1D and 2D Cole‐Cole‐inversion of time‐domain induced‐polarization data

Abstract

A new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole‐Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time‐domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole‐Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D. The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two‐dimensional resistivity model for each time channel. The time‐dependent resistivity of each cell was then interpreted as the response of a homogeneous half‐space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half‐space Cole‐Cole inversion. The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany.

Induced polarization response of porous media with metallic particles — Part 3: A new approach to time-domain induced polarization tomography

“…The Cole-Cole model is a simple parametric representation of the complex conductivity of porous media Macnae, 2015). There have been various attempts to extract the distribution of the Cole-Cole parameters using induced polarization tomography (Yoshioka and Zhdanov, 2005;Ghorbani et al, 2007;Hönig and Tezkan, 2007;Fiandaca et al, 2012).…”

Mapping of landfills using time‐domain spectral induced polarization data: the Eskelund case study

“…The standard procedure for inverting timedomain IP data commonly involves the use of the integral chargeability only, which is very restrictive. Some inversion algorithms using the entire time decay have been proposed - Yuval and Oldenburg (1997) and Hönig and Tezkan (2007) presented 2D inversions of TDIP (time-domain induced polarization) data with synthetic and field data applications. Some other papers deal with extracting spectral content from time-domain IP data (Tong et al 2006;Tarasov and Titov 2007;Titov et al 2010); however, these approaches do not take into account the shape of the transmitter waveform and the receiver transfer function.…”

Doubling the spectrum of time-domain induced polarization by harmonic de-noising, drift correction, spike removal, tapered gating and data uncertainty estimation

“…Recently, the interpretation and inversion of time-domain induced polarization (TDIP) data has changed as research is moving from only inverting for the integral changeability to also consider the spectral information and inverting for the full induced polarization (IP) response curves (Oldenburg 1997;Hönig & Tezkan 2007;Fiandaca et al 2012Fiandaca et al , 2013Auken et al 2015). Several examples of spectral TDIP applications for different purposes have been presented (Gazoty et al 2012a(Gazoty et al , 2013bChongo et al 2015;Fiandaca et al 2015;Johansson et al 2015;Doetsch et al 2015a,b).…”