Emmanuel John M. Carranza

Evidential belief functions for data-driven geologically constrained mapping of gold potential, Baguio district, Philippines

Abstract A data-driven application of the theory of evidential belief to map mineral potential is demonstrated with a redefinition of procedures to estimate evidential belief functions. The redefined estimates of evidential belief functions take into account not only the spatial relationship of an evidence with the target mineral deposit but also consider the relationships among the subsets of spatial evidences within a set of evidential data layer. Proximity of geological features to mineral deposits is translated into spatial evidence and evidential belief functions are estimated for the proposition that mineral deposits exist in a test area. The integrated maps of degrees of belief for the proposition that mineral deposits exist in a test area is classified into a binary mineral potential map. For the Baguio district (Philippines), the binary gold potential map delineates (a) about 74% of the training data (i.e., locations of large-scale gold deposits) and (b) about 64% of the validation data (i.e., locations of small-scale gold deposits). The results demonstrate the usefulness of a geologically constrained mineral potential mapping using data-driven evidential belief functions to guide further surficial exploration work in the search for yet undiscovered gold deposits in the Baguio district. The results also indicate the usefulness of evidential belief functions for mapping uncertainties in the geologically constrained integrated predictive model of gold potential.

Knowledge-Driven and Data-Driven Fuzzy Models for Predictive Mineral Potential Mapping

In this paper, we describe new fuzzy models for predictive mineral potential mapping: (1) a knowledge-driven fuzzy model that uses a logistic membership function for deriving fuzzy membership values of input evidential maps and (2) a data-driven model, which uses a piecewise linear function based on quantified spatial associations between a set of evidential evidence features and a set of known mineral deposits for deriving fuzzy membership values of input evidential maps. We also describe a graphical defuzzification procedure for the interpretation of output fuzzy favorability maps. The models are demonstrated for mapping base metal deposit potential in an area in the south-central part of the Aravalli metallogenic province in the state of Rajasthan, western India. The data-driven and knowledge-driven models described in this paper predict potentially mineralized zones, which occupy less than 10% of the study area and contain at least 83% of the “model” and “validation” base metal deposits. A cross-validation of the favorability map derived from using one of the models with the favorability map derived from using the other model indicates a remarkable similarity in their results. Both models therefore are useful for predicting favorable zones to guide further exploration work.

Artificial Neural Networks for Mineral-Potential Mapping: A Case Study from Aravalli Province, Western India

This paper describes a GIS-based application of a radial basis functional link net (RBFLN) to map the potential of SEDEX-type base metal deposits in a study area in the Aravalli metallogenic province (western India). Available public domain geodata of the study area were processed to generate evidential maps, which subsequently were encoded and combined to derive a set of input feature vectors. A subset of feature vectors with known targets (i.e., either known mineralized or known barren locations) was extracted and divided into (a) a training data set and (b) a validation data set. A series of RBFLNs were trained to determine the network architecture and estimate parameters that mapped the maximum number of validation vectors correctly to their respective targets. The trained RBFLN that gave the best performance for the validation data set was used for processing all feature vectors. The output for each feature vector is a predictive value between 1 and 0, indicating the extent to which a feature vector belongs to either the mineralized or the barren class. These values were mapped to generate a predictive classification map, which was reclassified into a favorability map showing zones with high, moderate and low favorability for SEDEX-type base metal deposits in the study area. The method demarcates successfully high favorability zones, which occupy 6% of the study area and contain 94% of the known base metal deposits.

Geologically Constrained Fuzzy Mapping of Gold Mineralization Potential, Baguio District, Philippines

An application of the theory of fuzzy sets to the mapping of gold mineralization potential in the Baguio gold mining district of the Philippines is described. Proximity to geological features is translated into fuzzy membership functions based upon qualitative and quantitative knowledge of spatial associations between known gold occurrences and geological features in the area. Fuzzy sets of favorable distances to geological features and favorable lithologic formations are combined using fuzzy logic as the inference engine. The data capture, map operations, and spatial data analyses are carried out using a geographic information system. The fuzzy predictive maps delineate at least 68% of the known gold occurrences that are used to generate the model. The fuzzy predictive maps delineate at least 76% of the “unknown” gold occurrences that are not used to generate the model. The results are highly comparable with the results of previous stream-sediment geochemical survey in the area. The results demonstrate the usefulness of a geologically constrained fuzzy set approach to map mineral potential and to redirect surficial exploration work in the search for yet undiscovered gold mineralization in the mining district. The method described is applicable to other mining districts elsewhere.

