Conversion of Induced Polarization Data and Their Uncertainty from Time Domain to Frequency Domain Using Debye Decomposition

Abstract

The time-domain (TD) induced polarization (IP) method is used as an extension of direct current (DC) resistivity measurements to capture information on the ability of the subsurface to develop electrical polarization. In the TD, the transient voltage decay is measured after the termination of the current injection. To invert tomographic TD IP data sets into frequency-domain (FD) models of complex electrical resistivity, a suitable approach for converting TD IP transients and their corresponding uncertainties into the FD is essential. To apply existing FD inversion algorithms to TD IP measurements, a conversion scheme must transform the measured decay curves into FD impedances and also propagate the corresponding measurement uncertainty from the TD to the FD. Here, we present such an approach based on a Debye decomposition (DD) of the decay curve into a relaxation-time distribution and the calculation of the equivalent spectrum. The corresponding FD data error can be obtained by applying error propagation through all of these steps. To accomplish the DD we implement a non-linear Gauss–Newton inversion scheme. We test the conversion scheme in a synthetic study and demonstrate its application to field data on a tomographic TD IP data set measured on the Maletoyvaemskoie ore field (Kamchatka, Russia). The proposed conversion scheme yields accurate impedance data for relaxation processes, which are resolved by the TD measurements. The error propagation scheme provides a reasonable FD uncertainty estimate, as confirmed by a Monte Carlo analysis of the underlying parameter distributions.