Extensions to the Phenomenological Theory of Induced Polarization

In the induced polarization method of geophysical exploration, the frequency dependence or dispersion of the complex resistivity of the medium is exploited. We present here a general formulation of the method for the idealized situation where two well-defined regions are both polarizable. The objective is to express the measured or apparent complex resistivity in terms of the complex resistivities of each region. We show that the resultant frequency dependence is not simply a weighted sum of the two constitutive parts except in the case where both media are weakly polarizable. In general, the higher order interaction causes distortion of the resultant frequency response in addition to the first-order dilution effect that is well known. Some comments about the related time domain or transient responses are also included. Finally, we show the connection with the magnetic induced polarization (MIP) method where an analogous development of the dilution and distortion factors follows rather easily.