Christakos Random Field Models in Earth Sciences

1. Auflage 2013
ISBN: 978-1-4832-8830-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 474 Seiten, Web PDF

This book is about modeling as a prinicipal component of scientific investigations. In general terms, modeling is the funamental process of combining intellectual creativity with physical knowledge and mathematical techniques in order to learn the properties of the mechanisms underlying a physical phenomenon and make predictions. The book focuses on a specific class of models, namely, random field models and certain of their physical applications in the context of a stochastic data analysis and processing research program. The term application is considered here in the sense wherein the mathematical random field model is shaping, but is also being shaped by, its objects.This book explores the application of random field models and stochastic data processing to problems in hydrogeology, geostatistics, climate modeling, and oil reservoir engineering, among others Researchers in the geosciences who work with models of natural processes will find discussion of; - Spatiotemporal random fields - Space transformation - Multidimensional estimation - Simulation - Sampling design - Stochastic partial differential equations

George Christakos is a Professor in the Department of Geography at San Diego State University (USA) and in the Institute of Island & Coastal Ecosystems, Ocean College at Zhejiang University (China). He is an expert in spatiotemporal random field modeling of natural systems, and his teaching and research focus on the integrative analysis of natural phenomena; spatiotemporal random field theory; uncertainty assessment; pollution monitoring and control; human exposure risk and environmental health; space-time statistics and geostatistics.

Autoren/Hrsg.

Christakos, George

Inhaltsverzeichnis

1;Front Cover;1
2;Random Field Models in Earth Sciences;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Foreword;18
7;Preface;22
8;Chapter 1. Prolegomena;30
8.1;1. The Science of the Probable and the Random Field Model;30
8.2;2. The Physical Significance of the Random Field Model;35
8.3;3. The Mathematics of Random Fields;40
8.4;4. The Philosophical Theses of the Stochastic Research Program;42
8.5;5. The Practice of the Stochastic Research Program and the Spectrum of Its Applications;45
9;Chapter 2. The Spatial Random Field Model;50
9.1;1. Introduction;50
9.2;2. Basic Notions;51
9.3;3. Characterization of Spatial Random Fields by Means of Their Second-Order Statistical Moments—Correlation Theory;60
9.4;4. Certain Geometrical Properties of Spatial Random Fields;69
9.5;5. Spectral Characteristics of Spatial Random Fields;78
9.6;6. Auxiliary Hypotheses;84
9.7;7. Homogeneous Spatial Random Fields;86
9.8;8. Isotropic Spatial Random Fields;98
9.9;9. Scales of Spatial Correlation;105
9.10;10. Relationships between the Spatial and the Frequency Domains—The Uncertainty Principle;105
9.11;11. Spatial Random Fields with Homogeneous Increments;107
9.12;12. On the Ergodicity Hypotheses of Spatial Random Fields;127
9.13;13. Information and Entropy of Spatial Random Fields;132
10;Chapter 3. The Intrinsic Spatial Random Field Model;136
10.1;1. Introduction;136
10.2;2. Generalized Spatial Random Fields;137
10.3;3. Spatial Random Fields with Space Homogeneous Increments or Intrinsic Spatial Random Fields;144
10.4;4. Discrete Linear Representations of Spatial Random Fields;164
10.5;5. Stochastic Differential and Difference Equations;175
11;Chapter 4. The Factorable Random Field Model;182
11.1;1. Introduction;182
11.2;2. The Theory of Factorable Random Fields;183
11.3;3. Nonlinear Transformations of Factorable Random Fields;189
11.4;4. Construction of Factorable Random Fields;190
11.5;5. The Nonlinear State-Nonlinear Observation System;194
12;Chapter 5. The Spatiotemporal Random Field Model;197
12.1;1. Introduction;197
12.2;2. Spatiotemporal Natural Processes—A Review;198
12.3;3. Ordinary Spatiotemporal Random Fields;204
12.4;4. Generalized Spatiotemporal Random Fields;216
12.5;5. Spatiotemporal Random Fields of Order v/µ (Ordinary and Generalized);225
12.6;6. Stochastic Partial Differential Equations;235
12.7;7. Discrete Linear Representations of Spatiotemporal Random Fields;238
13;Chapter 6. Space Transformations of Random Fields;244
13.1;1. Introduction;244
13.2;2. Space Transformations;245
13.3;3. Space Transformation Representations of Spatial Random Fields;252
13.4;4. Stochastic Differential Equation Models;255
13.5;5. Criteria of Permissibility;265
14;Chapter 7. Random Field Modeling of Natural Processes;267
14.1;1. Introduction;267
14.2;2. Descriptive Features of Natural Processes and the Basic Working Hypotheses;269
14.3;3. Duality Relations between the Natural Process and the Spatial Random Field Model—Examples from the Geosciences;274
14.4;4. Certain Practical Aspects of Spatial and Temporal Variability Characterization;284
14.5;5. Qualitative (Soft) Information;304
14.6;6. Some Final Comments about the Stochastic Research Program;321
15;Chapter 8. Simulation of Natural Processes;323
15.1;1. Introduction;323
15.2;2. The Physical Significance of Simulation;324
15.3;3. Simulation of Random Fields;328
15.4;4. Simulation of Spatial Random Field by Space Transformations—Examples;331
15.5;5. Techniques of One-Dimensional Simulation;345
15.6;6. Simulation of Integrated Natural Processes;350
15.7;7. Simulation of Dynamic Stochastic Systems;351
15.8;8. The Effect of Measurement Error;353
15.9;9. Simulation of Spatial Random Fields by Means of Frequency Domain Techniques;354
15.10;10. The Lower-Upper Triangular Matrix Technique;355
15.11;11. The Karhunen-Loeve Expansion Technique;357
15.12;12. Simulation of Vector Spatial Random Fields;358
15.13;13. Simulation of Non-Gaussian Spatial Random Fields;361
15.14;14. Simulation in Space-Time;364
16;Chapter 9. Estimation in Space and Time;366
16.1;1. Introduction;366
16.2;2. A Brief Review of Nonstochastic Estimators and the Emergence of Stochastic Estimation;368
16.3;3. Optimum Stochastic Spatial Estimation;370
16.4;4. Certain Classes of Linear Spatial Estimators;375
16.5;5. Properties and Physical Interpretations of Linear Spatial Estimators;386
16.6;6. Nonlinear Estimation;399
16.7;7. Optimal Estimation of Spatiotemporal Random Fields;408
16.8;8. A Bayesian/Maximum-Entropy View of the Estimation Problem;415
17;Chapter 10. Sampling Design;430
17.1;1. Introduction;430
17.2;2. About Sampling;432
17.3;3. Simple Global Approaches to Sampling Design;444
17.4;4. Optimal Linear Estimation Approaches to Global Sampling Design;448
17.5;5. Local Sampling Design Approaches;462
17.6;6. Statistical Inference Problems in Sampling Design;466
17.7;7. The Design of Spatiotemporal Sampling Networks;467
17.8;8. A Taxonomy of Site Exploration Tasks;468
17.9;9. Terminal Decision Analysis and Sampling Design;469
18;References;476
19;Index;488