Computers & Geosciences 54 (2013) 97–98

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Book Review

Geostatistics: Modeling Spatial Uncertainty, Jean-Paul Chil �es,Pierre Delfiner. Second ed., Wiley Series in Probability andStatistics, John Wiley & Sons, Inc., Hoboken, New Jersey (2012).699pp. ISBN: 978-0-470-18315-1

Geostatistics basically concerns with the description of acharacteristic that varies in space and is originally developed todeal with mineral resource estimation problem in mining. Due tothe spatial feature of the characteristic, geostatistical applicationsare now extended to many fields in the earth sciences other thanmining, including the subsurface, the land, the atmosphere, andthe oceans. A recent study made by Hengl et al. (2009) on thebibliometric indices of geostatistics shows that it is an activescientific field, expanding fast. Considering new perspectives, newdevelopments and an explosion in the applications of geostatis-tical methods, the authors revised and updated the first editionwithout increasing the size of the book. The most noticeablechange is the removal of the chapter related to stochastichydrology and the distribution of some material included in itthroughout the relevant chapters. Some chapters (e.g., multi-variate methods) are largely rewritten with a number of additionsand some (nonlinear methods and conditional simulations) arerestructured and updated. Some chapters such as preliminariesand intrinsic model of order k remain the same. Another change tothe second edition is that footnotes are given immediately at thebottom of the page, not at the end of the chapter, providing readerwith great comfort.

The first edition of Geostatistics: Modeling Spatial Uncertainty

appeared in 1999, and in reviewing it in Computers & Geosciences,2001, vol. 27, pp. 121–123, L. Zheng wrote, ‘y it covers a widerange of theoretical and technical issues involved in modelingspatial uncertainty and performing geostatistical analyses. Itsmajor features include its comprehensive scope, the rich contentand full details, the clear presentation, and a good balancebetween theory and application. Although this book may not bea good choice for beginners, it is no doubt a must-read for anyonewho wants to gain a comprehensive view and an insightfulunderstanding of this specialized discipline’. I strongly agreeand during the review process, I have used it as a reference formy research and gained some interesting research ideas.

The book begins with an introductory chapter defining types ofproblems considered in each chapter and presenting a strikingexample demonstrating that geostatistical methods are ratherdescriptive. Chapter 1 defines basic mathematical, statistical andphilosophical properties of random functions that are usefulmodels for regionalized variables. These are needed for thesubsequent chapters. In particular, shaking jar example illustrat-ing a notion of random functions is very instructive and memor-able. Throughout the book it is easy to find such kind ofinteresting examples. Chapter 2, one of the most voluminouschapters, is devoted to structural analysis of a regionalizedvariable. The variogram is the fundamental tool. To characterize

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the spatial variability the authors introduce exploratory dataanalysis tools such as the h-scattergram, the variogram cloudand the sample variogram. The chapter proceeds with theoreticaland practical details of a variogram analysis, including variogrammodels, model fitting, variography in the presence of a drift. Inthis chapter we see addition of new material such as spatialdeclustering, non-Euclidean coordinate system and removal of asimple example of variography in the presence of a drift. I feelmyself oriented towards practice and found the removal of theintroductory example incorrect. Chapter 3 deals with linearkriging. Types of kriging that are covered include simple kriging,ordinary kriging, universal kriging and kriging with external drift.The topics with little of interest such as kriging of a spatialaverage and kriging under inequality constraints are also treatedexplicitly and in detail. Beside the theoretical issues the practicalapplication of geostatistics to the design of the channel tunnel isextensively discussed. This edition contains a more completetreatment of ordinary kriging and a number of additions such asthree elegant solutions to problem of neighborhood selection inkriging, a new truncation model in the presence of outliers and anew form of kriging, Poisson kriging.

Kriging can be extended to broader forms of nonstationaritythan the Universal Kriging model. Chapter 4 deals with thisextension, namely intrinsic model of order k (IM-k). In keepingwith their background in the Center for Geostatistics at Fontaine-bleau, the authors devote to considerable space to IM-k. Illumi-nating examples of processes with apparent drift but no geneticdrift are provided to explain the motivation behind the concept ofgeneralized increment of order k. Two forms of intrinsic randomfunctions of order k are defined. Generalized covariance andvariogram functions and estimation in the IM-k model are studiedextensively. Chapter 5 covers multivariate extension of kriging,referred to as cokriging. The general principles for usual variantsof cokriging are given together with simplifications, includingproportional covariance model and collocated cokriging. Estima-tion of derivatives that finds interesting applications in the fieldssuch as geology, petroleum and meteorology are addressed aswell as potential field interpolation which is used in building a 3Dmodel of geological interfaces. Thereafter multivariate randomfunctions are presented in usual form with cross-covariances,cross-variograms, linear model of coregionalization and factorialkriging but pseudo cross covariance/variogram is missed. Thechapter ends up with space-time models which certainly deservea separate book. Chapter 6 addresses the estimation of nonlinearfunctional of a variable, in particular the determination ofcumulative distribution function. The issues are first presentedat global scale and then at local scale. There are basically twoapproaches to estimation of conditional distributions: data-based(e.g., indicator kriging) and model-based (e.g., disjunctive kriging)methods. The authors rather focus on the latter with specialemphasis on isofactorial models. For the objective of going fromthe point support to the larger support, they present numerous

Book Review / Computers & Geosciences 54 (2013) 97–9898

change of support models but miss a recent development, Covar-iance Matching Constrained Kriging suggested by Aldworth andCressie (2003), which is an optimal linear predictor that matchesnot only first moments but second moments (including covar-iances) as well.

The last chapter, approximately one quarter of the book, is onconditional simulation. It starts with an introductory exampleillustrating the need for conditional simulation. The authorsclassify simulation methods into three categories: continuousvariable simulation, categorical variable simulation and object-based simulation and for each category present a variety ofmethods. Continuous variable simulation includes sequentialsimulation, covariance matrix decomposition and probability-field simulation. This section also covers various methods ofnonconditional simulation. Categorical variable simulation han-dles with sequential indicator simulation, iterative methods basedon Markov chains and truncated Gaussian simulation. Object-based simulation contains Boolean models. The authors go beyondstandard conditioning and deal with multipoint simulation, simu-lated annealing, gradual deformation and Bayesian approach aswell. The chapter concludes with two case studies, one from anickel deposit, and other from an oil reservoir. An Appendix (13p.)contains some classic definitions and results used in the book, aswell as simulation formulas for a few covariance models. The bookconcludes with author and subject indexes (57p.).

The book includes few exercises and in addition the authorsmake few references to software tools that one might apply thetheory to actual data sets. On the other hand it is well written,clearly organized, and generally free of typos and other errors.Summarizing, Chil�es and Delfiner’s book certainly deservesrecommendation to anyone who is interested in geostatistics,either as a geostatistician or as a researcher in modeling spatialuncertainty.

References

Aldworth, J., Cressie, N., 2003. Prediction of nonlinear spatial functionals. Journalof Statistical Planning and Inference 112, 3–41.

Hengl, T., Minasny, B., Gould, M., 2009. A geostatistical analysis of geostatistics.Scientometrics 80 (2), 491–514.

A.Erhan Tercan n

Department of Mining Engineering, Hacettepe University,

06800 Beytepe, Ankara, Turkey

E-mail address: erhan@hacettepe.edu.tr

Received 8 November 2012

n Tel.: þ90 3122977677.