GIS@development July 2002: "Integrating exploration dataset in GIS using fuzzy inference modeling"

The Singhbhum Copper Belt, located in Jharkhand state in Eastern India, forms an arcuate linear zone (Fig.1) in the Precambrian Singhbhum Crustal Province (PSCB), houses over 250 million tonnes of copper ore of variable tenor and considered one of the most potential copper sulphide bearing stretch of the country. It is found that only 15% of the total 128 Km stretch of the copper belt shear zone between Bhatin and Badia yield maximum number of economic copper deposits. Five decades of exploration by GSI has generated huge inventory of spatial and related attribute data which need to be relooked again to find out new locales for further exploration, as ore reserves remained stagnant in this belt over a decade. Geological knowledge of an area may play the most important role, if not the only one, in finding out the mineral potential. But unfortunately, in most of the cases, this is a qualitative classification which cannot be transmitted in the modeling environment of GIS. A qualitative spatial representation between geological features in terms of predictive mineral potential model (taking into consideration the nature of known mineralisation), is by far the most vital part in any analysis.

The quantified spatial association between different themes based on exploration model and copper occurrences in PSCB, has already been quantified in an earlier publication (Mukhopadhyay et. al., 2002) by an intuitive knowledge driven approach. Same data layers and weight scheme have been used in this analysis to calculate values for fuzzy membership function and combined by fuzzy logic as inference engine.

GIS Modeling
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 a concept which takes care of the favourability zones on a gradational basis rather than simply classifying them into classes of membership or non membership. As fuzzy set is expressed on a continuous scale from 1 (full membership) to 0 (full non membership) (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.p., et. al. (1991) discussed five operators, which are found useful for combining 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 which deserve elaboration. (Bonham –Carter, 1994).

Fuzzy or is like Boolean or operator (logical union). The output membership values are controlled by the maximum value of input map. The function is defined as
m_Combination = Max (m_A, m_B, m_C, ……)
Fuzzy algebric product is defined as
m_Combination = ⁱ⁼¹Pⁿ (m_i ); Where m_i is the fuzzy membership values of i^th map and i= 1,2,3,..n
The combined fuzzy membership values tend to be very small due to multiplying effect of several numbers less than 1, i.e. the effect is decreasing.
Fuzzy algebric sum is complementary to algebric product and defined as:
m_Combination = 1 - _i=1Pⁿ (1 - m_i ); Where m_i is the fuzzy membership values of i^th map and i= 1,2,3,..n. The result of this operation is always larger than or equal to largest contributing fuzzy membership value i.e. the effect is increasing.
Fuzzy gamma operator is defined as:
m_Combination = (fuzzy algebric sum)^g * (Fuzzy algebric product)^(1-g)
The g value is arbitrary and ranges from 0 to 1. When g is equal to 0 then the combination is fuzzy algebric product. As g is equal to 1 then combination is fuzzy algebric sum.

Application of fuzzy operators on exploration dataset

Brief Geology and Mineralisation
The Singhbhum Shear Zone is developed along the southern fringe of the Proterozoic Fold Belt of North Singhbhum. This fold belt is sandwiched between the Early Archean Cratonic Nucleous represented by Singhbhum and Bonai Granite in the south and Proterozoic Chottanagpur Granite Complex to the north. The intervening gap area between the Singhbhum and Chottanagpur crustal province, is occupied by a curvilinear belt of metasedimentaries belonging to Dhanjori and Singhbhum Group of Proteropzoic age. The Singhbhum shear zone which has developed in this Proterozoic belt, is a northery dipping arcuate ductile shear zone (Ghosh and Sengupta, 1987) marked by lenticular mylonite zone. The width and trend of the shear zone is 10 km and SW-NE in the western part , gradually narrows down to 1 km and E-W in the central part and again widens to more than 5 km and NW-SE in southeastern part. In the southeastern part the shear zone splits into a number of N-S trending narrow shear zones (Banerji,1981). In the western part the shear zone branches out and follows the northern and southern boundary of Chakradharpur Granite Gneiss. The rocks within the Singhbhum shear zone form a tectonic mélange comprising of granite mylonite, quartz-mica phyllonite, quart-tourmaline rock and deformed volcanic and volcanoclastic rocks (Mukhopadhyay and Deb, 1995). The shear sense indicator suggests a thrust type of deformation (Mukhopadhyay and Deb, 1995). The copper mineralised zone runs parallel to Singhbhum Shear Zone.

The principal ore in this belt consists of chalcopyrite, pyrite and pyrrhotite. The ore zones form a number of parallel to sub-parallel discontinuous lodes aligned along the major tectonic grains of the area. Mode of occurrence varies from massive to braided veins, stringers, dissemination and discordant to sheet like bodies. Volcanic origin of the orebody has been suggested by several workers on the basis of d34 S data. Existence of both structural and stratigraphic control on ore localisation is apparent. The general trend of the orebody is controlled by the local trend of shear bands, these bands also act as a channel for remobilisation (Anon, GSI, 1991). Chloritisation, sericitisation, biotitisation, tourmalinisation and albitisation are common wall rock alteration products (Anon, GSI, 1991).