Applied geostatistics with SGeMS : a user's guide

The Stanford Geostatistical Modeling Software (SGeMS) is an open-source computer package for solving problems involving spatially related variables. It provides geostatistics practitioners with a user-friendly interface, an interactive 3-D visualization, and a wide selection of algorithms. This practical book provides a step-by-step guide to using SGeMS algorithms. It explains the underlying theory, demonstrates their implementation, discusses their potential limitations, and helps the user make an informed decision about the choice of one algorithm over another. Users can complete complex tasks using the embedded scripting language, and new algorithms can be developed and integrated through the SGeMS plug-in mechanism. SGeMS was the first software to provide algorithms for multiple-point statistics, and the book presents a discussion of the corresponding theory and applications. Incorporating the full SGeMS software (now available from www.cambridge.org/9781107403246), this book is a useful user-guide for Earth Science graduates and researchers, as well as practitioners of environmental mining and petroleum engineering.

Albert Tarantola

Foreword	p. ix
Preface	p. xi
List of programs	p. xiii
List of symbols	p. xv
1 Introduction	p. 1
2 General overview	p. 5
2.1 A quick tour of the graphical user interface	p. 5
2.2 A typical geostatistical analysis using SGeMS	p. 5
2.2.1 Loading data into an SGeMS project	p. 8
2.2.2 Exploratory data analysis (EDA)	p. 10
2.2.3 Variogram modeling	p. 10
2.2.4 Creating a grid	p. 12
2.2.5 Running a geostatistics algorithm	p. 13
2.2.6 Displaying the results	p. 14
2.2.7 Post-Processing the results with Python	p. 19
2.2.8 Saving the results	p. 21
2.2.9 Automating tasks	p. 21
2.3 Data file formats	p. 23
2.4 Parameter files	p. 24
2.5 Defining a 3D ellipsoid	p. 26
3 Geostatistics: a recall of concepts	p. 29
3.1 Random variable	p. 30
3.2 Random function	p. 33
3.2.1 Simulated realizations	p. 34
3.2.2 Estimated maps	p. 37
3.3 Conditional distributions and simulations	p. 38
3.3.1 Sequential simulation	p. 40
3.3.2 Estimating the local conditional distributions	p. 42
3.4 Inference and stationarity	p. 44
3.5 The variogram, a 2-point statistics	p. 48
3.6 The kriging paradigm	p. 50
3.6.1 Simple kriging	p. 51
3.6.2 Ordinary kriging and other variants	p. 54
3.6.3 Kriging with linear average variable	p. 57
3.6.4 Cokriging	p. 59
3.6.5 Indicator kriging	p. 61
3.7 An introduction to mp statistics	p. 62
3.8 Two-point simulation algorithms	p. 65
3.8.1 Sequential Gaussian simulation	p. 66
3.8.2 Direct sequential simulation	p. 67
3.8.3 Direct error simulation	p. 68
3.8.4 Indicator simulation	p. 69
3.9 Multiple-point simulation algorithms	p. 71
3.9.1 Single normal equation simulation (SNESIM)	p. 71
3.9.2 Filter-based algorithm (FILTERSIM)	p. 72
3.10 The nu/tau expression for combining conditional probabilities	p. 74
3.11 Inverse problem	p. 79
4 Data sets and SGeMS EDA tools	p. 80
4.1 The data sets	p. 80
4.1.1 The 2D data set	p. 80
4.1.2 The 3D data set	p. 81
4.2 The SGeMS EDA tools	p. 84
4.2.1 Common parameters	p. 85
4.2.2 Histogram	p. 85
4.2.3 Q-Q plot and P-P plot	p. 87
4.2.4 Scatter plot	p. 87
5 Variogram computation and modeling	p. 90
5.1 Variogram computation in SGeMS	p. 92
5.1.1 Selecting the head and tail properties	p. 92
5.1.2 Computation parameters	p. 93
5.1.3 Displaying the computed variograms	p. 98
5.2 Variogram modeling in SGeMS	p. 98
6 Common parameter input interfaces	p. 101
6.1 Algorithm panel	p. 101
6.2 Selecting a grid and property	p. 102
6.3 Selecting multiple properties	p. 103
6.4 Search neighborhood	p. 104
6.5 Variogram	p. 104
6.6 Kriging	p. 105
6.7 Line entry	p. 105
6.8 Non-parametric distribution	p. 106
6.9 Errors in parameters	p. 108
7 Estimation algorithms	p. 109
7.1 KRIGING: univariate kriging	p. 109
7.2 INDICATOR KRIGING	p. 113
7.3 COKRIGING: kriging with secondary data	p. 119
7.4 BKRIG: block kriging estimation	p. 122
8 Stochastic simulation algorithms	p. 132
8.1 Variogram-based simulations	p. 132
8.1.1 LUSIM: LU simulation	p. 133
8.1.2 SGSIM: sequential Gaussian simulation	p. 135
8.1.3 COSGSIM: sequential Gaussian CO-simulation	p. 139
8.1.4 DSSIM: direct sequential simulation	p. 143
8.1.5 SISIM: sequential indicator simulation	p. 147
8.1.6 COSISIM: sequential indicator co-simulation	p. 153
8.1.7 BSSIM: block sequential simulation	p. 157
8.1.8 BESIM: block error simulation	p. 163
8.2 Multiple-point simulation algorithms	p. 168
8.2.1 SNESIM: single normal equation simulation	p. 169
8.2.2 FILTERSIM: filter-based simulation	p. 191
9 Utilities	p. 215
9.1 TRANS: histogram transformation	p. 215
9.2 TRANSCAT: categorical transformation	p. 218
9.3 POSTKRIGING: post-processing of kriging estimates	p. 222
9.4 POSTSIM: post-processing of realizations	p. 224
9.5 NU-TAU MODEL: combining probability fields	p. 227
9.6 BCOVAR: block covariance calculation	p. 228
9.7 IMAGE PROCESSING	p. 233
9.8 MOVING WINDOW: moving window statistics	p. 234
9.9 TIGENERATOR: object-based image generator	p. 237
9.9.1 Object interaction	p. 239
10 Scripting, commands and plug-ins	p. 245
10.1 Commands	p. 245
10.1.1 Command lists	p. 246
10.1.2 Execute command file	p. 248
10.2 Python script	p. 249
10.2.1 SGeMS Python modules	p. 250
10.2.2 Running Python scripts	p. 250
10.3 Plug-ins	p. 252
Bibliography	p. 254
Index	p. 260

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