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This book provides a comprehensive introduction to multiple-point geostatistics, where spatial continuity is described using training images. Multiple-point geostatistics aims at bridging the gap between physical modelling/realism and spatio-temporal stochastic modelling. The book provides an overview of this new field in three parts. Part I presents a conceptual comparison between traditional random function theory and stochastic modelling based on training images, where random function theory is not always used. Part II covers in detail various algorithms and methodologies starting from basic building blocks in statistical science and computer science. Concepts such as non-stationary and multi-variate modeling, consistency between data and model, the construction of training images and inverse modelling are treated. Part III covers three example application areas, namely, reservoir modelling, mineral resources modelling and climate model downscaling. This book will be an invaluable reference for students, researchers and practitioners of all areas of the Earth Sciences where forecasting based on spatio-temporal data is performed.



Table of Contents

Preface, vii

Acknowledgments, xi

Part I Concepts

I.1 Hiking in the Sierra Nevada, 3

I.2 Spatial estimation based on random function theory, 7

I.3 Universal kriging with training images, 29

I.4 Stochastic simulations based on random function theory, 49

I.5 Stochastic simulation without random function theory, 59

I.6 Returning to the Sierra Nevada, 75

Part II Methods

II.1 Introduction, 87

II.2 The algorithmic building blocks, 91

II.3 Multiple-point geostatistics algorithms, 155

II.4 Markov random fields, 173

II.5 Nonstationary modeling with training images, 183

II.6 Multivariate modeling with training images, 199

II.7 Training image construction, 221

II.8 Validation and quality control, 239

II.9 Inverse modeling with training images, 259

II.10 Parallelization, 295

Part III Applications

III.1 Reservoir forecasting - the West Coast of Africa (WCA) reservoir, 303

III.2 Geological resources modeling in mining, 329

Coauthored by Cristian P´erez, Julian M. Ortiz, & Alexandre Boucher

III.3 Climate modeling application - the case of the Murray-Darling

Basin, 345

Index, 361