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http://dx.doi.org/10.7582/GGE.2021.24.4.158

Computation of the Time-domain Induced Polarization Response Based on Cole-Cole Model  

Kim, Yeon-Jung (Department of Geophysics, Kangwon National University)
Cho, In-Ky (Division of Geology and Geophysics, Kangwon National University)
Publication Information
Geophysics and Geophysical Exploration / v.24, no.4, 2021 , pp. 158-163 More about this Journal
Abstract
The frequency-domain induced polarization (IP) response based on Cole-Cole model is expressed as a simple equation in close form. However, it is difficult to compute the time-domain IP response based on Cole-Cole model or any other relaxation model because it cannot be written in closed form. In this study, using numerical experiments, we compared three numerical methods for calculating the time-domain IP response of the Cole-Cole model asymptotically: series expansion, digital linear filtering and Fourier transform. The series expansion method is inadequately accurate for certain time values and converges very slowly. A digital linear filter specially designed to calculate the time-domain IP response does not present the desired accuracy, especially at later times. The Fourier transform method can overcome the abovementioned problems and present the time-domain IP response with adequate accuracy for all time values, even though more computing time is required.
Keywords
time-domain induced polarization; Cole-Cole model; series expansion; filtering; Fourier transform;
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