Interpolation of induced polarization transients by the Generalized Cole-Cole relaxation model

We consider a Generalized Cole-Cole (GCC) model as representative of relaxations of electric voltages in time domain Induced Polarization. The purpose of this paper is to present an inversion scheme for determining the parameters describing this relaxation mechanism. The first step consists of interpolating any observed transient by a sum of real exponential terms through application of the rapid and efficient Prony’s algorithm. With the set of exponential parameters we construct the corresponding experimental discrete decay spectrum, which is then compared with precalculated GCC theoretical spectra. This permits an initial guess of the GCC parameters. Then, by Gauss linearization of the frequency-dependent part of the GCC complex resistivity expression, the final values of the GCC parameters are determined by least-squares. The knowledge of these parameters is extremely important in practical application, for discriminating between various mineralized bodies, and for recognizing the presence of oil and hot fluid bearing reservoirs.