Nihar R. Sahoo, P.Jothimani and G. K. Tripathy
Tata Infotech Ltd, SEEPZ, Mumbai, 400 096
Email: [email protected]
GIS-based analysis of spatial data has been a new specialized process, capable of analyzing complex problem of evaluating and allocating natural resources for targeting potential areas for mineral exploration. This paper explains developing a data-driven decision-tree approach with multi-criteria evaluations in mineral potential mapping at the Hutti-Maski schist belt. An inference network based spatial data integration has been attempted which allows for incorporation of uncertainties into a predictive model. The procedure has produced a posterior probability map identifying favorable areas for gold exploration
Fig 1: Decision tree of the integration of the spatial datasets
GIS in Natural Resources Development
Land resource evaluation and allocation is one of the most fundamental activities of resource development (FAO, 1976). With the advent of GIS, there is ample of opportunities for a more explicitly reasoned land evaluation. Prediction of suitable areas for mineral exploration in a virgin area of specific type are problems that require use of various procedures and tools for development of decision rule and the predictive modeling of expected outcomes. GIS has come out as an emerging tool to address the need of decision makers and to cope with problems of uncertainties. A decision rule typically contains procedures for combining criteria into a single composite index and a statement of how alternatives are to be compared using this index. It is as simple as threshold applied to a single criterion. It is structured in the context of a specific objective. An objective is thus a perspective that serves to guide the structuring of decision rules. To meet a specific objective, it is frequently the case that several criteria will need to be integrated and evaluated, called multi-criteria evaluations. Weighted linear combinations and concordance-disconcordance analysis (Voogd, 1983 and Carver, 1991) are two most common procedures in GIS based multi-criteria evaluations. In the former, each factor is multiplied by a weight and then summed to arrive at a final suitability index, while in the later, each pair of alternatives is analyzed for the degree to which it outranks the other on the specified criteria. The former is straight forward in a raster GIS, while the later is computationally impractical when a large number of alternatives are present.
Information vital to the process of decision support analysis, is rarely perfect in earth sciences. This leads to uncertainties, which arises from the manner in which criteria are combined and evaluated to reach a decision. When uncertainty is present, the decision rule needs to incorporate modifications to the choice function or heuristic to accommodate the propagation of uncertainty through the rule and replace the hard decision procedures of certain data with soft-data of uncertainty. Bayesian probability theory (Bonham-Carter et al., 1988; 1990; 1995), Dempster-Shafer theory (Cambell et al., 1982) and fuzzy set theory (Duda et al., 1977) have been extensively in use in mineral targeting.
Fig 2A: Known mineral occurences at the Hutti-Maski schist belt
Fig 2B: Posterior probability map of potential areas for gold targetting
Theory of multi-criteria evaluation
Multi-criteria evaluation is primarily concerned with how to combine the information from several criteria to form a single index of evaluation. In case of Boolean criteria (constraints), the solution usually lies in the union (logical OR) or intersection (logical AND) of conditions. However, for continuous factors, a weighted linear combination (Voogd, 1983) is a usual technique. As the criteria are measured at different scales, they are standardised and transformed such that all factor maps are positively correlated with suitability. Establishing factor weights is the most complicated aspect, for which the most commonly used technique is the pair-wise comparison matrix.
Evaluation of the relationship between evidence (criteria) and belief is a forward chaining expert system. In this system the propagation of favourability measure through the inference network may include the Bayesian updating and fuzzy logic for computation of posterior values of favourability given evidence(s). In the real world, the evidences and hypotheses are uncertain. We cope with the problem by assigning probability values to evidences (Duda et al., 1977). There is unidirectional propagation of evidences through a hierachial network carries on towards an ultimate hypotheses.
In a rule based inference system, the rules are usually of the form:
If E1 and E2 and E3…………. and En, then H,
Where, Ei(i = 1,2……n) is the ith evidence and H is the associated hypotheses.
