Page 274 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Data-Driven Modeling of Mineral Prospectivity 277

of being more likely absent in C ji than would be expected due to chance. Accordingly,
th
the Bel C ji in equation (8.8a) is a the relative strength of the spatial association of the j
th
C mi class in the i X i spatial evidence map with D compared to the strengths of spatial
th
th
associations of the other m C mi classes in the i X i spatial evidence map with D.
th
th
The Dis C ji for the j C ji (j=1,2,…,m) class of the i X i (i=1,2,…,n) spatial evidence
map with respect to D is re-defined and estimated as

W
Dis = C ji D , (8.9a)
C ji m
¦ W
= j 1 C ji D

N (C ji ) − N (C ∩ D )
ji
N (C )
where W = ji (8.9b)
C ji D N (T ) − N (D ) − [N (C ji ) − N (C ∩ D )]
ji
N (T ) − N (C ji )

and D means pixels or unit cells not known to contain D. The numerator in equation
(8.8b) is the conditional probability that D does not exist given the presence of C ji. It
means simply that a target mineral deposit occurs outside C ji. The denominator in
equation (8.8b) is the conditional probability that D does not exist given the absence of
C ij. It means simply that a target mineral deposit occurs in C ji. Thus, W is the
C ji D
relative weight of C ji in terms of D being more likely absent instead of being more likely
present in C ji than would be expected due to chance. Conversely, W is the relative
C ji D
weight of C ji in terms of D being more likely present instead of being more likely
absent in C ji than would be expected due to chance. Accordingly, the Dis C ji in equation

th
th
(8.9a) is the relative strength of the spatial association of the j C mi class in the i X i
spatial evidence map with D (but not with D) compared to the strengths of spatial
th
th
associations of the other m C mi classes in the i X i spatial evidence map with D .
th
There are two effects when the relative strengths of spatial associations of j C mi
th
th
classes in the i X i spatial evidence map with D and D are considered. First, for every j
th
C ji class in the i X i spatial evidence map, the values of Bel C ji and Dis C ji estimated
according to equations (8.8a) and (8.9a), respectively, are constrained to the unit interval
th
[0,1], which is consistent with the concept of probability. Second, for every j C ji class in
th
the i X i spatial evidence map, the sum of the values of Bel C ji and Dis C ji is less than
[1], which allows modeling of Unc C ji , thus