Direct estimation of the distribution of relaxation times from induced‐polarization spectra using a Fourier transform analysis

Abstract

International audienceThe analysis of low-frequency spectral induced polarization data involves the determination of the distribution of relaxation times either from time-domain or frequency domain measurements. The classical approach is to assume a simple transfer function (e.g., a Cole-Cole function) and to determine, by a deterministic or a stochastic fitting procedure, the parameters of this transfer function (for instance the four Cole-Cole parameters). Some other methods (based on optimization) have been developed recently avoiding the choice of a specific transfer function that can bias data interpretation. We have developed a new approach based on the Fourier transform also avoiding the use of a specific analytical transfer function. The use of the Fourier transform is a classical approach to retrieve the kernel of a Fredholm integral equation of the first kind (especially in potential field theory) and this corresponds exactly to the problem we want to solve. We adapt the Fourier transform approach to retrieve the distribution of the relaxation times (for instance to process low-frequency induced polarization data). Problems resulting from the use of this approach with noisy data are prevented by using Wiener filtering. As far as induced polarization is concerned, we found that it is necessary to fit the high-frequency dielectric contribution of the spectra and to remove this contribution from the quadrature conductivity data before inverting the distribution of the relaxation times. Our approach is benchmarked with analytical pair solutions and then tested by using synthetic and experimental data sets

Spectral Induced Polarization measurements on New Zealand sands ‐ dependence on fluid conductivity

“…which is the formulation used by, for example, Revil and Florsch (2010). Although the relaxation times in each formulation are different (Tarasov and Titov 2013), they are related by (Florsch et al 2012). As the high frequency rise in the SIP phase is not related to the surface polarization effects of interest, and same measurements also lead to anomalously low values of τ, and high values of c compared to the other measurements (Fig.…”

“…(Florsch et al ). As the high frequency rise in the SIP phase is not related to the surface polarization effects of interest, and requires a more complex model to adequately represent it, equation () has been used to fit the measurements on both samples only in the frequency range from 0.01–3 Hz.…”

“…de Lima and Sharma ; Chelidze and Gueguen ; Titov et al . ; Chen and Orr ; Leroy et al ; Vaudelet et al ; Revil ) and on the correlation of measured SIP parameters with hydraulic properties (e.g. Slater and Lesmes ; Binley et al ; Slater ; Revil and Florsch ; Koch et al ).…”

Estimation of sediment texture from spectral induced polarisation data using cluster and principal component analysis

“…). Of course, the formalism used in the decomposition approach needs to be carefully considered when establishing relationships between model parameters and sediment properties (Florsch, Camerlynck, and Revil ; Tarasov and Titov ).…”

“…; Kraschwitz et al . ; Revil and Florsch ; Volkmann and Klitzsch ; Koch, Revil, and Holliger ; Revil, Koch, and Holliger ; Revil et al . ; Revil, Florsch, and Camerlynck ; Slater et al .…”