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About this book

1.1 Overview V ARIOWIN 2.2 is a collection of four Windows™ programs - Prevar2D, Vari02D with PCF, Model, and Grid Display - that are used for spatial data analysis and variogram modeling of irregularly spaced data in two dimensions. Prevar2D builds a pair comparison file (PCF), that is, a binary file containing pairs of data sorted in terms of increasing distance. Pair comparison files can be built from subsets in order to reduce memory requirements. Vari02D with PCF is used for spatial data analysis of 2D data. It uses an ASCII data file and a binary pair comparison file produced by Prevar2D. Features implemented in Vari02D with PCF include: • the possibility to characterize the spatial continuity of one variable or the joined spatial continuity of two variables, • variogram surfaces for identifying directions of anisotropies, • directional variograms calculated along any direction, • several measures of spatial continuity. Not only the variogram but also the standardized variogram, the covariance, the correlogram, and the madogram are used to measure spatial continuity. • h-scatterplots to assess the meaning of these measures, • the identification and localization of pairs of data adversely affecting the measure of spatial continuity. Once identified, these pairs can be masked from the calculation interactively. • variogram clouds for identifying pairs of data values having the most influence on the measure of spatial continuity. Those pairs can also be located on the sample map.

Table of Contents

Frontmatter

1. Introduction

Overview
VARIOWIN 2.2 is a collection of four Windows™ programs — Prevar2D, Vario2D with PCF, Model, and Grid Display — that are used for spatial data analysis and variogram modeling of irregularly spaced data in two dimensions.
Prevar2D builds a pair comparison file (PCF), that is, a binary file containing pairs of data sorted in terms of increasing distance. Pair comparison files can be built from subsets in order to reduce memory requirements.
Vario2D with PCF is used for spatial data analysis of 2D data. It uses an ASCII data file and a binary pair comparison file produced by Prevar2D. Features implemented in Vario2D with PCF include:
  • The possibility to characterize the spatial continuity of one variable or the joined spatial continuity of two variables,
  • Variogram surfaces for identifying directions of anisotropies,
  • Directional variograms calculated along any direction,
  • Several measures of spatial continuity. Not only the variogram but also the standardized variogram, the covariance, the correlogram, and the madogram are used to measure spatial continuity.
  • H-scatterplots to assess the meaning of these measures,
  • The identification and localization of pairs of data adversely affecting the measure of spatial continuity. Once identified, these pairs can be masked from the calculation interactively.
  • Variogram clouds for identifying pairs of data values having the most influence on the measure of spatial continuity. Those pairs can also be located on the sample map.
  • The ability to save directional variograms in an ASCII file that can be used for subsequent modeling by the Model program.
The Model program is used to produce a 2D nested model of spatial continuity in an interactive way. Several directional variograms read from a variogram file produced by Vario2D with PCF are adjusted simultaneously by a 2D nested model. The adjustment is done with scroll bars. Each time a parameter of the 2D model is changed, cross sections through the 2D model are recalculated and redrawn on the experimental variograms used for the fitting procedure. The 2D nested model can be saved in a model file that is used to store the various parameters required for geostatistical estimation — kriging — or simulation.
Grid Display is used for producing pixel maps of experimental and modeled variogram surfaces that have previously been saved into grid files.
Yvan Pannatier

2. Quick Start

Abstract
In this chapter the four programs included in VARIOWIN 2.2 are used for the spatial analysis of a 2D Data set. The data files gossan2d.dat and gossan.dat are used for this demonstration. They are included with this release of VARIOWIN, and so you may repeat the exercise as a tutorial, or as a test for the software.
Yvan Pannatier

