Page 273 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

276 Chapter 8

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The degree of plausibility ( Pls 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, according to the relationships of
the EBFs (see Chapter 7, Fig. 7-18), estimated as

Pls C ji = Bel C ji + Unc C ji . (8.7)

There are two problems associated with the application of equations (8.4) to (8.6).
Firstly, because N (C ji ) = N (C ∩ D ) + [N (C ji ) − N (C ∩ D )] , it follows that
ji
ji
Unc C in equation (8.6) is equal to [0], whereas there is always uncertainty. Secondly,
ji
equations (8.4) and (8.5) represent conditional probability that a mineral deposit of the
type sought exists and does not exist, respectively, given C ij. The estimates of both
Bel C ji and Dis C ji via equations (8.4) and (8.5), respectively, thus represent the
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relationship of the j C ij class in the i X i spatial evidence map with D only but do not
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represent the relationship of the j C ij class with the other m C mi classes in the i X i
spatial evidence map. Chung and Fabbri (1993) aver that the relationships among the
classes in an evidential map, aside from their spatial relationships to D, must be
considered and represented in a mathematical function f (see equations (8.1) and (8.2))
for combining predictor maps of mineral prospectivity. The following modified
equations (Carranza, 2002; Carranza and Hale, 2003) have been proposed to overcome
the problems associated with equations (8.4) to (8.6).
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The Bel 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 C D
Bel C ji = m ji , (8.8a)
¦ W D
= j 1 C ji

N (C ∩ D )
ji
N (C )
ij
where W C ji D = N (D ) − N (C ∩ D ) . (8.8b)
ji
N (T ) − N (C ji )

The numerator in equation (8.8b) is the conditional probability that D exists given the
presence of C ji. It means simply that a target mineral deposit occurs in C ji. The
denominator in equation (8.8b) is the conditional probability that D exists given the
absence of C ij. It means simply that a target mineral deposit occurs outside C ji. Thus, the
W C ji D is the relative weight of every C ji in terms of D being more likely present instead