The effect of electromagnetic coupling parameters in spectral-induced polarization studies

Induced polarization (IP) method is a main geophysical method in deposits exploration. As an extension of the IP method, the spectral induced polarization (SIP) has been used extensively in mineral prospecting and increasingly in environmental investigations, hydro-geophysics, archaeo-geophysics, bio-geophysics. The reason for this extensive use is that SIP measurements are sensitive to the low-frequency capacitive properties of rocks and soils. One major limitation of SIP method is electromagnetic (EM) coupling effect. In SIP method, the amplitude and phase components of the earth’s resistivity are measured in a frequency range typically from 0.001 Hz to 10 kHz. At low frequencies, the inductive coupling effects impact the spectrum Ohmic responses and normal polarization effect of the subsurface material. In SIP literature, there are three types of the EM coupling effects: the first is the EM coupling effect removal methods from SIP field data. In the second method, the mutual impedance of the earth is calculated using the Cole-Cole equation as IP dispersion of the earth. SIP data and mutual impedance are compared using an inversion algorithm in order to recover the earth IP parameters. Since the SIP method employs alternating fields using grounded wires, this method should be characterized as an EM method. The third method uses a current cable arrangement in order to reduce the EM coupling effects from SIP data.
Many different models have been proposed for the description of the dispersive behavior of the IP. However, the most widely used model is the Cole–Cole model. This model describes the resistivity dispersion observed in the field data from areas with metallic mineral content. It is also used to estimate various subsurface properties of nonmetallic soil and rocks in IP frequency domain investigations (SIP). A multiple Cole–Cole model is typically a more general and proper model than a single Cole–Cole model for describing IP data with various dispersion ranges caused either by multiple-length scales in sediments or by coupling effects in the IP measurements. The Cole–Cole model parameters are widely used to interpret both time- and frequency-domain induced polarization data. Among many studies in which the Cole–Cole parameters are estimated from the SIP measurements on soils and rocks, a majority of them use least squares (deterministic) methods.
The previous studies have shown that the geometry of an array such as electrode spacing (e.g., dipole–dipole electrode array) has an important effect on mutual impedance. In this study, by using the dipole–dipole array on a homogeneous polarizable half-space, the electromagnetic coupling effect on mutual impedance is investigated. The aim of this work is an investigation of the Cole–Cole parameters effects on the mutual impedance of a polarizable half-space. Since Sunde’s mutual impedance equation is widely used for an impolarizable earth (real resistivity), the effect of a polarizable earth has been less investigated. We use the Nyquist plot to show the mutual impedance response of theoretical and field data.
The results show that if the Cole–Cole parameters including time constant (τ), frequency constant(c) or chargeability (m) of the half-space are small, the IP response is very small compared with the EM coupling response and thus the Cole–Cole parameters recovered from the inversion algorithms are less reliable. In practice, the above-mentioned terms occur when there are small particles of ore, extended grain size distribution of ore or low-grade ore in porphyry deposit. It is worth mentioning that the chargeability of the earth in environmental investigations also has a small value.