Page 222 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

224 Chapter 7

generic analysis of information (i.e., mineral prospectivity) embedded in a fuzzy set of
values is via defuzzification (Fig. 7-10), so that discrete spatial entities or geo-objects
representing, for example, prospective and non-prospective areas, are recognised or
mapped. Hellendoorn and Thomas (1993) describe a number of criteria for
defuzzification. However, in GIS-based mineral prospectivity mapping, the optimal
method of defuzzifying a fuzzy model of mineral prospectivity is to construct its
prediction-rate curve (see Fig. 7-2) against some cross-validation occurrences of mineral
deposits of the type sought in a study area.
The prediction-rate curve of the fuzzy model of epithermal Au prospectivity in Fig.
7-16A indicates that, if 20% of the case study area is considered prospective, then it
performs equally as well as the multi-class index overlay model of epithermal Au
prospectivity shown in Fig. 7-9. The predictive model in Fig. 7-16A, which is obtained
by using γ=0.5, performs equally as well as a predictive model obtained by using γ=0 in
the final step of the inference network (Fig. 7-15). Their prediction-rate curves (Fig. 7-
16B) are identical and both of them have better prediction-rates than a predictive model
obtained by using γ=1 in the final step of the inference network (Fig. 7-16B). These
results imply that the contributions of complementary pieces of spatial evidence provide
better predictions than the contributions of supplementary pieces of spatial evidence.
These results are therefore realistic because epithermal Au mineralisation requires
complementary effects of both structural controls (represented by proximity to NNW-
and NW-trending faults/fractures) and heat source controls (represented by proximity to
intersections of NNW- and NW-trending faults/fractures; see Chapter 6). In addition, the
presence of stream sediment geochemical anomalies is important in indicating locations
of anomalous sources. However, the predictive model obtained by using γ=1 in the final
step of the inference network is better than the predictive models obtained by using γ=0
and γ=0.5 in the final step of the inference network in the sense that the former predicts
all cross-validation deposits if 60% of the case study area is considered prospective
whereas the former predict all cross-validation deposits if 100% of the case study area is
considered prospective (Fig. 7-16B).
The poor performance of the predictive models obtained by using γ=0 and γ=0.5 in
the final step of the inference network (Fig. 7-15), in terms of correct delineation of all
the cross-validation deposits, is due to classes of evidence with fuzzy membership scores
of zero, especially the classes of fuzzy ANOMALY evidence (Table 7-VI). In Fig. 7-
16A the locations of four cross-validation deposits have output fuzzy prospectivity
values of zero. In order to demonstrate the deleterious effect using a fuzzy membership
score of zero, those classes of fuzzy evidence with fuzzy membership scores of zero in
Table 7-VI are re-assigned the lowest non-zero fuzzy membership scores in the
individual fuzzy sets as shown in Table 7-VII.
The new predictive map (Fig. 7-17A) shows low (rather than zero) fuzzy
prospectivity values at the locations of the four cross-validation deposits not delineated
correctly by the predictive map in Fig. 7-16A. The new results show improvements
mainly for the predictive maps obtained by using γ=0.5 and γ=0 in the final step of the
inference network, which now delineate correctly all cross-validation deposits if 65%