Knowledge Driven GIS Modelling Techniques for Copper Prospectivity Mapping in Singhbhum Copper Belt – A Retrospection The predictive model was generated by summing up the various derived maps (comprising of lithological, structural, geochemical, wall rock alteration and geophysical) that provide evidence for copper mineralisation into one or more mineral favourability maps. The overlap combination process of the images involves the weighing and union of evidences by a map combination rule i.e. Index overlay method. The intermediate factor maps are combined to generate maps resulted in the highest cumulative weights in the area where all the recognition criteria co-exist. As discussed earlier in the index overlay method each class of every map is given a different score as well as the maps themselves receiving different weights allowing for a more flexible weighting system. The individual score of the map elements have been discussed in the publication by Mukhopadhyay et. al. (2002a). The map scores assigned to the individual layers of evidences and the inference model is also discussed in detail in the publication listed above. The process and assignment of weights are illustrated in detail in a paper by Mukhopadhyay et. al. (2002a) and the inference network & final result is summarized in Fig.2.  Fig 2. Diagram showing the flowchart and final GIS model of Singhbhum copper Belt By Index Overlay Method c) Fuzzy Inference Modelling: In the classical GIS modeling, the process converts the multiclass maps into binary predictor pattern. The pattern assumes a boundary between favourable and unfavourable ground (Carranza and Hale, 2000). However, the boundary between these two classes is imprecise and thus fuzzy (Carranza and Hale, 2001). Hence, classifying predictor maps on the basis of their mineral favourability needs an imprecise concept that takes care the favourability zones on a gradational basis rather than simply classifying them into classes of membership or nonmembership. As fuzzy set is expressed on a continuous scale from 1 (full membership) to 0 (full nonmembership) (Bonham-Carter, 1994), the inference engine generates map on a gradational pattern depending on the fuzzy membership value, which also takes into consideration the probability and possibility of finding mineral potential in actual ground. In the fuzzy system, the extraction and combination of different evidences, is carried out by operators. An et. al. (1991) discussed five operators, which are found useful for combing the exploration dataset. These are fuzzy and, fuzzy or, fuzzy algebric product, fuzzy algebric sum and fuzzy gamma operators. Out of these five operators: the last four operators have been used in this analysis. The pricipal approaches taken for calculating fuzzy membership values are illustrated below.
d) Vector Fuzzy Modelling: The fuzzy logic methodology discussed above is highly applicable where GIS modeling is based on a conceptual approach i.e. based on a conceptual deposit model. To overcome the deficiencies of gamma (‘g’) function in fuzzy inference modelling, a new and more powerful fuzzy logic method called ‘Vectorial Fuzzy Logic’ is introduced based on vector mathematics that allows a measure of confidence to be included in the prospectivity analysis (Knox-Robinson, 2000). This is probably a unique GIS analytical methodology that takes into consideration the confidence in predicting prospectivity besides grade the area into zones of prospectivity with relative confidence. This method generates two values in each location, one for ‘prospectivity’ related to a particular spatial relationship and the other defining the ‘measure of confidence’. This also takes care of three needs simultaneously: i) particular spatial relationship is represented by confidence of a prospectivity value, ii) the confidence represents overall importance of each spatial relationship relative to other, iii) the confidence value allows the null data value to be used. The two quantities, prospectivity and confidence are treated as vectors, prospectivity as direction of the vector and confidence as magnitude of vector (Knox-Robinson, 2000). In vector fuzzy logic, each prospectivity value (ranging from 0 to 1) is multiplied by p/2 and the resultant number is used to represent the direction, in radians, of the vector. Thus, mutually orthogonal vectors can represent the lowest and highest prospectivity. The length of the vector is used to represent the confidence of the prospectivity value, null value is represented as zero length vector i.e. zero prospectivity. The combination involves calculation of resultant vector for prospectivity (equation 1) and length of the resultant vector related to the confidence of prospectivity (equation 2) (Knox-Robinson, 2000). 
Where mi is the fuzzy prospectivity value for the ith input layer (0 £ m i £ 1, i varies from 1 to n), li is the confidence value for ith input layer, mc is the combined prospectivity value and lc is combined confidence on prospectivity. |