The Generalized Skin Depth for Polarized Porous Media Based on the Cole–Cole Model

Abstract

In the field of frequency-domain electromagnetic detection, skin depth is an important parameter for electromagnetic data interpretation and imaging. The classic skin depth formula is calculated based only on conductivity; the induced-polarization effect in real earth is not considered, so the imaging results have obvious errors. To solve these problems, based on plane wave theory and the Cole–Cole conductivity model, a generalized skin depth formula of polarized media is derived in the frequency domain. The accuracy of the generalized skin depth is verified through comparison with the classical skin depth. To show the practicability of this study, the theoretical data with induced polarization (IP) effects are used to explain the generalized skin depth for polarized porous media. The generalized skin depth calculation for a typical porous polarization model is related not only to conductivity, but also to polarization parameters, such as chargeability, characteristic time constant, and frequency dependence. At low-frequency excitation, the generalized skin depth formula can be used to calculate the propagation depth of electromagnetic waves relatively accurately for porous polarized media. This method can be applied to the calculation of electromagnetic wave propagation depths in complex dispersive media. Compared with non-polarized media, in porous polarized media, under low-frequency excitation, the electromagnetic wave propagates deeper, allowing the detection of deeper objects. The data interpretation and imaging of polarized porous media by the generalized skin depth formula have higher accuracy.