Introduction to Geo statistics By Ye Zhang

Introduction to Geo statistics  By  Ye Zhang
Series: Geostatistics
Publisher: Dept. of Geology & Geophysics University of Wyoming
Publication Year: 2011
About the Book

Contents i
0.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1 Overview 1

2 Probability Theory Review 15
ii CONTENTS
3 Spatial Analysis 33
3.1 Conventional Analysis (Nongeostatistical) . . . . . . . . . . . . . 33
3.1.1 Data Posting . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.2 Contour Map . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.3 Symbol Map . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.4 Indicator Map . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.5 Moving Window . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Spatial Continuity Analysis (Geostatistical) . . . . . . . . . . . . 37
3.2.1 Experimental Variogram . . . . . . . . . . . . . . . . . . . 39
3.2.2 h-Scatterplot . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Variogram versus Univariate Statistics . . . . . . . . . . . 44
3.2.4 Higher Dimensions & Statistical Anisotropy . . . . . . . . 46
3.2.5 Pure Nugget Variogram . . . . . . . . . . . . . . . . . . . 51
3.2.6 Standard Deviation of ˆγ(h) . . . . . . . . . . . . . . . . . 56
3.2.7 Irregular Data: Variogram Search Envelope . . . . . . . . 57
3.2.8 Exploring Anisotropy . . . . . . . . . . . . . . . . . . . . 60
3.2.9 Spatial Continuity Analysis: Outline . . . . . . . . . . . . 65
3.2.10 Issues… . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3 Chapter Project . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Suggested Reading . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 Variogram Modeling 75
4.1 Basic Permissible Models . . . . . . . . . . . . . . . . . . . . . . 75
4.1.1 Positive Definiteness . . . . . . . . . . . . . . . . . . . . . 75
4.1.2 Basic Variogram Functions . . . . . . . . . . . . . . . . . 77
4.1.3 1D Variogram Model—Statistical Isotropy . . . . . . . . . 81
4.1.4 Higher Dimensional Model—Statistical Anisotropy . . . . 81
4.1.5 Nested Model . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2 Model-Fitting “Rules of Thumb” . . . . . . . . . . . . . . . . . . 83
4.3 Chapter Project . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4 Suggested Reading . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 Estimation 91
5.1 The Problem of Estimation . . . . . . . . . . . . . . . . . . . . . 91
5.2 Nongeostatistical (Deterministic) Estimation . . . . . . . . . . . 95
5.2.1 Global Estimation . . . . . . . . . . . . . . . . . . . . . . 95
5.2.2 Local Estimation . . . . . . . . . . . . . . . . . . . . . . . 96
5.3 Estimation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4 Geostatistical (Probabilistic) Estimation . . . . . . . . . . . . . . 98
5.4.1 Random Function Models . . . . . . . . . . . . . . . . . . 99
5.4.2 Ordinary Kriging . . . . . . . . . . . . . . . . . . . . . . . 101
5.4.3 Cokriging & Collocated Cokriging . . . . . . . . . . . . . 112
5.4.4 Kriging with moving neighborhood . . . . . . . . . . . . . 116
5.5 Chapter Project . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.6 Suggested Reading . . . . . . . . . . . . . . . . . . . . . . . . . . 119
CONTENTS iii
6 Advanced Topics 121
6.1 Cross Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 Other Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2.1 Simple Kriging . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2.2 Indicator Kriging . . . . . . . . . . . . . . . . . . . . . . . 124
6.2.3 Block Kriging . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.3 Geostatistical Simulation . . . . . . . . . . . . . . . . . . . . . . 127
6.3.1 Cholesky Decomposition . . . . . . . . . . . . . . . . . . . 130
6.3.2 Conditional Simulation . . . . . . . . . . . . . . . . . . . 133
6.3.3 Sequential Gaussian Simulation (SGS) . . . . . . . . . . . 136
6.4 Chapter Project . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.5 Suggested Reading . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7 Final Project 143
7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 What to hand in . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.3 Additional notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8 Geostatistics Final Exam 149

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