 43

4.2   Bootstrap and Spatial Bootstrap, 47

4.3   Transfer of Uncertainty, 54

5.   Variograms and Volume Variance................................................... 59

5.1   Geometric Anisotropy, 60

5.2   Variogram Calculation, 69

5.3   Variogram Modeling and Volume Variance, 78

6.   Kriging................................................................................................ 85

6.1   Stationary Kriging, 86

6.2   Nonstationary Kriging, 92

6.3   Screening Effect of Kriging, 97

7.   Gaussian Simulation........................................................................ 103

7.1   Bivariate Gaussian Distribution, 104

7.2   Conditioning by Kriging, 110

7.3   Gaussian Simulation, 117


8.   Indicators.......................................................................................... 125

8.1   Variogram of Objects, 127

8.2   Indicator Variograms and the Gaussian Distribution, 133

8.3   Indicator Simulation for Categorical Data, 137

9.   Multiple Variables............................................................................ 143

9.1   Linear Model of Coregionalization, 144

9.2   Gaussian Cosimulation, 149

9.3   Multiscale Cokriging, 159

10. Special Topics................................................................................... 167

10.1 Decision Making in the Presence of Uncertainty, 168

10.2 Trend Model Construction     , 175

10.3 Multiple Point Statistics , 182

11. Closing Remarks.............................................................................. 193

Bibliography........................................................................................... 197

Index....................................................................................................... 205


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