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.     

A Modified Weights-of-Evidence Method for Mineral Potential Prediction Based on Structural Equation Modeling

Structural equation modeling (SEM) was applied here to modify the ordinary weights-of-evidence (WofE) method for calculating posterior probability to improve conditional independence (CI) in the application of this method mineral potential prediction. The new method attempts to reduce the effect of CI by defining new binary patterns with an optimum combination of cutoff values of patterns. The solution is calculated through SEM, and the goodness of fit between evidence and mineral deposit occurrences is evaluated by a specified target function. The main difference between the new WofE and ordinary WofE is that evidence in the new method maintains a balance between the significance for mineral potential prediction and CI, rather than the significance for mineral prediction only as in ordinary WofE. A case study of prediction of potential for hydrothermal Au mineral deposits in Nova Scotia, Canada, is discussed here. The results indicate that the new method performs better than the ordinary WofE.

     

Weights of Evidence Modeling of Mineral Potential: A Case Study Using Small Number of Prospects,Abra, Philippines

Weights of evidence (WofE) modeling usually is applied to map mineral potential in areas with large number of deposits/prospects. In this paper, WofE modeling is applied to a case study area measuring about 920 km² with 12 known porphyry copper prospects. A pixel size of 100 m × 100 m was used in the spatial data analyses to represent in a raster-based GIS lateral extents of prospects and of geological features considered as spatial evidence. Predictor maps were created based on (a) estimates of studentized values of positive spatial association between prospects and spatial evidence; (b) proportion of number of prospects in zones where spatial evidence is present; and (c) geological interpretations of positive spatial association between prospects and spatial evidence. Uncertainty because of missing geochemical evidence is shown to have an influence on tests of assumption of conditional independence (CI) among predictor maps with respect to prospects. For the final predictive model, assumption of CI is rejected based on omnibus test but is accepted based on a new omnibus test. The final predictive model, which delineates 30% of study area as zones with potential for porphyry copper, has 83% success rate and 73% prediction rate. The results demonstrate plausibility of WofE modeling of mineral potential in large areas with small number of mineral prospects.     

Fuzzy Weights of Evidence Method and Its Application in Mineral Potential Mapping

This paper proposes a new approach of weights of evidence method based on fuzzy sets and fuzzy probabilities for mineral potential mapping. It can be considered as a generalization of the ordinary weights of evidence method, which is based on binary or ternary patterns of evidence and has been used in conjunction with geographic information systems for mineral potential mapping during the past few years. In the newly proposed method, instead of separating evidence into binary or ternary form, fuzzy sets containing more subjective genetic elements are created; fuzzy probabilities are defined to construct a model for calculating the posterior probability of a unit area containing mineral deposits on the basis of the fuzzy evidence for the unit area. The method can be treated as a hybrid method, which allows objective or subjective definition of a fuzzy membership function of evidence augmented by objective definition of fuzzy or conditional probabilities. Posterior probabilities calculated by this method would depend on existing data in a totally data-driven approach method, but depend partly on expert's knowledge when the hybrid method is used. A case study for demonstration purposes consists of application of the method to gold deposits in Meguma Terrane, Nova Scotia, Canada.     

Developing a geographic expert system for regional mapping of volcanogenic massive sulfide (VMS) deposit potential

A personal computer-based geographic information system (GIS) is used to develop a geographic expert system (GES) for mapping and evaluating volcanogenic massive sulfide (VMS) deposit potential. The GES consists of an inference network to represent expert knowledge, and a GIS to handle the spatial analysis and mapping. Evidence from input maps is propagated through the inference network, combining information by means of fuzzy logic and Bayesian updating to yield new maps showing evaluation of hypotheses. Maps of evidence and hypotheses are defined on a probability scale between 0 and 1. Evaluation of the final hypothesis results in a mineral potential map, and the various intermediate hypotheses can also be shown in map form.The inference net, with associated parameters for weighting evidence, is based on a VMS deposit model for the Chisel Lake deposit, a producing mine in the Early Protoerzoic Snow Lake greenstone belt of northwest Manitoba. The model is applied to a small area mapped at a scale of 1:15,840. The geological map, showing lithological and alteration units, provides the basic input to the model. Spatial proximity to contacts of various kinds are particularly important. Three types of evidence are considered: stratigraphic, heat source, and alteration. The final product is a map showing the relative favorability for VMS deposits. The model is implemented as aFortran program, interfaced with the GIS. The sensitivity of the model to changes in the parameters is evaluated by comparing predicted areas of elevated potential with the spatial distribution of known VMS occurrences.     

