Jean-Paul Chilès is Deputy Director of the Center of Geosciences and Geoengi??neering at MINES ParisTech, France.

Pierre Delfiner is Principal of PetroDecisions, a consulting firm based in Paris, France.

Preface to the Second Edition ix

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 Space Time 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. Lantuéjoul) 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