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 time‐domain 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 re‐parameterisations for inverting field data will contribute to narrow the gap between induced polarization theory, laboratory findings, and field applications.

Time-domain induced polarization -an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion,

The induced polarization phenomenon, both in time-domain (TD) and frequencydomain (FD), is often parameterized 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 here suggest three reparametrizations of the Cole-Cole model, namely the Maximum Phase Angle (MPA) Cole-Cole model, the Maximum Imaginary Conductivity (MIC) Cole-Cole model and the Minimum Imaginary Resistivity (MIR) Cole-Cole model. The MPA Cole-Cole model uses the maximum phase 𝜑 𝑚𝑎𝑥 and the inverse of the phase peak frequency, 𝜏 𝜑 , instead of the intrinsic chargeability 𝑚 0 and the time constant adopted in the classic Cole-Cole model; the MIC Cole-Cole model uses the maximum imaginary conductivity 𝜎 ′′ 𝑚𝑎𝑥 instead of the 𝑚 0 , and the time constant 𝜏 𝜎 of the Cole-Cole model in its conductivity form; the MIR Cole-Cole model uses the minimum imaginary resistivity 𝜌 ′′ 𝑚𝑖𝑛 instead of the 𝑚 0 , and the time constant 𝜏 𝜌 of the Cole-Cole model in its resistivity form. The effects of the three re-parameterizations have been tested on synthetic TD and FD 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-parameterizations the model parameters are less correlated with each other and, consequently, better resolved for both TD and FD data. The increase in model resolution is particularly significant for models that are poorly resolved using the classic Cole-Cole parameterization, for instance for low values of the frequency exponent or with

The principle of equivalence is known to cause nonuniqueness in interpretations of direct current (DC) resistivity data. Low-or high-resistivity equivalences arise when a thin geologic layer with a low/high resistivity is embedded in a relative high-/low-resistivity background formation causing strong resistivity-thickness correlations. The equivalences often make it impossible to resolve embedded layers. We found that the equivalence problem could be significantly reduced by combining the DC data with full-decay time-domain induced polarization (IP) measurements. We applied a 1D Markov chain Monte Carlo algorithm to invert synthetic DC data of models with low-and high-resistivity equivalences. By applying this inversion method, it is possible to study the space of equivalent models that have an acceptable fit to the observed data, and to make a full sensitivity analysis of the model parameters. Then, we include a contrast in chargeability into the model, modeled in terms of spectral Cole-Cole IP parameters, and invert the DC and IP data in combination. The results show that the addition of IP data largely resolves the DC equivalences. Furthermore, we present a field example in which DC and IP data were measured on a sand formation with an embedded clay layer known from a borehole drilling. Inversion results show that the DC data alone do not resolve the clay layer due to equivalence problems, but by adding the IP data to the inversion, the layer is resolved.

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