The use of dempster-shafer model and GIS in integration of geoscientific data for porphyry copper potential mapping, north of Shahr-e-Babak, Iran
Majid Hashemi Tangestani Farid Moore
Dept. of Geology, Faculty of Sciences
Shiraz University, 71454, Shiraz, Iran
The Dempster-Shafer belief theory, as a knowledge-driven approach for map combination, is used for porphyry copper potential mapping, in an under-explored area, north of Shahr-e-Babak, Iran. The evidential function provides a theoretical basis for uncertainty management in data integration in an exploration project. The results of this approach show that strong support is found in the west-central part of the study area, where porphyry copper deposits are known. Plausibility for the proposition is also high in the west-central parts and coincides with the zone having strong support. The uncertainty is low in the west-central parts where there are more efficient data layers with respect to the proposition. Uncertainty is high in the zones where either there are fewer data layers or the data can not provide strong support for the proposition or its negation.
Exploration projects carried out in unexplored regions are mostly based on geoscientific information that are integrated and processed by the use of GIS-based decision making models. Although some of the map-based approaches allow one to estimate probabilities based on known exploration target occurrences (Bonham-Carter et al. 1988, Rencz et al. 1994, Scott 2000), recent advances in exploration models and decision support systems make it possible to quantify specific map information even when there are small known or no target mineral occurrences in an exploration area (An et al. 1991, An 1992, Wright and Bonham-Carter 1996). Because many regions in Iran are not well-explored and only a few occurrences or deposits are known, the Dempster-Shafer belief approach could be tested and evaluated for porphyry copper potential mapping and new target-area recognition.
The Dempster-Shafer belief theory (Dempster 1968 and Shafer 1976) is an alternative mechanism to the fuzzy logic theory for knowledge representation and map combination. This method has been discussed in a mineral exploration context using a data set (An 1992, An et al. 1994a, and 1994b, Chung and Fabbri 1993, Chung and Moon 1991). Wright and Bonham-Carter (1996) applied the method to combine a variety of geophysical data sets to predict base metal and iron-formation deposits in an area north and west of the Rusty Lake-Snow lake Greenstone Belts, Manitoba, Canada. Aminzadeh (1994) also describes the application of this model in oil exploration.
Belief Function Theory
A detailed theoretical exposition and a formalization of the belief function approach can be found in Dempster (1968) and Shafer (1976). It is a knowledge-driven approach (Bonham-Carter 1994), with some advantages and disadvantages as compared with fuzzy logic (Zadeh 1965). For example, one advantage of this approach is that it allows the user to represent uncertainty in the knowledge representation, because the interval between support (lower belief function or a conservative estimate for a proposition) and plausibility (an optimistic assessment that the evidence supports a proposition) can be considered as a confidence band. Missing data also could be modelled in Dempster-Shafer approach by defining the plausibility as 1, the support as 0, so the uncertainty as 1. Evidences from two or more maps are combined using Dempster’s rule of combination (Wright and Bonham-Carter 1996, and Equations 1-3 cited here). The combined support, plausibility, disbelief, and uncertainty can each be separately mapped, although only two of these quantities are independent. This contrasts with the fuzzy logic output, which consists only of a single map- the combined fuzzy membership. The output map in fuzzy model only evaluates the favourability for porphyry copper mineralization in various levels for the study area, but the outputs in D-S model represent a conservative estimate of the favourability, an optimistic estimate of favourability, and related uncertainties in different images.