Page 271 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

274 Chapter 8

th
C ji class in the i X i evidential map is equal to 1. From these two equalities, therefore,
Pls = Bel+Unc or Bel = Pls–Unc. The degree of Unc influences the relation between Bel
th
th
and Dis. If Unc = 0 (i.e., any j C ji class in the i X i evidential map is ‘totally accurate
and precise’ with respect to D), then Bel+Dis = 1 and the relation between Bel and Dis
th
th
for the j C ji class in the i X i evidential map is binary (i.e., Bel = 1–Dis or Dis = 1–Bel),
th
th
as in the theory of probability. If Unc = 1 (i.e., any j C ji class in the i X i evidential map
th
is ‘totally inaccurate and imprecise’ with respect to D), then Bel and Dis for the j C ji
th
class in the i X i evidential map are both equal to zero. That is, if there is complete
uncertainty, then there can be neither belief nor disbelief. Usually, however, Unc is
th
th
neither equal to 0 nor equal to 1 (i.e., any j C ji class in the i X i evidential map is neither
‘totally accurate and precise’ nor ‘totally inaccurate and imprecise’ with respect to D).
Therefore, in the usual case that 0<Unc<1, then Bel = 1–Dis–Unc or Dis = 1–Bel–Unc.
This means that, because uncertainty is usually present, the relation between Bel and Dis
th
for a given piece of evidence is usually not binary. This further means that, for any j C ji
th
class in the i X i evidential map that is used to evaluate the proposition of mineral
prospectivity, not only Bel and Dis but also Unc must be modeled.
Most of the published applications of EBFs to mineral prospectivity mapping are
knowledge-driven (Moon 1990, 1993; Chung and Moon, 1991; Moon et al., 1991; An,
1992; An et al., 1992, 1994a, 1994b; Chung and Fabbri, 1993; Wright and Bonham-
Carter, 1996; Likkason et al., 1997; Carranza, 2002; Tangestani and Moore, 2002;
Chapter 7 of this volume). Knowledge-driven estimation of EBFs is suitable for
modeling of mineral prospectivity in frontier or less-explored mineralised landscapes
where there are no or very few known locations of mineral deposits of the type sought.
Data-driven estimation of EBFs, however, can be performed in modeling of mineral
prospectivity in moderately- to well-explored mineralised landscapes where there are
several known locations of mineral deposits of the type sought (see references cited in
Table 8-1).
The minimum number of deposit-type locations used in data-driven estimation of
EBFs depends on the size of a study area, because data-driven estimates of EBFs, like
estimates of wC ji for C ji classes in X i evidential maps via application of other data-driven
techniques, are based on size of study area. However, a minimum deposit density (e.g.,
ratio of the number of deposit-type pixels (or unit cells) to the number of ‘study area’
pixels) that results in geologically meaningful data-driven estimates of wC ji for C ji
classes in X i evidential maps has not yet been established. Data-driven estimates of EBFs
are meaningful if they represent geologically sound empirical spatial associations
between mineral deposits of the type sought and certain geological features (see Chapter
7). Nevertheless, Carranza (2002) showed geologically meaningful results of
applications of data-driven EBFs to mineral prospectivity mapping based on (a) 12
2
locations of porphyry Cu deposits in an area of roughly 920 km and (b) 17 locations of
2
vein-type Cu-Au deposits in an area of roughly 1,450 km . These imply that application
of data-driven EBFs to model mineral prospectivity in the present case study area, where