Page 251 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

254 Chapter 8

mineral prospectivity is usually subjective. The following discussions explain and
demonstrate analytical tools that can aid in the objective selection of a suitable square
unit cell size for GIS-based data-driven modeling of mineral prospectivity.
The choice of a suitable unit cell size must be based on the spatial configuration or
pattern of locations of a-priori samples, i.e., the known locations of mineral deposits of
the type sought. In sampling theory, this strategy is referred to as retrospective sampling,
which is applied to previously sampled areas, as opposed to prospective sampling, which
is applied to unsampled areas. Because known locations of mineral deposits are usually
depicted as points in data-driven modeling of mineral prospectivity, especially in
regional- to district-scales of mapping, algorithms of point pattern analysis for measures
of dispersion (Boots and Getis, 1988; Rowlingson and Diggle, 1993), which are
independent of the size of a study area, can be used to determine distances from every
deposit-type location and the corresponding probabilities associated with these distances
that there is one neighbour deposit-type location situated next to another deposit-type
location. The range of distances in which there is zero probability of one neighbour
deposit-type location situated next to another deposit-type location is a set of choices for
a suitable unit cell size. Fig. 8-1 shows the results of the application of measures of
dispersion via point pattern analysis to different types of mineral deposits and to
geothermal prospects in four different areas. For each area, the results suggest different
ranges of suitable unit cell sizes for data-driven modeling of prospectivity for the types
of Earth resources under examination. For data-driven modeling of prospectivity for
epithermal Au deposits in the Aroroy district (Philippines), a suitable unit cell size is at
most 560 m. For data-driven modeling of prospectivity for epithermal Au deposits in the
Cabo de Gata area (Spain), a suitable unit cell size is at most 160 m. For data-driven
modeling of geothermal prospectivity in West Java (Indonesia), a suitable unit cell size
is at most 750 m. For data-driven modeling of prospectivity for alkalic porphyry Cu-Au
deposits in British Columbia, a suitable cell size is at most 330 m. The results of the
application of measures of dispersion via point pattern analysis (e.g., Fig. 8-1) are
considered further in a graphical analysis, which is described below, to aid the objective
selection of a suitable unit cell size for GIS-based data-driven modeling of mineral
prospectivity.
Based on a unit cell size [denoted hereafter as N(•)], a study area T has N(T) total
number of unit cells, has N(D) number of unit cells each containing just one D deposit-
type location and has N(T)–N(D) number of unit cells not containing D. An a-priori
estimate of prospectivity (i.e., in the absence of spatial evidence) of mineral deposits of
the type sought in a study area is the ratio [N(D)] : [N(T)–N(D)]. This ratio represents the
spatial contrast between mineralised cells and barren cells. Empirically, the ratio [N(D)] :
[N(T)–N(D)] must be a very small value because mineralisation is a relatively rare
geological phenomenon, meaning that N(•) must be suitably fine. All possible N(•)
within the range of distances with zero probability of one neighbour D situated next to
another D (Fig. 8-1) result in very small values of the ratio [N(D)] : [N(T)–N(D)].
However, Fig. 8-2 shows that the ratio [N(D)] : [N(T)–N(D)] increases exponentially as