Geostatistics_ Modeling Spatial Uncertainty, Second Edition.pdf

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Geostatistics fﬁrs 28 January 2012; 13:1:56

WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, Iain M. Johnstone, Geert Molenberghs, David W. Scott, Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg Editors Emeriti: Vic Barnett, J. Stuart Hunter, Joseph B. Kadane, Jozef L. Teugels A complete list of the titles in this series appears at the end of this volume. fﬁrs 28 January 2012; 13:1:56

Geostatistics Modeling Spatial Uncertainty Second Edition JEAN-PAUL CHILE` S BRGM and MINES ParisTech PIERRE DELFINER PetroDecisions fﬁrs 28 January 2012; 13:1:56

Copyright r 2012 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciﬁcally disclaim any implied warranties of merchantability or ﬁtness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of proﬁt or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. ISBN: 978-0-470-18315-1 Library of Congress Cataloging-in-Publication Data is available. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 fﬁrs 28 January 2012; 13:1:56

Contents Preface to the Second Edition Preface to the First Edition Abbreviations Introduction Types of Problems Considered, 2 Description or Interpretation?, 8 1. Preliminaries 1.1 Random Functions, 11 1.2 On the Objectivity of Probabilistic Statements, 22 1.3 Transitive Theory, 24 2. Structural Analysis 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 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 Fitting a Variogram Model, 109 Fluctuation, 138 ftoc 28 January 2012; 13:4:27 ix xiii xv 1 11 28 v

vi 3. Kriging CONTENTS 147 Introduction, 147 3.1 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 Introduction, 238 Intrinsic Random Functions of Order k, 252 4.1 4.2 A Second Look at the Model of Universal Kriging, 240 4.3 Allowable Linear Combinations of Order k, 245 4.4 4.5 Generalized Covariance Functions, 257 4.6 4.7 Generalized Variogram, 281 4.8 Automatic Structure Identiﬁcation, 286 4.9 Stochastic Differential Equations, 294 Estimation in the IRF Model, 269 299 386 5. Multivariate Methods Introduction, 299 Simple Cokriging, 302 5.1 5.2 Notations and Assumptions, 300 5.3 5.4 Universal Cokriging, 305 5.5 Derivative Information, 320 5.6 Multivariate Random Functions, 330 5.7 5.8 Shortcuts, 360 SpaceTime Models, 370 6. Nonlinear Methods Introduction, 386 6.1 6.2 Global Point Distribution, 387 6.3 6.4 6.5 Local Point Distribution: Simple Methods, 392 Local Estimation by Disjunctive Kriging, 401 Selectivity and Support Effect, 433 ftoc 28 January 2012; 13:4:27

vii 478 629 642 689 CONTENTS 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. Lantu ´ejoul), 470 7. Conditional Simulations Introduction and Deﬁnitions, 478 Turning Bands, 502 7.1 7.2 Direct Conditional Simulation of a Continuous Variable, 489 7.3 Conditioning by Kriging, 495 7.4 7.5 Nonconditional Simulation of a Continuous Variable, 508 7.6 7.7 Object-Based Simulations: Boolean Models, 574 7.8 7.9 Additional Topics, 606 7.10 Case Studies, 615 Simulation of a Categorical Variable, 546 Beyond Standard Conditioning, 590 Appendix References Index ftoc 28 January 2012; 13:4:27

In memory of Georges MATHERON (19302000) ftoc 28 January 2012; 13:4:27

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