Quantitative Prediction and Evaluation of Mineral Resources Based on GIS: A Case Study in Sanjiang Region,Southwestern China

Quantitative prediction and evaluation of mineral resources are one of the important topics of mathematical geology. On the basis of GIS technologies and weights of evidence modeling, MapGIS is integrated with GIS and mineral-resource prediction and evaluation. The final product is a predictor map of posterior probabilities of occurrence of the discrete event within a small unit cell. Predictor layers were created on a digital database that includes 1:200,000 scale geological, and geochemical, and geophysical maps, and remote-sensing images in study area. According to metallogenetic factors extractiont and weights of evidence modeling, there are four main metal ore belts in the study area: (1) the Batang belt; (2) the Lei Wuqi belt; (3) the Basu-Chayu belt; and (4) the Ganzi-Litang belt. The predictor map of posterior probabilities show that 29% of study area as zones with potential for porphyry copper, and 81% known mineral occurrences success rate is circled in the metallogenetic posterior probabilities map. The results demonstrate plausibility of weights-of-evidence modeling of mineral potential in large areas with small number of mineral prospects.     

Geologically Constrained Probabilistic Mapping of Gold Potential, Baguio District, Philippines

Binary predictor patterns of geological features are integrated based on a probabilistic approach known as weights of evidence modeling to predict gold potential. In weights of evidence modeling, the log _e of the posterior odds of a mineral occurrence in a unit cell is obtained by adding a weight, W ⁺ or W ^– for presence of absence of a binary predictor pattern, to the log _e of the prior probability. The weights are calculated as log _e ratios of conditional probabilities. The contrast, C = W ⁺ – W ^–, provides a measure of the spatial association between the occurrences and the binary predictor patterns. Addition of weights of the input binary predictor patterns results in an integrated map of posterior probabilities representing gold potential. Combining the input binary predictor patterns assumes that they are conditionally independent from one another with respect to occurrences.     

Spatial Modeling for Base-Metal Mineral Exploration Through Integration of Geological Data Sets

This study involves the integration of information interpreted from data sets such as LandsatTM, Airborne magnetic, geochemical, geological, and ground-based data of Rajpura—Dariba,Rajasthan, India through GIS with the help of (1) Bayesian statistics based on the weights ofevidence method and (2) a fuzzy logic algorithm to derive spatial models to target potentialbase-metal mineralized areas for future exploration. Of the 24 layers considered, five layers(graphite mica schist (GMS), calc-silicate marble (CALC), NE-SW lineament 0–2000 mcorridor (L4-NESW), Cu 200–250 ppm, and Pb 200–250 ppm) have been identified from theBayesian approach on the basis of contrast. Thus, unique conditions were formed based onthe presence and absence of these five map patterns, which are converted to estimate posteriorprobabilities. The final map, based on the same data used to determine the relationships, showsfour classes of potential zones of sulfide mineralization on the basis of posterior probability.In the fuzzy set approach, membership functions of the layers such as CALC, GMS, NE-SWlineament corridor maps, Pb, and Cu geochemical maps have been integrated to obtain thefinal potential map showing four classes of favorability index.     

A MaxEnt Model for Mineral Prospectivity Mapping

Mineral prospectivity mapping is an important preliminary step for mineral resource exploration. It has been widely applied to distinguish areas of high potential to host mineral deposits and to minimize the financial risks associated with decision making in mineral industry. In the present study, a maximum entropy (MaxEnt) model was applied to investigate its potential for mineral prospectivity analysis. A case study from the Nanling tungsten polymetallic metallogenic belt, South China, was used to evaluate its performance. In order to deal with model over-fitting, varying levels of β _j -regularization were set to determine suitable β value based on response curves and receiver operating characteristic (ROC) curves, as well as via visual inspections of prospectivity maps. The area under the ROC curve (AUC = 0.863) suggests good performance of the MaxEnt model under the condition of balancing model complexity and generality. The relative importance of ore-controlling factors and their relationships with known deposits were examined by jackknife analysis and response curves. Prediction–area (P–A) curves were used to determine threshold values for demarcating high probability of tungsten polymetallic deposit occurrence within small exploration area. The final predictive map showed that high favorability zones occupy 14.5% of the study area and contain 85.5% of the known tungsten polymetallic deposits. Our study suggests that the MaxEnt model can be efficiently used to integrate multisource geo-spatial information for mineral prospectivity analysis.     

