Alok Porwal

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.

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.

Extended Weights-of-Evidence Modelling for Predictive Mapping of Base Metal Deposit Potential in Aravalli Province, Western India

Approaches to mineral potential mapping based on weights of evidence generally use binary maps, whereas, real-world geospatial data are mostly multi-class in nature. The consequent reclassification of multi-class maps into binary maps is a simplification that might result in a loss of information. This paper describes results of using multi-class evidential maps in an extended weights-of-evidence model vis-a-vis results of using binary evidential maps in a simple-weights-of-evidence model. The study area in the south-central part of Aravalli province (western India) hosts a number of SEDEX-type base metal deposits in Proterozoic supracrustal rocks. Recognition criteria for base metal deposits were represented as both multi-class and binary evidential maps. The known mineral deposits were divided into two subsets, viz., the training and the validation subsets. The training subset was used to calculate, for the evidential maps, the weights, contrasts, and posterior probabilities and their variances. The distributions of expected frequencies of base metal deposits estimated from the posterior probabilities and the observed frequencies were compared using standard goodness-of-fit tests to verify conditional independence of the input evidential maps. The posterior probabilities from both the models were mapped and interpreted to classify the study area into zones favorable, permissive, and non-permissive for base metal deposit occurrence. As compared to the simple weights-of-evidence model, the extended weights-of-evidence model results in more robust and finely differentiated posterior probabilities in favorable and permissive zones and has a better prediction rate. The results also reveal that the statistical properties of the weights of evidence, the contrasts, and the posterior probabilities are not significantly degenerated by using multi-class evidential maps in weights-of-evidence modelling.

Probabilistic Fuzzy Logic Modeling: Quantifying Uncertainty of Mineral Prospectivity Models Using Monte Carlo Simulations

Significant uncertainties are associated with the definition of both the exploration targeting criteria and computational algorithms used to generate mineral prospectivity maps. In prospectivity modeling, the input and computational uncertainties are generally made implicit, by making a series of best-guess or best-fit decisions, on the basis of incomplete and imprecise information. The individual uncertainties are then compounded and propagated into the final prospectivity map as an implicit combined uncertainty which is impossible to directly analyze and use for decision making. This paper proposes a new approach to explicitly define uncertainties of individual targeting criteria and propagate them through a computational algorithm to evaluate the combined uncertainty of a prospectivity map. Applied to fuzzy logic prospectivity models, this approach involves replacing point estimates of fuzzy membership values by statistical distributions deemed representative of likely variability of the corresponding fuzzy membership values. Uncertainty is then propagated through a fuzzy logic inference system by applying Monte Carlo simulations. A final prospectivity map is represented by a grid of statistical distributions of fuzzy prospectivity. Such modeling of uncertainty in prospectivity analyses allows better definition of exploration target quality, as understanding of uncertainty is consistently captured, propagated and visualized in a transparent manner. The explicit uncertainty information of prospectivity maps can support further risk analysis and decision making. The proposed probabilistic fuzzy logic approach can be used in any area of geosciences to model uncertainty of complex fuzzy systems.

Suppression of vegetation in multispectral remote sensing images

Vegetation cover is an impediment to the interpretation of multispectral remote sensing images for geological applications, especially in densely vegetated terrains. In order to enhance the underlying geological information in such terrains, it is desirable to suppress the reflectance component of vegetation. This article adapts the forced invariance technique proposed by Crippen and Blom (2001) for the suppression of the vegetation reflectance component in a densely vegetated study area in northern Zhejiang province, eastern China. The approach uses a three-step process that comprises: (i) masking of barren or sparsely vegetated areas using a normalized difference vegetation index (NDVI) mask in order to retain their original spectral information through the subsequent processing; (ii) applying a forced invariance technique to subtract the spectral response of vegetation only in vegetated areas; and (iii) combining the processed vegetated areas with the masked barren or sparsely vegetated areas followed by a histogram equalization to eliminate the differences in colour scales between these two types of area. An evaluation based on comparison with the geological map shows that the forced invariance technique results in significant enhancement of the geological information in the processed image.

A Local Brightness Normalization LBN algorithm for destriping Hyperion images

A hybrid algorithm based on global moments matching and local brightness normalization is proposed for correcting vertical stripes in Hyperion images. Two types of vertical stripes are identified: (1) global stripes comprising entire columns of dark pixels with brightness values lower than the global brightness, and (2) local stripes comprising intermittent segments of pixels within a specific column that have lower brightness values compared with the local neighbourhood brightness. The proposed algorithm operates in four steps. First, a minimum noise fraction-transformation-based filtering is used to minimize spatially decorrelated noise. Then no-data pixels values are corrected. Next, global stripes are demarcated and corrected. Finally, local stripes are flagged and corrected. Applications of the proposed algorithm to two Hyperion datasets show significant reduction in vertical stripes.

Random Forest-Based Prospectivity Modelling of Greenfield Terrains Using Sparse Deposit Data: An Example from the Tanami Region, Western Australia

AbstractData-driven prospectivity modelling of greenfields terrains is challenging because very few deposits are available and the training data are overwhelmingly dominated by non-deposit samples. This could lead to biased estimates of model parameters. In the present study involving Random Forest (RF)-based gold prospectivity modelling of the Tanami region, a greenfields terrain in Western Australia, we apply the Synthetic Minority Over-sampling Technique to modify the initial dataset and bring the deposit-to-non-deposit ratio closer to 50:50. An optimal threshold range is determined objectively using statistical measures such as the data sensitivity, specificity, kappa and per cent correctly classified. The RF regression modelling with the modified dataset of close to 50:50 sample ratio of deposit to non-deposit delineates 4.67% of the study area as high prospectivity areas as compared to only 1.06% by the original dataset, implying that the original “sparse” dataset underestimates prospectivity.

Integration of contextual knowledge in unsupervised sub-pixel classification

In this paper, we investigate the use of coarse image features for predicting class label distributions at a finer scale. The major contributions of this work are 1) use of coarse image features to improve the optimization formulation of conventional rank based approaches 2) use of inter class compatibility information from coarse images to refine the predicted target distribution 3) an enhanced unsupervised variogram based sub-pixel mapping approach 4) inclusion of abundance estimation uncertainty in the unmixing process. The proposed modifications on rank based and variogram based approaches have produced an accuracy improvement of 10–15%. The sensitivities of these approaches towards tunable parameters are also analyzed.