A numerical study on the relation between the electrical spectra of a mixture and the electrical properties of the components of the mixture

•We simulate the complex conductivity of rocks.•The electrical properties of the component control some characteristics of the electrical spectroscopy.•We discuss the comparability of the numerical method with the Cole–Cole model.•We provide a new idea for the explanation of electrical spectra dispersion of rocks.

To understand the effect of the components' electrical properties on the electrical spectra of a mixture, a three-dimensional finite difference method (3D-FDM) is employed to extract the effective permittivity and conductivity of mixtures. The simulation results indicate that: (1) the variation of the conductivity of the inclusion and the host could control the effective permittivity of the mixtures at the low frequency side; (2) the variation of the permittivity of the host and the inclusion could control the effective conductivity of the mixtures at the high frequency side; (3) with the increase of the permittivity of the inclusion and the host whose permittivity has a fixed ratio,ttra the spectral curve of the effective permittivity shifts to the upper-left corner and that of the effective conductivity shifts to the left; (4) with the increase of the conductivity of the inclusion and the host whose conductivity has a fixed ratio, the spectral curve of the effective permittivity shifts to the right and that of the effective conductivity shifts to the upper-right corner. Therefore, this study revealed some intrinsic physical quality of the electrical spectra of mixtures and provided a new idea for the explanation of electrical spectra dispersion of rocks.