A Comparative Analysis of Weights of Evidence,Evidential Belief Functions,and Fuzzy Logic for Mineral Potential Mapping Using Incomplete Data at the Scale of Investigation

Large amounts of digital data must be analyzed and integrated to generate mineral potential maps, which can be used for exploration targeting. The quality of the mineral potential maps is dependent on the quality of the data used as inputs, with higher quality inputs producing higher quality outputs. In mineral exploration, particularly in regions with little to no exploration history, datasets are often incomplete at the scale of investigation with data missing due to incomplete mapping or the unavailability of data over certain areas. It is not always clear that datasets are incomplete, and this study examines how mineral potential mapping results may differ in this context. Different methods of mineral potential mapping provide different ways of dealing with analyzing and integrating incomplete data. This study examines the weights of evidence (WofE), evidential belief function and fuzzy logic methods of mineral potential mapping using incomplete data from the Carajás mineral province, Brazil to target for orogenic gold mineralization. Results demonstrate that WofE is the best one able to predict the location of known mineralization within the study area when either complete or unacknowledged incomplete data are used. It is suggested that this is due to the use of Bayes’ rule, which can account for “missing data.” The results indicate the effectiveness of WofE for mineral potential mapping with incomplete data.     

A Modified Weights-of-Evidence Method for Regional Mineral Resource Estimation

Weights-of-evidence (WofE) modeling and weighted logistic regression (WLR) are two methods of regional mineral resource estimation, which are closely related: For example, if all the map layers selected for further analysis are binary and conditionally independent of the mineral occurrences, expected WofE contrast parameters are equal to WLR coefficients except for the constant term that depends on unit area size. Although a good WofE strategy is supposed to achieve approximate conditional independence, a common problem is that the final estimated probabilities are biased. If there are N deposits in a study area and the sum of all estimated probabilities is written as S, then WofE generally results in S > N. The difference S − N can be tested for statistical significance. Although WLR yields S = N, WLR coefficients generally have relatively large variances. Recently, several methods have been developed to obtain WofE weights that either result in S = N, or become approximately unbiased. A method that has not been applied before consists of first performing WofE modeling and following this by WLR applied to the weights. This method results in modified weights with unbiased probabilities satisfying S = N. An additional advantage of this approach is that it automatically copes with missing data on some layers because weights of unit areas with missing data can be set equal to zero as is generally practiced in WofE applications. Some practical examples of application are provided.     

Classification of Soil Groups Using Weights-of-Evidence-Method and RBFLN-Neural Nets

Weights-of-Evidence (WofE) and Radial Basis Function Link Net (RBFLN) were applied to soil group mapping in eastern Finland. The data consisted of low altitude airborne geophysical measurements, Landsat 5 TM-satellite image, and digital elevation model (DEM) and slope information derived from it. Probability maps were constructed for each soil group one by one and combined into a prediction map of soil groups using maximum posterior probability (WofE) or pattern membership (RBFLN). Self-Organizing Map (SOM) and Sammon’s Mapping were applied for selecting the data sets for modeling and visualizing the data. The soil types belonging to each soil group used in the Arc-SDM modeling were defined by clusters revealed by the SOM and Sammon’s Mapping algorithms. The soil types with similar characters were collected in the same cluster. Numerical evaluation of the models’ performance was performed using the confusion matrix. The Ratio of Correct Classifications (RCC) for the best WofE model was 0.64 in the training area and 0.61 in the testing area. The RCC for the best RBFLN model was 0.62. Modeling of soil groups using Arc-SDM is time consuming because models need to be constructed for each soil group before combining them into a final prediction map. In this study a simple method was tested for combining the maps. In the future, more attention should be paid to combining the posterior probability models and also to selecting data sets used for modeling.     

Evaluation of Weights of Evidence to Predict Epithermal-Gold Deposits in the Great Basin of the Western United States

