Comment on: Tarasov, A. & Titov, K., 2013, On the use of the Cole–Cole equations in spectral induced polarization, Geophys. J. Int., 195, 352–356

Abstract

A recent paper by Tarasov and Titov suggested that the Cole-Cole conductivity models should be preferred to the Pelton resistivity model in fitting induced polarization responses. Each model has four parameters: resistivity rho (or its inverse conductivity sigma), chargeability m, time parameter tau and frequency dependence c. Tarasov and Titov showed that in fitting experimental data, 3 of the parameters directly correspond across the two formulations, but that there is a difference between the Pelton and Cole-Cole model in that parameter tau is only the same at low frequency, but is an entangled function with m and c at high frequencies in the Pelton formulation. This claim of inconsistent tau was based on using the Pelton complex resistivity formulation and the Cole-Cole complex conductivity equation to analyse complex conductivity data as a function of frequency. However, if Pelton and Cole-Cole models are used to fit complex resistivity, rather than fitting conductivity, then it is the Cole-Cole model that has an entangled parameter at high chargeability m values. Simple testing shows that a Pelton model used to fit resistivity has all four model parameters directly corresponding with conductivity data fitted with a Cole-Cole model. The conclusion is that Cole-Cole and Pelton models in fact require identical independent parameters that can fit experimental or synthetic data, provided the Pelton resistivity formulation is restricted to fitting to resistivity data, and the Cole-Cole conductivity formulation is restricted to fitting conductivity results.