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This book deals with the estimation of natural ressources using a Monte Carlo methodology. It includes a set of tools to describe the morphological, statistical and stereological properties of spatial random models. Furthermore the author presents a wide range of spatial models, including random sets and functions, point processes and object populations applicable to the geosciences. This book results from a series of courses given in the USA and Latin America to civil, mining and petroleum engineers as well as graduate students in statistics. It is the first book discussing the geostatistical simulation techniques in such a specific way.
From the contents: The Tools: Investigating stochastic models; Definition of a probability space; Random functions, sets etc; Variographic tools; The covariograms; The covariance function and the variogram; The integral range; Basic morphological concepts; Stereology - Some basic notions.- The Algorithms: Basics about simulations; Uniform distributions; Non-uniform distribution; Iterative algorithms for simulation; Rate of convergence of iterative algorithms; Exact simulations.- The Models: Point processes; Tesselations; Boolean model; Object based models; Gaussian random function; Gaussian variations; Substitution random functions.
From the reviews of the first edition: "Geostatistical simulations have mainly been developed during the last decade. ! this is the first book that is entirely dedicated to this subject. ! it has been a good initiative by C. Lantuejoul to compile this book and it will become a basic reference work, partly because it is the first work dedicated entirely to this new subject of geostatistics. ! The book mainly aims at researchers who are using geostatistical simulations and who would like to know more about the theoretical background ! ." (Andre Vervoort, Geologica Belgica, Vol. 7 (3-4), 2004) "The author has dedicated the book to Georges Matheron, founder of modern geostatistics. Well organized is the book in three parts, namely (i) the tools, (ii) the algorithm and (iii) the models. ! It certainly fills a gap and is therefore welcome to the geostatistics market." (Erik W. Grafarend, Zentralblatt MATH, Vol. 990 (15), 2002)
