GSLIB Geostatistical Software Library and User's Guide

Transcription

1 GSLIB Geostatistical Software Library and User's Guide Second Edition Clayton V. Deutsch Department of Petroleum Engineering Stanford University Andre G. Journel Department of Geological and Environmental Sciences Stanford University New York Oxford OXFORD UNIVERSITY PRESS 1998

2 Contents I Introduction 3 I.I About the Source Code 6 II Getting Started 9 II. 1 Geostatistical Concepts: A Review 9 II.1.1 The Random Function Concept 11 II. 1.2 Inference and Stationarity Variogram Kriging Stochastic Simulation GSLIB Conventions Computer Requirements Data Files Grid Definition Program Execution and Parameter Files Machine Precision Variogram Model Specification A Straightforward 2D Example A 2D Example with Zonal Anisotropy Search Strategies Data Sets Problem Set One: Data Analysis 40 III Variograms Measures of Spatial Variability GSLIB Variogram Programs Regularly Spaced Data gam Irregularly Spaced Data gamv 53 III. 5 Variogram Maps varmap Application Notes Problem Set Two: Variograms 62 vn

3 viii CONTENTS IV Kriging 63 IV.l Kriging with GSLIB 63 IV.1.1 Simple Kriging 64 IV.1.2 Ordinary Kriging 65 IV.1.3 Kriging with a Trend Model 66 IV.1.4 Kriging the Trend 69 IV. 1.5 Kriging with an External Drift 70 IV.1.6 Factorial Kriging 71 IV.1.7 Cokriging 73 IV.1.8 Nonlinear Kriging 75 IV.1.9 Indicator Kriging 76 IV.l.10 Indicator Cokriging 86 IV.1.11 Probability Kriging 87 IV.l.12 Soft Kriging: The Markov-Bayes Model 88 IV.l.13 Block Kriging 92 IV.l.14 Cross Validation 94 IV.2 A Straightforward 2D Kriging Program kb2d 95 IV.3 A Flexible 3D Kriging Program kt3d 96 IV.4 Cokriging Program cokb3d 100 IV.5 Indicator Kriging Program ik3d 103 IV.6 Application Notes 106 IV.7 Problem Set Three: Kriging 108 IV.8 Problem Set Four: Cokriging 115 IV.9 Problem Set Five: Indicator Kriging 116 V Simulation 119 V.I Principles of Stochastic Simulation 119 V.I.I Reproduction of Major Heterogeneities 122 V.1.2 Joint Simulation of Several Variables 123 V.1.3 The Sequential Simulation Approach 125 V.1.4 Error Simulation 127 V.I.5 Questions of Ergodicity 128 V.1.6 Going Beyond a Discrete CDF 134 V.2 Gaussian-Related Algorithms 139 V.2.1 Normal Score Transform 141 V.2.2 Checking for Bivariate Normality. 142 V.2.3 Sequential Gaussian Simulation 144 V.2.4 LU Decomposition Algorithm 146 V.2.5 The Turning Band Algorithm 147 V.2.6 Multiple Truncations of a Gaussian Field, V.3 Indicator-Based Algorithms 149 V.3.1 Simulation of Categorical Variables 151 V.3.2 Simulation of Continuous Variables 152 V.4 p-field Simulation 155 V.5 Boolean Algorithms 156

4 CONTENTS ix V.6 Simulated Annealing 158 V.6.1 Simulation by Simulated Annealing 159 V.6.2 Postprocessing with Simulated Annealing 166 V.6.3 Iterative Simulation Techniques 167 V.7 Gaussian Simulation Programs 169 V.7.1 LU Simulation lusim 169 V.7.2 Sequential Gaussian Simulation sgsim 170 V.7.3 Multiple Truncations of a Gaussian Field gtsim V.8 Sequential Indicator Simulation Programs 175 V.8.1 Indicator Simulation sisim 175 V.8.2 p-field Simulation pf sim 181 V.9 A Boolean Simulation Program ellipsim 182 V. 10 Simulated Annealing Programs 183 V.10.1 Simulated Annealing sasim 183 V.10.2 An Annealing Postprocessor anneal 187 V.ll Application Notes 189 V.12 Problem Set Six: Simulation 191 VI Other Useful Programs 199 VI. 1 PostScript Display 199 VI.1.1 Location Maps locmap 201 VI.1.2 Gray- and Color-Scale Maps pixelplt 202 VI.1.3 Histograms and Statistics histplt 204 VI. 1.4 Normal Probability Plots probplt 206 VI.1.5 Q-Q and P-P plots qpplt 207 VI.1.6 Bivariate Scatterplots and Analysis scatplt 208 VI.1.7 Smoothed Scatterplot Display bivplt 210 VI.1.8 Variogram Plotting vargplt 211 VI.2 Utility Programs 211 VI.2.1 Coordinates addcoord and rotcoord 211 VI.2.2 Cell Declustering declus. 213 VI.2.3 Histogram and Scattergram Smoothing 214 VI.2.4 Random Drawing draw 222 VI.2.5 Normal Score Transformation nscore 223 VI.2.6 Normal Score Back Transformation backtr 226 VI.2.7 General Transformation trans 227 VI.2.8 Variogram Values from a Model vmodel 230 VI.2.9 Gaussian Indicator Variograms bigaus 231 VI.2.10 Library of Linear System Solvers 232 VI.2.11 Bivariate Calibration bicalib 235 VI.2.12 Postprocessing of IK Results postik 236 VI.2.13 Postprocessing of Simulation Results postsim

5 CONTENTS Appendices A Partial Solutions to Problem Sets 241 A.I Problem Set One: Data Analysis 241 A.2 Problem Set Two: Variograms 253 A.3 Problem Set Three: Kriging 266 A.4 Problem Set Four: Cokriging 271 A.5 Problem Set Five: Indicator Kriging 283 A.6 Problem Set Six: Simulations 296 B Software Installation 325 B.I Installation 325 B.2 Troubleshooting 327 C Programming Conventions 329 C.I General 329 C.2 Dictionary of Variable Names 330 C.3 Reference Lists of Parameter Codes 336 D Alphabetical Listing of Programs 339 E List of Acronyms and Notations 341 E.I Acronyms 341 E.2 Common Notation 342 Bibliography 347 Index 363