In a full fledged inference net, many pieces of evidences are linked to a single final hypotheses using the combination rules of conjunction, disjunction and independence (Bayes).
N different pieces of evidences are assumed to be conditionally independent and the posterior
odds O(H/E) are obtained as
O(H/E1, E2……….En) = O(H) åLEi.
Where, LE is the likelihood of estimate.
Likelihood of estimate, LE is calculated on the basis of the importance of the presence or absence of a criteria on the presence of hypothesis (presence of mineral occurrence). Details on this has been discussed in Bonham-Carter et al.(1990).
The evidence is true only if all the contributing pieces of evidences are true, i.e.,
if E = E1 and E2,and……and En, the joint probability is calculated using fuzzy set theory as
P(E/E’) = Mini(P(Ei/H).
The evidence is true if any of the pieces of evidence is true, that is
if E1 or E2 ….or En,
the joint probability is calculated using fuzzy set theory as
P(E/E’) = Maxi(P(Ei/H)).
When p indicator patterns are considered simultaneously, each unit cell is assigned a posterior probability derived from the prior logits as
logit(d/1,2…….p) = W(1)+………….+ W(p)+ logit(d),
and the posterior probability is calculated as
Mineral potential mapping at the Hutti-Maski schist belt – A case study
The Archaean Hutti-Maski greenstone belt consists predominantly of metavolcanics and subordinate metasediments. This association of rock is surrounded by multiple phases of intrusive diapiric granitoids. Vescicular metabasalt is the host rock for these auriferous lodes. These lodes are localized along shear zones, granite-metabasalt contacts, granophyre-metabasalt contacts and fold axes. The geometry and orientation of the lodes is affected by shear zone. Groundwater and weathered bedrock were most suitable media for detecting the dispersion halos related to mineralization. The generated pedogeochemical, hydrogeochemical, lineament proximity and lithological data were closely associated with the known gold occurrences (Sahoo and Pandalai, 1999; 2000, Sahoo et al., 2000).
Developing the Decision-tree
The data sets that would suffice in targeting potential zones for gold exploration were put to a raster GIS (IDRISI) and analysed empirically the spatial relationship of the factors with the known gold occurrences. The datasets include the lithological map, lineament maps, water chemistry data, trace element concentrations in soil and known deposit map. These maps were rasterised at 30m resolution and all of them were coregistered with a base map. A series of binary maps, i.e. a map showing whether a characteristic is present or not were prepared. During processing, the operations performed were generation of required map classes and selection of lineaments between map classes using vector-raster and introduction of dilation (buffering) to produce proximity maps. The maps used as predictors (evidence) such as proximity of lineament, proximity of favorable geochemical signature and presence/absence of rock-type were modelled with the hypothesis, known mineral occurrences. The optimization is carried out through a decision tree analysis, which partitions the dataset, using the predictor variable at a time, to produce mutually exclusive subsets.
In decision tree approach, integration of pieces of evidences, given hypotheses are combined and updated by propagation of probability for each pixel in a raster GIS. The primary evidence maps are either true-false type with probability values of 1 or 0 respectively or the proximity to feature type with uncertain values 0 and 1. In this paper, the uncertainties associated with the evidence maps are efficiently propagated with the use of fuzzy-logic and Bayesian probabilities while integrating the maps. The predictive modelling strategy for mapping favorable areas for gold targeting involves a decision tree containing few levels of decisions (Fig. 1). The decision model uses boolean operations and Bayesian probability functions to evaluate hypotheses in terms of one or more pieces of evidences. As hypotheses are evaluated, the prior probability is reevaluated to produce posterior probability. The inference engine program was external to the GIS and was interfaced with it. Where geological data was uncertain, the model used fuzzy-logic. The maps were then combined using weights to evaluate how important the presence or absence of a characteristic is, based on the mineral occurrence present in the area.
