Re-parameterisations of the Cole-Cole model for improved spectral inversion of induced polarization data

The induced polarization phenomenon, both in time domain and frequency domain, is often parameterised using the empirical Cole-Cole model. To improve the resolution of model parameters and to decrease the parameter correlations in the inversion process of induced polarization data, we suggest here three re-parameterisations of the Cole-Cole model, namely the maximum phase angle Cole-Cole model, the maximum imaginary conductivity Cole-Cole model, and the minimum imaginary resistivity Cole-Cole model. The maximum phase angle Cole-Cole model uses the maximum phase φmax and the inverse of the phase peak frequency, τφ, instead of the intrinsic charge-ability m0 and the time constant adopted in the classic Cole-Cole model. The maximum imaginary conductivity Cole-Cole model uses the maximum imaginary conductivity σmax″ instead of m0 and the time constant τσ of the Cole-Cole model in its conductivity form. The minimum imaginary resistivity Cole-Cole model uses the minimum imaginary resistivity ρmin″ instead of m0 and the time constant τρ of the Cole-Cole model in its resistivity form. The effects of the three re-parameterisations have been tested on synthetic timedomain and frequency-domain data using a Markov chain Monte Carlo inversion method, which allows for easy quantification of parameter uncertainty, and on field data using 2D gradient-based inversion. In comparison with the classic Cole-Cole model, it was found that for all the three re-parameterisations, the model parameters are less correlated with each other and, consequently, better resolved for both time-domain and frequency-domain data. The increase in model resolution is particularly significant for models that are poorly resolved using the classic Cole-Cole parameterisation, for instance, for low values of the frequency exponent or with low signal-to-noise ratio. In general, this leads to a significantly deeper depth of investigation for the φmax, σmax″, and ρmin″ parameters, when compared with the classic m0 parameter, which is shown with a field example. We believe that the use of reparameterisations for inverting field data will contribute to narrow the gap between induced polarization theory, laboratory findings, and field applications.