Page 247 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

250 Chapter 8

P = f (X i ,! , X n ) . (8.1)
D

For a study area, the map of D (i.e., the target variable) and each of the individual maps
of explanatory/predictor variables are usually partitioned into equal-sized unit cells,
which are usually squares. That is, relative indices of prospectivity (P D) are expressed as
degrees of likelihood of deposit-type occurrence per unit cell. Each of the individual
maps of X i spatial evidential features are discretised further into a number of C ji
(j=1,2,…,m) classes of evidence. For each unit cell in the study area, P D can be defined
further as:

P = f (wC ji ," , wC mn ) , (8.2)
D

where wC ji represents evidential weights (i.e., degree of spatial associations) of C ji
classes of individual X i spatial evidential features with respect to D. The evidential
weights relate to the degree of spatial coincidence or association between D and every
C ji in X i maps. Unit cells characterised by high values of wC ji in most, if not all, maps of
X i, therefore, have spatial geological attributes that are similar to (in terms of spatial
association with) the unit cells containing the known locations of D. Equations (8.1) and
(8.2), thus, simultaneously involve interpolative and extrapolative analyses of unit cells
that likely contain unknown (or undiscovered) locations of D based on the spatial
associations of C ji in X i maps with unit cells containing the known locations of D.
In Chapter 6, the methods for quantifying spatial associations between a map of
deposit-type locations and individual maps of relevant geoscience spatial data do not
lead directly to the derivation of values of wC ji for C ji classes in X i maps of spatial
evidential features. However, there are different data-driven techniques for deriving
directly values of wC ji for C ji classes in X i maps of spatial evidential features with respect
to D (i.e., creating predictor maps) and then combining these predictor maps, via an
integration function f (equation (8.2)), in order to obtain a predictive model of
prospectivity (i.e., a map of P D) for mineral deposits of the type sought. Chung and
Fabbri (1993) proposed a unified mathematical framework for spatial predictive
modeling of geo-objects (e.g., geohazard-prone areas, prospective areas, etc.).
There are two types of mathematical techniques for GIS-based data-driven predictive
modeling of mineral prospectivity: bivariate and multivariate. Bivariate techniques
(Table 8-I) involve pairwise analysis of spatial association between a map of D and a
map of X i with C ji classes. In the applications of bivariate techniques, predictor maps are
explicitly created and then integrated after the pairwise analyses of spatial associations.
Weights-of-evidence modeling is the most commonly used bivariate technique.
Multivariate techniques (Table 8-II) involve simultaneous analysis of spatial associations
between a map of D and maps of X i with C ji classes. In the applications of multivariate
techniques, predictor maps are usually created automatically and then integrated ‘on-the-
fly’ or dynamically whilst the spatial associations between a map of D and maps of X i