Geologically-Constrained Probabilistic Mapping of Gold Potential, Baguio District, Philippines
Emmanuel John M. Carranza and Martin Hale
Geological patterns based on the quantified spatial correlation between a number of geological features and the locations of mineral occurrences.
Whereas in its simplest form the binary code of a unit cell or pixel represents presence or absence of a mineral occurrence, the binary pattern of a predictor curvilinear geological feature represents the presence or absence of mineral occurrence points in unspecified cell(s) or pixel(s) within the area of the pattern. The areal extent of such patterns needs to be set, for example by using appropriate cutoff distance away from the predictor curvilinear geological features.
Using Bayes' rule, two probabilities can be computed in which a binary predictor pattern contains a mineral occurrence. The loge of each of these probabilities are the weight for the binary predictor pattern present, W+, and the weight for the binary predictor pattern absent, W-, respectively. If a binary predictor pattern is positively correlated with mineral occurrence points, W+ is positive and the contrast, C=3DW+-W- is a measure of the spatial correlation between a geological feature and a set of mineral occurrence points. The Studentized C (i.e., the ratio of C to its standard deviation) provides the basis for determining cutoff distances from the linear and curvilinear geological features when these features are converted into binary predictor patterns. The loge of the posterior odds of a mineral occurrence given the presence/absence of a binary predictor pattern is then obtained by adding the weights of the binary predictor patterns to the loge of the prior odds. Combining the binary predictor patterns results in a map of posterior odds, which when converted to posterior probabilities, represents favourability for mineral potential. Combining the binary predictor maps assumes that these maps are conditionally independent from one another with respect to the mineral occurrence points. Conditional independence is tested through pairwise calculation of chi-square values and, from the map of posterior probabilities, by comparing the predicted and observed number of mineral occurrences.
The Baguio datasets consist of (1) geological maps, (2) lineaments representing mapped faults/fractures, (3) large-scale gold occurrences data, and (4) small-scale gold occurrences data. The results show that the input binary maps of importance for predicting known large-scale and small-scale gold occurrences are (1) proximity to Late Miocene - Pleistocene intrusive complexes, (2) proximity to the Late Oligocene - Early Miocene Agno Batholith, (3) proximity to NE-trending lineaments, (4) presence of the Zigzag and Pugo Formations, and (5) proximity to NW-trending lineaments. Pairwise chi-square tests show that the binary predictor patterns are conditionally independent with respect to the large-scale gold occurrences. On the other hand, the map of proximity to intrusive complexes and the map of proximity to the Agno Batholith show conditional dependence with respect to the small-scale gold occurrences. However, the resulting map of posterior probabilities indicates that conditional independence is not violated when these maps are used. The resulting map of posterior probabilities based on the large-scale gold occurrences shows that 79 percent of the known large-scale gold occurrences are associated with zones having posterior probabilities greater than, or equal to, the prior probability. In this map, 58 percent of the known small-scale occurrences are associated with the zones of gold potential. The resulting map of posterior probabilities based on the small-scale gold occurrences shows that 70 percent of the known small-scale gold occurrences are associated with zones having posterior probabilities equal to, or greater than, the prior probability. In this map, 56 percent of the known large-scale gold occurrences are associated with the zones of gold potential. Both predictive maps indicate that the probabilistic approach to mineral potential mapping is effective for the Baguio district datasets in that they predict several zones of gold potential that are close to the known gold occurrences.
IV International Conference on GeoComputation
, Mary Washington College, Fredericksburg, VA, USA, 25-28 July 1999.