Page 275 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

278 Chapter 8

W C D W C D
Unc C ji = 1 − m ji − m ji = 1 − Bel C ji − Dis C ji . (8.10)
¦ W C D ¦ W
j=1 ji j=1 C ji D

The re-defined equations for GIS-based data-driven estimations of Bel, Dis and Unc
for mineral prospectivity mapping thus take into account (a) the relative proportions of
known deposit-type locations in every class of spatial evidence (see the numerators of
equations (8.8b) and (8.9)), which define the spatial associations between the deposit-
type locations and classes of spatial evidence in individual evidential maps and (b) the
relative weights and thus relationships among the classes of evidence in each evidential
map with respect to D and D .
Applications of equations (8.8a), (8.9a) and (8.10) to hypothetical data shown in Fig.
8-10 indicate that classes of spatial evidence with the highest density of deposit-type
locations [i.e., N(C j∩D)÷N(C j)] have the highest Bel C j , lowest Dis C j and lowest

Unc C j . Conversely, the hypothetical example in Fig. 8-10 indicates that classes of
spatial evidence with the lowest density of deposit-type locations have the lowest
Bel C j , highest Dis C j and highest Unc C j . The data-driven estimates of EBFs based on

the artificial data (Fig. 8-10) indicate that (a) the Bel is a measure of relative strengths of
spatial associations between geo-objects of interest and classes of spatial evidence and
(b) both the Dis and Unc are ‘inverse’ measures of relative strengths of spatial
association between geo-objects of interest and classes of spatial evidence. It is further
shown in the case study that the applications of the re-defined equations for GIS-based
data-driven estimations of EBFs for mineral prospectivity mapping result in values of
Bel portraying empirical spatial associations between deposit-type locations and
geological features that are comparable to and interpretable as the results of applications
of the methods for quantifying spatial associations described and explained in Chapter 7.
In the application of equations (8.8) and (8.9) for GIS-based data-driven estimations
of EBFs for mineral prospectivity mapping, one must take note of the result that
W C ji D = 0 (equation (8.8b)). This means that N (C ji ∩ D ) = 0 , which results in

Bel C ji = 0 (equation (8.8a)). If W C ji D = 0 , then the corresponding estimate of W C ji D
(which actually is not equal to zero since N (C ji ) − [N (C ji ∩ D )] ≠ 0 ; equation (8.9b))
must be discarded and instead the W is replaced with or re-set to [0] (Fig. 8-11). By
C ji D
doing this, the corresponding Dis C ji = 0 (equation (8.9a)) and the corresponding
Unc C ji = 1 (equation (8.10)). The logic of this is that if there is no belief then there is
also no disbelief but there is only uncertainty.