Application of the fractal method to determine the membership function parameter for geoelectrical data (case study: Hamyj copper deposit, Iran)

Abstract

The selection of a suitable membership function and its parameters plays a critical role in the integration of layer information by the fuzzy method. In this paper, parameters of membership function for induced polarization (IP) and resistivity (RS) data (in the Hamyj copper deposit) have been determined by the threshold parameter of IP and resistivity data, already determined by expert opinion or drilling data. The Hamyj deposit is located about 80 km west of Birjand city, South Khorasan province, Iran. In this area, resistivity and induced polarization data have been surveyed by dipole-dipole array. In this paper, outlier-induced polarization data have been corrected by the Doerffel method and then IP and resistivity data have been inversed by the Newton and Gauss-Newton methods. The threshold of the IP data is recognized by statistical (gap statistic) and fractal (concentration-area) methods. The determined threshold by the fractal method is higher than the gap statistic. These two thresholds have been used to determine the S-shape function for the IP data. The thresholds of the RS data are recognized by the fractal method. These two thresholds have been used to determine the Z-shape function for the RS data. The integration of geoelectrical layer information has been carried out by the Gama method. Finally, the best drilling points were proposed based on fuzzy modelling for the area. The results show that the optimum exploration borehole is located at a depth of 25 m.