This text provides an advanced introduction to the theory and applications of geostatistics, including tools for description, modeling spatial continuity, spatial prediction, assessment of local uncertainty, and stochastic simulation.

The papers in this volume provide a comprehensive account of the current methods and work in geostatistics, including recent theoretical developments and applications. Topics featured include: stochastic simulations, space-time modelling, and Bayesian framework.

These proceedings of the IAMG 2014 conference in New Delhi explore the current state of the art and inform readers about the latest geostatistical and space-based technologies for assessment and management in the contexts of natural resource exploration, environmental pollution, hazards and natural disaster research. The proceedings cover 3D visualization, time-series analysis, environmental geochemistry, numerical solutions in hydrology and hydrogeology, geotechnical engineering, multivariate geostatistics, disaster management, fractal modeling, petroleum exploration, geoinformatics, sedimentary basin analysis, spatiotemporal modeling, digital rock geophysics, advanced mining assessment and glacial studies, and range from the laboratory to integrated field studies. Mathematics plays a key part in the crust, mantle, oceans and atmosphere, creating climates that cause natural disasters, and influencing fundamental aspects of life-supporting systems and many other geological processes affecting Planet Earth. As such, it is essential to understand the synergy between the classical geosciences and mathematics, which can provide the methodological tools needed to tackle complex problems in modern geosciences. The development of science and technology, transforming from a descriptive stage to a more quantitative stage, involves qualitative interpretations such as conceptual models that are complemented by quantification, e.g. numerical models, fast dynamic geologic models, deterministic and stochastic models. Due to the increasing complexity of the problems faced by today’s geoscientists, joint efforts to establish new conceptual and numerical models and develop new paradigms are called for.

Earth science is becoming increasingly quantitative in the digital age. Quantification of geoscience and engineering problems underpins many of the applications of big data and artificial intelligence. This book presents quantitative geosciences in three parts. Part 1 presents data analytics using probability, statistical and machine-learning methods. Part 2 covers reservoir characterization using several geoscience disciplines: including geology, geophysics, petrophysics and geostatistics. Part 3 treats reservoir modeling, resource evaluation and uncertainty analysis using integrated geoscience, engineering and geostatistical methods. As the petroleum industry is heading towards operating oil fields digitally, a multidisciplinary skillset is a must for geoscientists who need to use data analytics to resolve inconsistencies in various sources of data, model reservoir properties, evaluate uncertainties, and quantify risk for decision making. This book intends to serve as a bridge for advancing the multidisciplinary integration for digital fields. The goal is to move beyond using quantitative methods individually to an integrated descriptive-quantitative analysis. In big data, everything tells us something, but nothing tells us everything. This book emphasizes the integrated, multidisciplinary solutions for practical problems in resource evaluation and field development.

ACKNOWLEDGEMENTS xvii LIST OF PARTICIPANTS xix PLENARY SESSIQNS KRIGE D.G., GUARASCIO M. and CAMISANI-CALZOLARI F.A. Early South African qeostatistical techniques in today's perspective ... 1 MATHERON G. The internal consistency of models in qeostatistics ... 21 MONESTIEZ P., HABIB R. and AUDERGON J.M. Estimation de la covariance et du varioqramme pour une fonction aleatoire a support arborescent : application a l'etude des arbres fruitiers ... 39 CHILES J.P. Modelisation qeostatistique de reseaux de fractures ... 57 BRUNO R. and RASPA G. Geostatistical characterization of fractal models of surfaces 17 RIVOIRARD J. Models with orthoqonal indicator residuals ... 91 OMRE H., HALVORSEN K.B. and BERTEIG V.A Bayesian approach to kriqinq ... 109 THEQRY I SWITZER P. Non-stationary spatial covariances estimated from monitorinq data ... 127 CHAUVET P. Quelques aspects de l'analyse structurale des FAI-k a 1 dimension ... 139 vi TABLE OF CONTENTS DOWD P.A. Generalised cross-covariances ... 151 CRESSIE N. The many faces of spatial prediction ..-- ... - ... --.-.-..-. 163 OBLED C. & BRAUD I. Analogies entre geostatistique et analyse en composantes principales de processus ou analyse EOFs ... 177 THEORY II JEULIN D. Sequential random functions models ... 189 CHAUTRU J.M. The use of Boolean random functions in geostatistics -.--.-- ... 201 SOARES A.O. Use of a mathematical morphology tool in characterizing covariance & of indicator data ... 213 ALLISON H.J. Regularization in geostatistics and in ill-posed inversed problems ... - . . - . - . . - ... - - ... 225 DONG A.