Abstract
In current applications of the Induced Polarization (IP) method, the Debye and Cole-Cole models are used to study relaxation and dispersion properties of rocks, though it is believed that this type of modelisation is confused and vague, because of the lack of a background physical description. In this paper, we show that the Debye model can physically be deduced as a consequence of the electrodynamic behaviour of a mixture of bound and unbound charged particles immersed in an external electric field. We also clarify that the Cole-Cole model is a synthetic model, which can physically be explained as a continuous distribution of Debye terms.
Highlights
Electrical relaxation and dispersion in rocks are observed in the Time-Domain (TD) and Frequency-Domain (FD), respectively, using any standard Induced Polarization (IP) device
We have demonstrated that the Debye impedivity model for rocks can physically be deduced as a consequence of the electrodynamic behaviour of a mixture of bound and unbound charged particles immersed in an external electrical field
We have clarified that the Cole-Cole impedivity model is a synthetic model, which can physically be explained as a continuous distribution of Debye terms
Summary
Electrical relaxation and dispersion in rocks are observed in the Time-Domain (TD) and Frequency-Domain (FD), respectively, using any standard Induced Polarization (IP) device. These effects are often investigated in mining and environmental exploration. Ohm’s law states that the current density is linearly related to the electrical field by a factor s, known as the conductivity, which is assumed independent of time t in the TD, or frequency w in the FD. To try to overcome this conceptual drawback, in this paper a mechanical approach is suggested to derive a generalised current density-to-electrical field relationship, allowing the physical properties of Debye and Cole-Cole descriptions to be fully investigated
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