Abstract
Cole‐Cole model parameters are widely used to interpret electrical geophysical methods and are obtained by inverting the induced polarization (IP) spectrum. This paper presents a direct inversion method for parameter estimation based on multifold least‐squares estimation. Two algorithms are described that provide optimal parameter estimation in the least‐squares sense. Simulations demonstrate that both algorithms can provide direct apparent spectral parameter inversion for complex resistivity data. Moreover, the second algorithm is robust under reasonably high noise.
Highlights
Spectral induced polarization (IP) is widely used in geological surveys (He et al, 1995; He, 1996; Milson, 1996; Luo and Zhang, 1998)
The interpretation of the IP data is often based on the Cole–Cole model (Cole and Cole, 1941; Luo and Zhang, 1998), under which the frequency behaviour of the complex IP impedance is approximated by an equivalent network, as shown in Figure 1 (Major and Silic, 1981)
The existing methods of parameter estimation are generally based on nonlinear iterative inversion (Pelton et al, 1984, 1978; Jaggar and Fell, 1988; Luo and Zhang, 1998)
Summary
Spectral induced polarization (IP) is widely used in geological surveys (He et al, 1995; He, 1996; Milson, 1996; Luo and Zhang, 1998). Interpretation based on the Cole–Cole model requires the parameters φ0, m, φ, and c to be estimated (Luo and Zhang, 1998). The existing methods of parameter estimation are generally based on nonlinear iterative inversion (Pelton et al, 1984, 1978; Jaggar and Fell, 1988; Luo and Zhang, 1998). Use least-squares estimation to express the compound parameter X = φc as a function of φ0 and c, which is expressed as φc = X (φ0, c).
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