Geostatistics: Modeling Spatial Uncertainty, 2nd Edition


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Praise for the First Edition

". . . a readable, comprehensive volume that . . . belongs on the desk, close at hand, of any serious researcher or practitioner." —Mathematical Geosciences

The state of the art in geostatistics

Geostatistical models and techniques such as kriging and stochastic multi-realizations exploit spatial correlations to evaluate natural resources, help optimize their development, and address environmental issues related to air and water quality, soil pollution, and forestry. Geostatistics: Modeling Spatial Uncertainty, Second Edition presents a comprehensive, up-to-date reference on the topic, now featuring the latest developments in the field.

The authors explain both the theory and applications of geostatistics through a unified treatment that emphasizes methodology. Key topics that are the foundation of geostatistics are explored in-depth, including stationary and nonstationary models; linear and nonlinear methods; change of support; multivariate approaches; and conditional simulations. The Second Edition highlights the growing number of applications of geostatistical methods and discusses three key areas of growth in the field:

  • New results and methods, including kriging very large datasets; kriging with outliers; nonse??parable space-time covariances; multipoint simulations; pluri-gaussian simulations; gradual deformation; and extreme value geostatistics

  • Newly formed connections between geostatistics and other approaches such as radial basis functions, Gaussian Markov random fields, and data assimilation

  • New perspectives on topics such as collocated cokriging, kriging with an external drift, discrete Gaussian change-of-support models, and simulation algorithms

Geostatistics, Second Edition is an excellent book for courses on the topic at the graduate level. It also serves as an invaluable reference for earth scientists, mining and petroleum engineers, geophysicists, and environmental statisticians who collect and analyze data in their everyday work.

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 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

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