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.