Integration of pedogeochemical and hydrogeochemical data
The continuous pedogeochemical and hydrogeochemical data were regressed with the binary response variable “deposit proximity”. The hydrogeochemical data included water quality parameters: sulphate, chloride, alkalinity, silica, Ca, Mg, Na, K, As and Sb. The pedogeochemical data included concentrations of As, Sb, Hg and Bi. The factor “deposit proximity” was coded using a corridor width of 0.5 km around the known mineral occurrences. Observations falling within this buffer zone were coded to 1, whereas others were coded to 0.
With hydrogeochemical data, the predicted gold occurrences at the ith location was calculated as
Y = bo + åbjXij.
In practice this was carried out by a step-wise method reducing the number of variables and coefficients requiring interpretation. These regression coefficients represent a multi-element geochemical signature for predicting gold mineralization. These predicted values were interpolated for all the pixels. Similar attempt was made for predicting target areas for gold exploration with the pedogeochemical data.
As both the predicted probability maps were not mutually exclusive, given the mineral occurrence map, Bayesian logic which uses conditional probability could not be used. So these maps were integrated with the use of fuzzy logic. As it was found that both the hydrogeohemical-parameters and pedogeochemistry were controlled by the gold mineralization, fuzzy-AND was used in the integration of the above two maps.
Binary Map Analysis
Integration of binary patterns was carried out with the use of conditional probabilities. The method was more convenient to use than multiple regression for two following reasons,
- It avoids the requirement to subdivide the region into cells, each cell associated with an attribute. In order to capture the geometrical information, large number of small sampling cells must be created and this is undesirable, because of the resulting large attribute file and degree of spatial auto-correlation (Wackernagel, 1995).
- Binary map method is better able to cope with the problem of missing data, as we had. Bayes rule assumes that the patterns are conditionally independent. Chi-square test was carried out to check for the mutual exclusiveness of different maps, given the deposit-proximity map.
- Preparation of binary favourable geochemical signature map (FavGeochem) Preparation of a binary favorable geochemical signature map (FavGeochem) was attempted with the use of conditional probabilities. Several maps of different contour-intervals were prepared. In order to determine the optimum cut-offs of contour interval, for classifying patterns into binary maps, the weights W+ and W- were calculated for a succession of cut-offs and under normal conditions, the maximum value of W+ – W- giving the cut-offs at which the predictive power of the resulting pattern is maximized.
- Integration of the lineaments and preparation of proximity map (FavLin) As most of the lineaments were assumed to have a control on the disposition of the auriferous lodes, and they were not conditionally independent, these maps were integrated with Fuzzy-OR. Preparation of a binary proximity map for lineament (FavLin) was attempted with the use of conditional probabilities. Several buffer zone of different widths were prepared and an optimum cut-off was selected on the technique as described earlier.
- Preparation of binary Favourable lithological map (FavLith)
Similar attempt was made to identify the conditional probability for the rock-type in targeting the gold occurrences. The weights for modelling posterior probabilities of the deposit occurring in 0.9 Km2 area (1 pixel) were as follows
Discussion and Conclusion
The final map is a posterior probability map, showing the suitability of target area delineation for gold deposits. From the weights, shown above it has been seen that the presence of lineaments down weights the probability of gold mineralization, whereas, the presence of favorable geochemical signature and lineament-proximity are strong positive factor. The rock-type is a moderately favorable factor. This technique of multi-crietria analysis in integrating several datasets of varied nature and modelling uncertainties has worked out excellent in mineral resource development. The posterior probability map has identified an unexplored gold potential zone in additions to the known gold potential zones. Decision tree approach of spatial data integration provides a way of identifying target areas for mineral exploration and land resource evaluation and allocation. The inference network is a powerful device for representing expert knowledge, fuzzy-logic and Bayesian logic, allowing for the incorporation of uncertainties into the model. It has an important advantage over expert systems that are limited to deterministic rules. GIS with its flexibility of experimentation and with the inference net model and ability to extract topological attributes from maps, works as a unique tool for land resource evaluation and allocation.
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