Geostatistics: Modeling Spatial Uncertainty, 2nd Edition

Preface to the First Edition xiii

Abbreviations xv

Introduction 1

Types of Problems Considered, 2

Description or Interpretation?, 8

1. Preliminaries 11

1.1 Random Functions, 11

1.2 On the Objectivity of Probabilistic Statements, 22

1.3 Transitive Theory, 24

2. Structural Analysis 28

2.1 General Principles, 28

2.2 Variogram Cloud and Sample Variogram, 33

2.3 Mathematical Properties of the Variogram, 59

2.4 Regularization and Nugget Effect, 78

2.5 Variogram Models, 84

2.6 Fitting a Variogram Model, 109

2.7 Variography in the Presence of a Drift, 122

2.8 Simple Applications of the Variogram, 130

2.9 Complements: Theory of Variogram Estimation and Fluctuation, 138

3. Kriging 147

3.1 Introduction, 147

3.2 Notations and Assumptions, 149

3.3 Kriging with a Known Mean, 150

3.4 Kriging with an Unknown Mean, 161

3.5 Estimation of a Spatial Average, 196

3.6 Selection of a Kriging Neighborhood, 204

3.7 Measurement Errors and Outliers, 216

3.8 Case Study: The Channel Tunnel, 225

3.9 Kriging Under Inequality Constraints, 232

4. Intrinsic Model of Order k 238

4.1 Introduction, 238

4.2 A Second Look at the Model of Universal Kriging, 240

4.3 Allowable Linear Combinations of Order k, 245

4.4 Intrinsic Random Functions of Order k, 252

4.5 Generalized Covariance Functions, 257

4.6 Estimation in the IRF Model, 269

4.7 Generalized Variogram, 281

4.8 Automatic Structure Identification, 286

4.9 Stochastic Differential Equations, 294

5. Multivariate Methods 299

5.1 Introduction, 299

5.2 Notations and Assumptions, 300

5.3 Simple Cokriging, 302

5.4 Universal Cokriging, 305

5.5 Derivative Information, 320

5.6 Multivariate Random Functions, 330

5.7 Shortcuts, 360

5.8 SpaceTime Models, 370

6. Nonlinear Methods 386

6.1 Introduction, 386

6.2 Global Point Distribution, 387

6.3 Local Point Distribution: Simple Methods, 392

6.4 Local Estimation by Disjunctive Kriging, 401

6.5 Selectivity and Support Effect, 433

6.6 Multi-Gaussian Change-of-Support Model, 445

6.7 Affine Correction, 448

6.8 Discrete Gaussian Model, 449

6.9 Non-Gaussian Isofactorial Change-of-Support Models, 466

6.10 Applications and Discussion, 469

6.11 Change of Support by the Maximum (C. Lantue´ joul), 470

7. Conditional Simulations 478

7.1 Introduction and Definitions, 478

7.2 Direct Conditional Simulation of a Continuous Variable, 489

7.3 Conditioning by Kriging, 495

7.4 Turning Bands, 502

7.5 Nonconditional Simulation of a Continuous Variable, 508

7.6 Simulation of a Categorical Variable, 546

7.7 Object-Based Simulations: Boolean Models, 574

7.8 Beyond Standard Conditioning, 590

7.9 Additional Topics, 606

7.10 Case Studies, 615

Appendix 629

References 642

Index 689