Page 148 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Analysis of Geologic Controls on Mineral Occurrence 149

A point pattern under consideration is thus compared to a point pattern of CSR. The null
hypothesis in point pattern analysis is, therefore, that the point pattern under examination
assumes CSR and that the geo-objects represented by the points are independent of each
other and each point is a result of a random (or Poisson) process. The plainest alternative
or ‘research’ hypothesis in point pattern analysis is that the point pattern under
investigation does not assume CSR and that the geo-objects represented by the points are
associated with each other because they were generated by common processes. Thus, if
occurrences of mineral deposits of the type sought are non-random, they may display a
clustered distribution or a more or less regular distribution. There are various techniques
by which the null hypothesis or the alternative hypothesis can be tested and they can be
grouped generally into two types of measures (Boots and Getis, 1988): (1) measures of
dispersion; and (2) measures of arrangement.
Measures of dispersion study the locations of points in a pattern with respect to the
study area. Measures of dispersion can be further subdivided into two classes: (a)
quadrat methods; and (b) distance methods. Quadrat methods make use of sampling
areas of a unit size and consistent shape (e.g., a square pixel), which can be either
scattered or contiguous, to measure and compare frequencies (or occurrences) of
observed points to expected frequencies of points in CSR. It is preferable to make use of
contiguous quadrats (e.g., a grid of square pixels) instead of scattered quadrats in the
analysis of the spatial distribution of occurrences of mineral deposits of the type sought.
That is because scattered quadrats are positioned at randomly selected locations,
producing a bias toward CSR. Choosing a quadrat size, however, is a difficult issue in
using contiguous quadrats: large quadrats tend to result in more or less equal
frequencies, which generate bias toward a regular or a clustered pattern; small quadrats
can break up clusters of points, resulting in a bias toward CSR. The best option is to
apply distance methods, which compare measured distances between individual points
under study with expected distances between points in CSR.
In a GIS, distance between two points is determined, based on the Pythagorean
theorem, as the square root of the sum of the squared difference between their easting (or
x) coordinates and the squared difference between their northing (or y) coordinates. In a
set of n points, measured distances from one point to each of the other points are referred
nd
st
rd
st
th
to as 1 -, 2 -, 3 - or (n-1) -order neighbour distances; the 1 -order neighbour distance
th
being the nearest neighbour distance. If, on the one hand, the mean of measured n -order
th
neighbour distances is smaller than the mean of expected n -order neighbour distances
in CSR, then the set of points under examination assumes a clustered pattern. If, on the
th
other hand, the mean of measured n -order neighbour distances is larger than the mean
th
of expected n -order neighbour distances in CSR, then the set of points under
examination assumes a regular pattern. The significance of the difference between the
th
th
mean of measured n -order neighbour distances and the mean of expected n -order
neighbour distances in CSR may be determined statistically based on the normal
distribution; for details, readers are referred to Boots and Getis (1988).
The occurrences of epithermal Au deposits in the Aroroy district (Philippines),
th
according to the results of analysis of up to the 6 -order neighbour distances (Table 6-I),