The weights-of-evidence method provides a simple approach to the integration of diverse geologic information. The application addressed is to construct a model that predicts the locations of epithermal-gold mineral deposits in the Great Basin of the western United States. Weights of evidence is a data-driven method requiring known deposits and occurrences that are used as training sites in the evaluated area. Four hundred and fifteen known hot spring gold–silver, Comstock vein, hot spring mercury, epithermal manganese, and volcanogenic uranium deposits and occurrences in Nevada were used to define an area of 327.4 km² as training sites to develop the model. The model consists of nine weighted-map patterns that are combined to produce a favorability map predicting the distribution of epithermal-gold deposits. Using a measure of the association of training sites with predictor features (or patterns), the patterns can be ranked from best to worst predictors. Based on proximity analysis, the strongest predictor is the area within 8 km of volcanic rocks younger than 43 Ma. Being close to volcanic rocks is not highly weighted, but being far from volcanic rocks causes a strong negative weight. These weights suggest that proximity to volcanic rocks define where deposits do not occur. The second best pattern is the area within 1 km of hydrothermally altered areas. The next best pattern is the area within 1 km of known placer-gold sites. The proximity analysis for gold placers weights this pattern as useful when close to known placer sites, but unimportant where placers do not exist. The remaining patterns are significantly weaker predictors. In order of decreasing correlation, they are: proximity to volcanic vents, proximity to east-west to northwest faults, elevated airborne radiometric uranium, proximity to northwest to west and north-northwest linear features, elevated aeromagnetics, and anomalous geochemistry. This ordering of the patterns is a function of the quality, applicability, and use of the data. The nine-pattern favorability map can be evaluated by comparison with the USGS National Assessment for hot spring gold–silver deposits. The Spearman's ranked correlation coefficient between the favorability and the National Assessment permissive tracts is 0.5. Tabulations of the areas of agreement and disagreement between the two maps show 74% agreement for the Great Basin. The posterior probabilities for 51 significant deposits in the Great Basin, both used and not used in the model, show the following: 26 classified as favorable; 25 classified as permissive; and 1, Florida Canyon, classified as nonpermissive.The Florida Canyon deposit has a low favorability because there are no volcanic rocks near the deposit on the Nevada geologic map used. The largest areas of disagreement are caused by the USGS National Assessment team concluding that volcanic rocks older than 27 Ma in Nevada are not permissive, which was not assumed in this model. The weights-of-evidence model is evaluated as reasonable and delineates permissive areas for epithermal deposits comparable to expert's delineation. The weights-of-evidence model has the additional characteristics that it is well defined, reproducible, objective, and provides a quantitative measure of confidence.     

Development of a technique to decompose heterogeneous mapping units in a categorical map of the biotic environment using correlated categorical data

In this article a technique is presented to estimate the proportions of different map categories in a series of heterogeneous mapping units, using information on the degree of spatial correlation with other categorical data. The technique has been applied to decompose ecotope complexes in a categorical map of the biotic environment in Flanders, using secondary information on land cover and soil type. Because the conditional probability of an ecotope occurring given a certain soil type depends on the frequency with which the ecotope occurs in an area, determining the probability of occurrence of an ecotope from the conditional probabilities can lead to predictions that contradict prior knowledge about the composition of the different mapping units. A measure expressing the affinity of an ecotope for a soil type is proposed and is used as an alternative to conditional probability in the estimation procedure. The proposed method has been tested in a study area for which detailed field observations were collected, and proves to work well if reliable a priori knowledge about the composition of complex mapping units is available.     

Bayesian and multivariate methods applied to favorability quantification in Recôncavo Basin and Ribeira Belt, Brazil

A methology to define favorable areas in petroleum and mineral exploration is applied, which consists in weighting the exploratory variables, in order to characterize their importance as exploration guides. The exploration data are spatially integrated in the selected area to establish the association between variables and deposits, and the relationships among distribution, topology, and indicator pattern of all variables. Two methods of statistical analysis were compared. The first one is the Weights of Evidence Modeling, a conditional probability approach (Agterberg, 1989a), and the second one is the Principal Components Analysis (Pan, 1993). In the conditional method, the favorability estimation is based on the probability of deposit and variable joint occurrence, with the weights being defined as natural logarithms of likelihood ratios. In the multivariate analysis, the cells which contain deposits are selected as control cells and the weights are determined by eigendecomposition, being represented by the coefficients of the eigenvector related to the system’s largest eigenvalue. The two techniques of weighting and complementary procedures were tested on two case studies: 1. Recôncavo Basin, Northeast Brazil (for Petroleum) and 2. Itaiacoca Formation of Ribeira Belt, Southeast Brazil (for Pb-Zn Mississippi Valley Type deposits). The applied methdology proved to be easy to use and of great assistance to predict the favorability in large areas, particularly in the initial phase of exploration programs.     

