On the role of the J-E constitutive relationship in applied geoelectromagnetism

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.