Page 174 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Analysis of Geologic Controls on Mineral Occurrence 175

and d jx are minimal (i.e., P jx and P jy are close enough), which implies that most of the
points P jx lie preferentially at distances about Y jmax r from their respective nearest L i
neighbours. Hence, the distance Y jmax r is considered the distance at which there is
optimum spatial association between a set of points and a set of lines (or points).
Within a certain study area, a very large but finite number of possible APs can be
used for characterising spatial association between P jx and L i via the distance correlation
method. Because this method is sensitive to the position of an AP with respect to line
segments ⊥L i, as shown below, it is recommended to use not just one but many APs in
order to properly characterise the optimum spatial association between P jx and L i. For
simplicity, Carranza (2002) recommends using nine APs within and along the boundaries
of a study area: its centre (C); the mid-point of its north (N) boundary; its northeast (NE)
corner; the mid-point of its east (E) boundary; its southeast (SE) corner; the mid-point of
its south (S) boundary; its southwest (SW) corner; the mid-point of its west (W)
boundary; and its northwest (NW) corner. Based on at least one of these nine APs, it is
shown below (by application to the case study area) that the longest Y max is the
j
r
distance of optimum spatial association between P jx and L i. In the case of a positive
spatial association, more P jx points would lie at distances less than or equal to Y jmax r.
Hence, it can be expected that the mean r d jx d jy at distances less than or equal to Y jmax r
(hereafter denoted as proximal- r d jx d jy ) is greater than the mean r d jx d jy at distances

greater than Y jmax r (hereafter denoted as distal- r d jx d jy ). In the case of a negative
spatial association, more P jx points would lie at distances less than or equal to Y jmax r.
Hence, it can be expected that the proximal- r d jx d jy is less than the distal- r d jx d jy .

The following sequence of procedures can be followed in a raster-based GIS in order
to quantify spatial association between P jx and L i via the distance correlation method.
1. On each L i nearest to a point P jx, determine P j0 visually. (Note that in case the
geological feature is a ‘point’, then the ‘point’ becomes P j0).
2. Digitise line segments ⊥L i (broken lines in Fig. 6-13) starting from P j0 and passing
through P jx. Note that each ⊥L i is perpendicular to its respective L i. The length of
each ⊥L i should be at least equal to the length of the longest X j plus twice the
standard deviation of all X j. This is mainly based on experience or empiricism but not
on any formalism. That is, points P jx may lie preferentially at a certain narrow range
(i.e., small standard deviation) of distances X j from L i and such distance range may
happen to be very close to the maximum X j. Thus, to find Y jmax r properly, the length
of each ⊥L i should be at most twice the length of the longest X j in order to compare
the proximal- r d jx d jy with the distal- r d jx d jy .
3. Create points P jy along the line segments at regular distance intervals Y j from P j0.
Hence, P jy and P j0 are the same when Y j =0. This can be achieved by converting the
line segments to points at a specified distance interval.
4. Digitise nine APs as recommended above. Create a map of distances from each AP.