SOME PROBLEMS OF THE PHENOMENOLOGICAL APPROACH IN THE THEORY OF ELECTROMAGNETIC FIELD IN A POROUS MEDIUM SATURATED WITH FLUIDS

V. V. Filatov

Siberian Research Institute of Geology, Geophysics and Mineral Resources, Novosibirsk, Russia

The paper discusses interpretation of parameters applied by the phenomenological approach based on the Cole–Cole approximation. It was shown that the use of the fractal medium model and equations in fractional derivatives enables more general substantiation of such parameters. In particular, the physical meaning of the power parameter in the Cole–Cole formula was discussed, which correlates the relaxation time and the typical dimensions of elements of the medium microstructure. The use of solution equations in fractional derivatives enables adjustment of relaxation times distribution under the Cole–Cole approximation in cases when there is a complex process in the medium, driven by a combination of time decays corresponding to a set of various Cole–Cole parameters, by using the Kohlrausch-Williams-Watts law as a relaxation model. The author demonstrates a similarity between the relaxation model of the induced polarisation theory and the resistivity variation model at an elastic impact (seismoelectric effect of the first kind). This allows predicting additional parameters of the inhomogeneous medium, e.g. porosity and permeability, based on the analysis of a total relaxation curve.

Keywords: electrical survey, electromagnetic field, phenomenological approach, porous medium, fluid saturation.

DOI 10.20403/2078-0575-2017-6s-139-146