On the analysis of Cole-Cole relaxation transients in the induced polarization prospecting method

In this paper we propose an inversion method of induced polarization Cole-Cole relaxation curves, based on the application of Prony's theorem. To this purpose, we analyze at first the relationships between Debye and Cole-Cole decay spectra, and then verify that any Cole-Cole transient can be expanded into a sum of Debye exponential terms to a high degree of approximation. Because of this evidence, we finally develop a least-squares regression procedure for determining the constituent parameters, which characterize the time behavior of a Cole-Cole relaxation mechanism.