Resolution of well-known resistivity equivalences by inclusion of time-domain induced polarization data

Abstract

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.