Logistic-Based Translation of Orogenic Gold Forming Processes into Mappable Exploration Criteria for Fuzzy Logic Mineral Exploration Targeting in the Kushaka Schist Belt,North-Central Nigeria

This paper applied a logistic-based fuzzy logic inference system to integrate critical factors that could control orogenic gold mineralization in part of the Kushaka schist belt, north-central Nigeria to develop a process-based mineral potential mapping (MPM) of the area. The critical factors from geophysical and geological dataset were weighted using logistic functions. The fuzzy logic inference system provides the capability to handle complex geological processes that culminated in orogenic gold mineralization as well as minimizing systemic uncertainties/fuzziness that often plague MPM. The results of this work show that granitic intrusions with fuzzy scores of 0.67–0.90 played a major role in generating high geothermal gradient in the area. Seventy percent of the existing gold mine sites in the area spatially coincide with metasedimentary rocks, having fuzzy scores of 0.7–0.9; this suggests metasedimentary rocks as being responsible for the production of gold fluid and ligands in the area. The evidence of hydrothermal activity, with fuzzy scores of 0.53 and 0.91, confirms the occurrence of mineralization associated with quartz veins and granite rocks. Lithological contacts and faults, having fuzzy scores of 0.60–0.80, presumably contribute to the localization of orogenic gold mineralization in the area. Emerging from the results, favorable zones for primary orogenic gold mineralization in the area occurred predominantly on granite gneiss and quartz veins. The mineral potential map was found consistent with the local geology, structural styles and hydrothermal alteration signatures in the area, and its validation using the existing locations of geochemical anomalies and prediction–area rate curve in the study area showed 75 and 72% agreement, respectively, thus confirming the reliability of the developed mineral potential map for resource management.

     

Indicator favorability theory for mineral potential mapping

Favorability methods produce a unique measure for mineral potential mapping and quantitative estimation of mineral resources. Indicator favorability theory is developed in this study to account for spatial (auto and cross) correlations of regionalized geological, geochemical, and geophysical fields based on the indicator concept. Target and explanatory indicators are introduced to describe, respectively, direct and indirect evidence of the mineralization of interest. Mineralization is represented by a combination () of a set of target indicators. Indicator favorability theory estimates a regionalized favorability function in two stages: (1) estimate a linear combination of target indicators by maximizing var() and (2) estimate favorability functionF by minimizing estimation variance var[F–]. The model is established on the basis of a conceptual model of target. The favorability estimates can be justified by correlation analysis and cross validation in control areas. The indicator favorability theory is demonstrated on a case study for gold-silver mineral potential mapping based on geophysical, structural, and geochemical fields.     

Measuring the Performance of Mineral-Potential Maps

D. P. Harris and others have proposed a new method for comparative analysis of favorability mappings. In their approach, Weights-of-Evidence (WofE) consistently shows poorer results than other more flexible methods. Information loss because of discretization would be a second drawback of WofE. In this paper, we discuss that the random cell selection method proposed by Harris and others necessarily results in higher success ratios for more flexible methods but this does not necessarily indicate that these methods provide better mineral-potential maps. For example, a good point density contouring method that does not use any geoscience background information also would score high in the random cell selection approach. Additionally, we show that discretization usually is advantageous because it prevents occurrences of overly high posterior probabilities. For more detailed comparison, we have conducted a number of experiments on 90 gold deposits in the Gowganda Area of the Canadian Shield comparing WofE with the more flexible weighted logistic regression method. Mineral occurrences should be modeled as discoveries at points instead of randomly sampling them together with their surrounding environments in small cells.     

Use of Fuzzy Membership Input Layers to Combine Subjective Geological Knowledge and Empirical Data in a Neural Network Method for Mineral-Potential Mapping

Use of GIS layers, in which the cell values represent fuzzy membership variables, is an effective method of combining subjective geological knowledge with empirical data in a neural network approach to mineral-prospectivity mapping. In this study, multilayer perceptron (MLP), neural networks are used to combine up to 17 regional exploration variables to predict the potential for orogenic gold deposits in the form of prospectivity maps in the Archean Kalgoorlie Terrane of Western Australia. Two types of fuzzy membership layers are used. In the first type of layer, the statistical relationships between known gold deposits and variables in the GIS thematic layer are used to determine fuzzy membership values. For example, GIS layers depicting solid geology and rock-type combinations of categorical data at the nearest lithological boundary for each cell are converted to fuzzy membership layers representing favorable lithologies and favorable lithological boundaries, respectively. This type of fuzzy-membership input is a useful alternative to the 1-of-N coding used for categorical inputs, particularly if there are a large number of classes. Rheological contrast at lithological boundaries is modeled using a second type of fuzzy membership layer, in which the assignment of fuzzy membership value, although based on geological field data, is subjective. The methods used here could be applied to a large range of subjective data (e.g., favorability of tectonic environment, host stratigraphy, or reactivation along major faults) currently used in regional exploration programs, but which normally would not be included as inputs in an empirical neural network approach.