A hybrid neuro - fuzzy model for mineral potential mapping

A GIS-based hybrid neuro-fuzzy approach to mineral potential mapping implements a Takagi–Sugeno type fuzzy inference system in a four-layered feed-forward adaptive neural network. In this approach, each unique combination of predictor patterns is considered a feature vector whose components are derived by knowledge-based ordinal encoding of the constituent predictor patterns. A subset of feature vectors with a known output target vector (i.e., unique conditions known to be associated with either a mineralized or a barren location), extracted from a set of all feature vectors, is used for the training of an adaptive neuro-fuzzy inference system. Training involves iterative adjustment of parameters of the adaptive neuro-fuzzy inference system using a hybrid learning procedure for mapping each training vector to its output target vector with minimum sum of squared error. The trained adaptive neuro-fuzzy inference system is used to process all feature vectors. The output for each feature vector is a value that indicates the extent to which a feature vector belongs to the mineralized class or the barren class. These values are used to generate a favorability map. The procedure is applied to regional-scale base metal potential mapping in a study area located in the Aravalli metallogenic province (western India). The adaptive neuro-fuzzy inference system demarcates high favorability zones occupying 9.75% of the study area and identifies 96% of the known base metal deposits. This result is significant both in terms of reduction in search area and the percentage of deposits identified.

Bayesian network classifiers for mineral potential mapping

In this paper, we describe three Bayesian classifiers for mineral potential mapping: (a) a naive Bayesian classifier that assumes complete conditional independence of input predictor patterns, (b) an augmented naive Bayesian classifier that recognizes and accounts for conditional dependencies amongst input predictor patterns and (c) a selective naive classifier that uses only conditionally independent predictor patterns. We also describe methods for training the classifiers, which involves determining dependencies amongst predictor patterns and estimating conditional probability of each predictor pattern given the target deposit-type. The output of a trained classifier determines the extent to which an input feature vector belongs to either the mineralized class or the barren class and can be mapped to generate a favorability map. The procedures are demonstrated by an application to base metal potential mapping in the proterozoic Aravalli Province (western India). The results indicate that although the naive Bayesian classifier performs well and shows significant tolerance for the violation of the conditional independence assumption, the augmented naive Bayesian classifier performs better and exhibits finer generalization capability. The results also indicate that the rejection of conditionally dependent predictor patterns degrades the performance of a naive classifier.

Mapping of anomalies in continuous and discrete fields of stream sediment geochemical landscapes

ABSTRACT In this study, continuous field models of geochemical landscapes were obtained by interpolating stream sediment geochemical data while discrete field models of geochemical landscapes were obtained by attributing stream sediment geochemical data to their sample catchment basins. This study aimed to: (1) compare and contrast anomaly maps derived from continuous and discrete field models of stream sediment geochemical landscapes; and (2) determine which empirical frequency distributions – those of original point data or those of pixels values in models of stream sediment geochemical landscapes – are more useful in mapping of anomalies in such geochemical landscapes. Anomalies were mapped by using the mean+2SDEV (standard deviation), median+2MAD (median absolute deviation) and concentration–area (C–A) fractal methods of identifying threshold values in a geochemical data set. The results of the study in the Aroroy gold district (Philippines) highlight the following findings. In mapping of anomalies in either continuous or discrete field models of stream sediment geochemical landscapes, the C–A fractal method performs best, followed by the median+2MAD method and then by the mean+2SDEV method. Anomalies mapped in discrete field models, compared to anomalies mapped in continuous field models, of stream sediment geochemical landscapes mostly have stronger positive spatial associations with the known epithermal Au deposit occurrences in the study area. Empirical frequency distributions of either the original point data or the pixels values in the models of stream sediment geochemical landscapes are similarly useful in applying the C–A fractal method, but not in applying either the median+2MAD or mean+2SDEV method, to map anomalies in either continuous or discrete field models of such geochemical landscapes.