3. Construction of a Pair Comparison File (PCF) with Prevar2D

Overview
Prevar2D constructs a PCF from data files that can hold any number of samples provided enough memory is available on the computer. This pair comparison file contains the number of pairs calculated, the sorted list of pairs, and the name of the data file from which the PCF was constructed.
A PCF can be constructed with theRun ! menu item, which is enabled after the user has validated the “ettings” dialog box displayed with theSettings | XY-Coordinates… menu item. This menu item is enabled when a data file [6.1] has been read into memory (use the File | Open Data File… menu item).
Prevar2D builds a pair comparison file in two steps:
1. All pairs belonging to the active subset [3.4] are first written to a binary file.
2. This binary file is then loaded into memory and pairs are sorted by increasing distance using the quicksort algorithm [Press et al., 1992]. At this stage an error message can be displayed if the memory available on the system is not sufficient to load the binary file. A possible solution is to increase the swapping space used by Windows.
Yvan Pannatier

4. Vario2D with PCF — A Program for Interactive Exploratory Variography

Overview
Vario2D with PCF performs exploratory variography on a 2D data set with the help of a pair comparison file [6.2] constructed with Prevar2D. Note that the program expects to find the data file [6.1] and the pair comparison file in the same directory.
Because Vario2D with PCF is a multiple-document interface (MDI) compliant application, several variographical views of the data can be tiled on screen, allowing the simultaneous examination of spatial continuity from several points of view. Figure 4.1 illustrates the content of those views and their relationships:
1.
The sample map is used to identify errors in the coordinates and data clustering. Pairs of data are also plotted on this map.
 
2.
An h-scatterplot is the bivariate equivalent of the histogram. In the same way that a histogram is an approximation of the underlying univariateprobability density function that characterizes the studied phenomenon, an h-scatterplot is an approximation of the underlying bivariate probability density function that characterizes the spatial continuity for a separation vectorh.
 
3.
The variogram surface is an effective way to detect anisotropies in the pattern of spatial continuity. Each cell of a variogram surface represents a measure of spatial continuity that summarizes an h- scatterplot. This diagram is used to identify preferential directions in which directional variograms should be calculated.
 
4.
A directional variogram, orexperimental variogram, displays the pattern of spatial continuity in a given direction. It is a cross section through a variogram surface. Each point of the variogram represents a measure of spatial continuity that summarizes an h-scatterplot. In order for the variogram to be a good representation of spatial continuity in a given direction, each one of its points must be a meaningful summary of its associated h-scatterplot. The construction of experimental variograms representing the pattern of spatial continuity in several directions is a fundamental step in any geostatistical study since those variograms are used to build a 2D model of spatial continuity.
 
5.
The variogram cloud shows the relationship between the magnitude of the pair separation vector and the variogram value of this pair [4.7.1]. A directional variogram can be considered as the moving average of a variogram cloud.
 
Yvan Pannatier

5. Model — Interactive Variogram Modeling

Overview
The Model program constructs a 2D nested model with the help of experimental (cross) variogram(s) produced by Vario2D with PCF [45]. It deals with 2D anisotropic modeling of one or two variables but does not provide any facility for constructing a global coherent model of coregionalization.
Directional variograms are read from a variogram file [6.5]. Scroll bars can change the parameters of the 2D nested model. Each time a parameter is modified, cross sections through the 2D model are redrawn along with the directional variogram(s) used to fit the model.
A 2D nested model can be fitted against any of the measures of spatial continuity available in Vario2D with PCF [4.7].
An indicative goodness of fit (IGF) is computed every time the model changes. The best IGF is stored in memory and can be recalled at any time. A user’s model can also be stored in memory.
The 2D nested model of spatial continuity can be saved as a grid file [6.3]. This file can then be used to produce a variogram surface representation of the 2D nested model.
Yvan Pannatier

6. Files Used Within VARIOWIN 2.2

Abstract
Within VARIOWIN, all steps of a variographic study can be recorded into files. This section describes the format, the default extension, and the usage of those files. A user who wishes to modify a file created by one of the programs included with VARIOWIN should read this section before proceeding.
Yvan Pannatier

Backmatter

Additional information