Page 162 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Analysis of Geologic Controls on Mineral Occurrence 163

features are spatially independent (i.e., they lack spatial association), the graph or curve
of cumulative proportion (or relative frequency or histogram) of measured nearest
distances [Ô(X)] is compared with the graph or curve of cumulative proportion of
expected nearest distances [Ê(X)] by computing the Kolmogorov-Smirnov statistic:

D= O ˆ (X ) E ( ˆ X ) . (6.4)
−

If D ≅ 0, then the set of point geo-objects of interest and the set of linear features are
spatially independent. If D is positive (i.e., >0), which means that the curve Ô(X) is
above or higher than the curve Ê(X), then there is positive spatial association between
the set of point geo-objects and the set of linear features. If D is negative (i.e., <0), which
means that the curve Ô(X) is under or lower than the curve Ê(X), then there is negative
spatial association between the set of point geo-objects and the set of linear features.
A positive, rather than a negative, spatial association between a set of point geo-
objects and a set of linear (or point or polygonal) features is important, because it
suggests that the latter represents a set of plausible factors (or spatial evidence) of
occurrence of the former. In order to determine graphically if Ô(X) is significantly
greater than Ê(X), an upper confidence band for the Ê(X) curve can be calculated as:

+
Û(X)= Ê (X) 9 . 21 (N+ M)/ 4 NM} 1 2 (6.5)
(

where M denotes the number of random points used to estimate Ê(X), N denotes the
2
number of point geo-objects used to estimate Ô(X) and 9.21 is a tabulated critical χ (or
chi-square) value for 2 degrees of freedom and significance level α=0.01 (other critical
2
χ values may be used for chosen α). In addition, the distance from the linear features in
which positive D values are highest or optimal is of interest, because within this distance
from the linear features there is significantly higher proportion of occurrence of point
geo-objects than would be expected due to chance (i.e., a random or Poisson process).
The distance from the linear geo-objects in which positive D values are highest or
optimal can be determined through a test of statistical significance of positive spatial
association by calculating the quantity:

β = 4D 2 NM /(N+ M ) , (6.6)

2
which is distributed approximately as χ with 2 degrees of freedom (Goodman, 1954;
Siegel, 1956); M and N are as defined for equation (6.5). The distance from the linear
2
geo-objects in which the estimated values of β exceed a critical χ value at a certain
significance level (α) represents the distance of optimal positive spatial association
between the point geo-objects and the set of linear features.
The following sequence of procedures, which are illustrated schematically in Fig. 6-
8, can be followed in a raster-based GIS in order to implement the distance distribution
method.