Where Are Porphyry Copper Deposits Spatially Localized? A Case Study in Benguet Province, Philippines

To provide guides for exploration of porphyry copper mineralization at a district scale, we examine the spatial association between known porphyry copper deposits and geologic features in Benguet, Philippines. The spatial associations between the porphyry copper deposits and strike-slip fault discontinuities, batholithic pluton margins and porphyry plutons are quantified using weights of evidence modeling. In the training and testing district, the porphyry copper occurrences are associated spatially with strike-slip fault discontinuities, batholithic pluton margins and contacts of porphyry plutons within distances of 3 km, 2.25 km, and 1 km, respectively. In addition, the porphyry plutons are associated spatially with strike-slip fault discontinuities and contacts of batholithic plutons within a distance of 2.25 km and 3 km, respectively. Based on these significant spatial associations, predictive maps are generated to delineate zones favorable for porphyry copper mineralization and zones favorable for emplacement of porphyry plutons in Benguet province, Philippines. Validations of the predictive models demonstrate their efficacy in pointing to zones for subsequent follow-up exploration work.

Logistic Regression for Geologically Constrained Mapping of Gold Potential, Baguio District, Philippines

An application of logistic regression to mapping of gold potential in the Baguio district of the Philippines is described. Categorical map data such as lithologic units and proximity classes of curvi-linear features, based on spatial association analyses, are quantified systematically and used as independent variables in logistic regression to predict the probability for presence or absence of gold mineralization. Regression experiments to compare between using all independent variables that are associated spatially with the response variable and using only statistically significant independent variables are performed. The results of the regression experiments are similar; however, the use of all independent variables produces slightly optimistic results but better prediction rates for the known gold deposits in the test district. At least 68% of the ‘model’ large-scale gold deposits and at least 76% of the ‘validation’ small-scale gold deposits were predicted correctly. The predicted geologically favorable zones are also similar to delineated geochemically anomalous zones. The technique presented using logistic regression as a data integration tool is effective for geologically constrained technique of mapping mineral potential.

A catchment basin approach to the analysis of reconnaissance geochemical - geological data from Albay province, Philippines

Abstract A systematic approach for identifying mineral exploration target areas from reconnaissance stream sediment data without sufficient a-priori control information has been demonstrated in a portion of western Albay Province in the southern Bicol Peninsula of the Philippines. The approach involved devising a rapid method of catchment basin mapping using a geographic information system (GIS) so that the areal influence of the catchment basins may be incorporated in the geochemical data analysis. Areal proportions of mapped rock units occurring in the sample catchment basins and observed Mn and Fe contents in stream sediments are used as independent variables in multiple regression analysis to predict element contents in stream sediments related to lithologic and chemical controls. The predicted element contents are filtered-out from the original data to leave residuals in which the effects of other factors (e.g., mineralization) may be seen. A simple correction for the effects of downstream dilution is applied; this allows for the different sizes of the sample catchment basins so that positive geochemical residuals are enhanced. The inter-relationship of the different positive residuals in ‘highly enriched’ samples are investigated through principal components analysis to determine and quantify an ‘anomalous geochemical signature’. Lastly, the ‘anomalous geochemical signature’ is integrated with ‘proximity’ to faults/fractures to determine favourable target areas. For the test region, the lithologic controls explain between 80% and 100% of the variability in most of the elements studied. Chemical controls account for generally less than 5% of the variability in the data. Most of the dilution-corrected residuals reveal high relative enrichment in certain areas underlain by andesite and/or diorite. An anomalous Cu-Mg-Fe-Zn geochemical signature is disclosed by the principal components analysis of the dilution-corrected residuals in ‘highly enriched’ samples. Most sample catchment basins defined by this ‘anomalous geochemical signature’ pertain to areas underlain by andesitic rocks. Integration of the ‘anomalous geochemical signature’ and ‘proximity’ to faults/fractures reveals that some of these anomalous sample catchment basins are favourable target areas. These areas are interpreted to contain andesite-hosted stockwork or stringer zones that once formed part of a complete stratigraphic sequence of a volcanogenic massive sulphide occurrence. The results demonstrate the usefulness and ability of the procedures followed to extract significant anomalies from the reconnaissance geochemical data without the benefit of sufficient a-priori control data to aid in anomaly recognition. Similar procedures could also be applied elsewhere.