Solved Problems in Geostatistics E-Book

Oy Leuangthong

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 252

Veröffentlichungsjahr: 2011

Beschreibung

This unique book presents a learn-by-doing introduction to geostatistics. Geostatistics provides the essential numerical tools for addressing research problems that are encountered in fields of study such as geology, engineering, and the earth sciences. Illustrating key methods through both theoretical and practical exercises, Solved Problems in Geostatistics is a valuable and well-organized collection of worked-out problems that allow the reader to master the statistical techniques for modeling data in the geological sciences. The book's scope of coverage begins with the elements from statistics and probability that form the foundation of most geostatistical methodologies, such as declustering, debiasing methods, and Monte Carlo simulation. Next, the authors delve into three fundamental areas in conventional geostatistics: covariance and variogram functions; kriging; and Gaussian simulation. Finally, special topics are introduced through problems involving utility theory, loss functions, and multiple-point geostatistics. Each topic is treated in the same clearly organized format. First, an objective presents the main concepts that will be established in the section. Next, the background and assumptions are outlined, supplying the comprehensive foundation that is necessary to begin work on the problem. A solution plan demonstrates the steps and considerations that have to be taken when working with the exercise, and the solution allows the reader to check their work. Finally, a remarks section highlights the overarching principles and noteworthy aspects of the problem. Additional exercises are available via a related Web site, which also includes data related to the book problems and software programs that facilitate their resolution. Enforcing a truly hands-on approach to the topic, Solved Problems in Geostatistics is an indispensable supplement for courses on geostatistics and spatial statistics a the upper-undergraduate and graduate levels.It also serves as an applied reference for practicing professionals in the geosciences.

Leseprobe

CONTENTS

Preface and Acknowledgments

CHAPTER 1 Introduction

1.1 Plan of this Book

1.2 The Premise of Geostatistics

1.3 Nomenclature

CHAPTER 2 Getting Comfortable with Probabilities

2.1 Parametric Probability Distributions

2.2 Variance of Linear Combinations

2.3 Standardization and Probability Intervals

CHAPTER 3 Obtaining Representative Distributions

3.1 Basic Declustering

3.2 Debiasing with Bivariate Gaussian Distribution

3.3 Comparison of Declustering Methods

CHAPTER 4 Monte Carlo Simulation

4.1 Impact of the Central Limit Theorem

4.2 Bootstrap and Spatial Bootstrap

4.3 Transfer of Uncertainty

CHAPTER 5 Variograms and Volume Variance

5.1 Geometric Anisotropy

5.2 Variogram Calculation

5.3 Variogram Modeling and Volume Variance

CHAPTER 6 Kriging

6.1 Stationary Kriging

6.2 Nonstationary Kriging

6.3 Screening Effect of Kriging

CHAPTER 7 Gaussian Simulation

7.1 Bivariate Gaussian Distribution

7.2 Conditioning by Kriging

7.3 Gaussian Simulation

CHAPTER 8 Indicators

8.1 Variogram of Objects

8.2 Indicator Variograms and the Gaussian Distribution

8.3 Indicator Simulation for Categorical Data

CHAPTER 9 Multiple Variables

9.1 Linear Model of Coregionalization

9.2 Gaussian Cosimulation

9.3 Multiscale Cokriging

CHAPTER 10 Special Topics

10.1 Decision Making in the Presence of Uncertainty

10.2 Trend Model Construction

10.3 Multiple Point Statistics

CHAPTER 11 Closing Remarks

Bibliography

Index

Copyright © 2008 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Leuangthong, Oy, 1974–Solved problems in geostatistics / Oy Leuangthong, Daniel Khan, Clayton V. Deutsch.p. cm.Includes bibliographical references and index.ISBN 978-0-470-17792-1 (pbk.)1. Geology—Statistical methods—Problems, exercises, etc. 2. Geology—Data processing—Problems, exercises, etc. I. Khan, K. Daniel, 1972– II. Deutsch, Clayton V. III. Title.QE33.2.582L48 2008550.72--dc222008007625

PREFACE AND ACKNOWLEDGMENTS

Reliable application of geostatistics for modeling regionalized variables requires knowledge about geostatistics and a lot of practice. There are many styles of learning, but a common thread is that people learn by working through problems. This book provides a set of problems that outline the central themes of geostatistics with worked solutions. Our hope is that this collection of problems will help students gain familiarity with the overarching principles, the common applications, and some of the intricate details of this rich subject.

The authors wish to acknowledge the teachers and researchers who have contributed to the growth and evolution of geostatistics. Some of these problems are derivatives of André Journel’s from back in the 1980s.

Oy would like to thank Shawn for always being so supportive in this and all other endeavours. She would also like to thank her son Brayden who, although too young to realize, provides the motivation to be efficient. Together they help provide a happy and balanced life.

Dan would like to acknowledge the selfless support of Joanna throughout his early career endeavors; the years add up quickly. Thanks also to his children Sofia, Aaron, and Sarah, who endured his absence during working hours.

Clayton would like to acknowledge Pauline for her enduring support for more than 20 years of geostatistical adventure. Jared read through most chapters and had some good input. Matthew and Rebecca complete the family. Clayton thanks them all.

CHAPTER 1

Introduction

Geostatistics has become increasingly popular for numerical modeling and uncertainty assessment in the earth sciences. The beginnings of geostatistics can be traced to innovation in the mining industry in the late 1950s and early 1960s. Application of geostatistics has expanded into other industries including reservoir characterization, meteorology, environmental, hydrogeology, and agriculture. The common features of problems addressed by geostatistics include variables regionalized in space, sparse data, and nonrandom patterns of heterogeneity.

The number of geostatistical theoreticians and practitioners is growing. A reasonable number of courses, books, and papers are available that document the techniques and principles of geostatistics. These include Armstrong (1998), Chilès and Delfiner (1999), Christakos (1992), Clark and Harper (2000), Cressie (1991), David (1977), Davis (1986), Deutsch (2002), Goovaerts (1997), Hohn (1988), Isaaks and Srivastava (1989), Journel (1989), Journel and Huijbregts (1978), Mallet (2002), Matern (1960), Matheron (1969, 1971), Yarns (1995), and Wackernagel (2003). Despite the resources available to the student of geostatistics, the discipline of geostatistics is relatively small and fast growing. There is no comprehensive textbook that explains theory, practice, and provides solved problems to guide the student through the learning process. This book provides a tour through important problems in geostatistics.

This book is aimed at a student of geostatistics. We are all students; some are just more formally recognized as such: senior undergraduate students and graduate students. Senior practicing geostatisticians interested in understanding the theoretical principles would be less formally recognized students. Young professionals who recently graduated in the geosciences or earth science related engineering are a special target of this book. Unfortunately, many universities have no requirement for classes in numerical geological modeling with geostatistics. The young professional faced with the task of geostatistical modeling without a formal class in the subject, needs a few key references. This book is one of those references.