Page 229 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Knowledge-Driven Modeling of Mineral Prospectivity 231

Unc Unc +Bel Unc +Bel Unc +Dis Unc +Dis Unc
Unc X 1 X 2 = X 1 X 2 X 1 X 2 X 2 β X 1 X 1 X 2 X 2 X 1 (7.16)

−
where =β 1 Bel X 1 Dis X 2 − Dis X 1 Bel X 2 , which is a normalising factor ensuring that
Bel +Unc +Dis 1 = . Equations (7.14) and (7.15) are multiplicative, so that the application
of an AND operation results in a map of integrated Bel and integrated Dis, respectively,
in which the output values represent support and lack of disbelief, respectively, for the
proposition being evaluated if pieces of spatial evidence in two input maps coincide (or
intersect). In contrast, equation (7.16) is both commutative and associative, so that the
application of an AND operation results in a map of integrated Unc in which the output
values are controlled by pieces of spatial evidence with large uncertainty in either of the
two input maps. Therefore, an AND operation is suitable in combining two pieces of
complementary spatial evidence (say, X 1 and X 2) in order to support the proposition of
mineral prospectivity. In mineral exploration, proximity to faults/fractures and stream
sediment geochemical anomalies can represent two sets of complementary spatial
evidence of mineral deposit occurrence, because several types of mineral deposits,
including epithermal Au, are localised along faults/fractures and, if exposed at the
surface, can release metals into the drainage systems and cause anomalous
concentrations of metals in stream sediments. (After application of equations (7.14)–
(7.16), Pls X 1 X 2 is derived according to the relationships of the EBFs explained above.)
The formulae for combining EBFs of two spatial evidence maps (X 1, X 2) according
to an OR operation are defined as (An et al., 1994a):

Bel Bel +Bel Unc +Bel Unc
Bel X 1 X 2 = X 1 X 2 X 1 β X 2 X 2 X 1 (7.17)

Dis Dis +Dis Unc +Dis Unc
Dis X 1 X 2 = X 1 X 2 X 1 β X 2 X 2 X 1 (7.18)

Unc Unc
Unc X 1 X 2 = X 1 β X 2 (7.19)

where β is the same as in equations (7.14)–(7.16). Equations (7.17) and (7.18) are both
commutative and associative, so that the application of OR operation results in a map of
integrated Bel and integrated Dis, respectively, in which the output values are controlled
by pieces of spatial evidence with large belief or large disbelief in either of the two input
maps. In contrast, equation (7.19) is multiplicative, so that the application of an OR
operation results in a map of integrated Unc in which the output values is controlled by
pieces of spatial evidence with low uncertainty in either of the two input maps.
Therefore, an OR operation is suitable in combining two pieces of supplementary (as