Page 161 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

162 Chapter 6

SPATIAL ASSOCIATION OF MINERAL DEPOSITS AND GEOLOGIC FEATURES
Certain types of mineral deposits exhibit spatial associations with certain geological
features because the latter play a role in localisation of the former. For example, igneous
intrusions provide heat that causes formation of hydrothermal convection cells whilst
faults/fractures provide plumbing systems for circulation of convective hydrothermal
fluids (from which mineral deposits may precipitate). The spatial association dealt
herewith refers to the distance or range of distances at which certain types of mineral
deposits, which are usually represented or mapped as points, are preferentially located
from certain geologic features, which can be represented or mapped as points, lines or
polygons. This spatial association can be regarded as spatial dependence; that is, the
occurrence of certain types of mineral deposits depends upon the locations of certain
geological features. The smaller the distance of spatial association, the stronger the
spatial dependence. Analysis of spatial associations between occurrences of mineral
deposits of the type sought and certain geological features is thus instructive in
conceptual modeling of mineral prospectivity.
Methods for analysis of spatial association between occurrences of certain types of
mineral deposits and certain geologic features can be classified into two groups: (1)
methods that lead directly to the creation and then integration of predictor maps in
predictive modeling of mineral prospectivity; and (2) methods that are exploratory in
nature and are useful mainly in conceptual modeling of mineral prospectivity. Methods
belonging to the former group are explained and demonstrated in Chapter 8. Two
methods belonging to the latter group are explained and demonstrated in this chapter: (1)
distance distribution method; and (2) distance correlation method.
Distance distribution method

The theoretical model of the distance distribution method, which characterises spatial
association between a set of point geo-objects and another set of (point, linear or
polygonal) geo-objects, was formalised and demonstrated by Berman (1977). Further
demonstrations, with certain adaptations, of this method in determining spatial
associations between occurrences of certain types of mineral deposits and curvi-linear
geological features can be found in Simpson et al. (1980), Bonham-Carter et al. (1985),
Bonham-Carter (1985, 1994), Berman (1986), Carranza (2002) and Carranza and Hale
(2002b). Variants of the distance distribution method are commonly called proximity or
buffer analysis (e.g., Ponce and Glen, 2002; Bierlein et al., 2006; Park et al., 2007). The
procedures described below for GIS-based application of the distance distribution
method are adapted from Bonham-Carter et al. (1985) and Bonham-Carter (1985, 1994).
Consider the observed nearest (i.e., Euclidean) distances, O(X), between individual
points (in a set of point geo-objects of interest) and certain lines (in a set of linear geo-
objects). Consider further the expected nearest (i.e., Euclidean) distances, E(X), between
individual random points (in a set of random point geo-objects representing a set of
Poisson processes) and certain lines (in the same set of linear geo-objects). In order to
test a null hypothesis that the set of point geo-objects of interest and the set of linear