Statistics and Computing

1 Introduction.- 1.1 Overview.- 1.2 History.- 1.3 Warning : This Is a Methodological User's Guide.- 1.4 Notation Used Within This User's Guide.- 1.5 Minimum Requirements.- 1.6 Content of the Release.- 1.7 Installation Procedure.- 1.7.1 Note to Windows 95 Users.- 1.7.2 Note to Windows NT Users.- 1.8 Uninstallation Procedure.- Acknowledgments.- References.- 2 Quick Start.- 2.1 Prevar2D - Construction of a Pair Comparison File.- 2.2 Vario2D with PCF - Exploratory Variography.- 2.3 Model - Interactive Variogram Modeling.- 2.4 Grid Display - Displaying Grid Files as Pixel Maps.- 3 Construction of a Pair Comparison File (PCF) with Prevar2D.- 3.1 Overview.- 3.2 What Is a PCF?.- 3.3 Working with a PCF.- 3.3.1 Advantages.- 3.3.2 Problems.- 3.3.3 Overcoming DOS Memory Limitations.- 3.4 Building a PCF from a Subset.- 3.5 What Should Be Done with Duplicate Data Points?.- Further Reading.- 4 Vario2D with PCF - A Program for Interactive Exploratory Variography.- 4.1 Overview.- 4.2 Working with Subsets.- 4.3 H-Scatterplots and Cross H-Scatterplots.- 4.3.1 Working with H-Scatterplots.- 4.4 Variogram Surface and Cross Variogram Surface.- 4.5 Directional Variogram and Directional Cross Variogram.- 4.6 Variogram Cloud and Cross Variogram Cloud.- 4.7 Measures of Spatial Continuity Available Within Vario2D with PCF.- 4.7.1 Variogram and Cross Variogram.- 4.7.2 Standardized Variogram and Standardized Cross Variogram.- 4.7.3 Covariance and Cross Covariance.- 4.7.4 Correlogram and Cross Correlogram.- 4.7.5 Madogram and Cross Madogram.- Further Reading.- 5 Model - Interactive Variogram Modeling.- 5.1 Overview.- 5.2 Variogram Models.- 5.2.1 Nugget Effect Model.- 5.2.2 Spherical Model.- 5.2.3 Exponential Model.- 5.2.4 Gaussian Model.- 5.2.5 Power Model.- 5.3 Interactive Construction of a 2D Nested Model.- 5.3.1 The Modeling Window.- 5.3.2 Modeling a Nested Structure.- 5.3.3 Indicative Goodness of Fit (IGF).- 5.3.4 The Plot Window.- 5.4 The Linear Model of Coregionalization.- Further Reading.- 6 Files Used Within VARIOWIN 2.2.- 6.1 Data Files (.DAT).- 6.2 Pair Comparison Files (.PCF).- 6.3 Grid Files (.GRD).- 6.4 Variogram Surface Files (.VS).- 6.5 Variogram Files (.VAR).- 6.6 Variogram Cloud Files (.CLD).- 6.7 Model Files (.MOD).- Further Reading.- Appendix A Geostatistical Concepts.- A.1 Random Variables, Regionalized Variables, and Random Functions.- A.2 Moments Considered in Linear Geostatistics.- A.2.1 First-Order Moment - Mathematical Expectation.- A.2.2 Second-Order Moments.- A.3 Ergodicity.- A.4 Hypothesis of Stationarity.- A.4.1 Strict Stationarity.- A.4.2 Second-Order Stationarity.- A.4.3 Intrinsic Hypothesis.- A.5 Why Do We Need to Model Variograms?.- A.6 The Multivariate Gaussian Random Function.- Further Reading.