Analytical model for a polarizable medium at radio and lower frequencies

Abstract

The Maxwell equations are written and discussed in the frequency domain for a medium exhibiting electrical polarization at radio and lower frequencies, in the range of linearity between current density and electric-field intensity. A complex function of frequency is proposed for the conductivity, which is able to describe all the families of available experimental curves for rock samples in the natural state, showing the effect of polarization. Such a function is a constitutive relation for the polarizable medium in the frequency domain. The concept of ‘abnormal’ dielectric constant for rocks is discussed in the context of the physical mechanisms responsible for the effect of electrical polarization at radio frequencies and below. Such a concept, always possible theoretically, only introduces confusion in the understanding of the basic physical mechanisms involved. As an alternative the extensive use of the concept of a total current complex conductivity is suggested.