Resistivity and Induced Polarization Response for a Borehole Model

Explicit results for the electrical resistivity and the induced polarization responses are obtained for a four-electrode array on the axis of a fluid-filled borehole. Quasi-static theory is employed and all electromagnetic coupling effects are neglected, but the resistivities of the constitutive media may be complex and frequency dependent. We show that, in general, the frequency dependence of the apparent resistivity is a complicated function of the various parameters. In fact, even when the drill hole fluid is nonpolarizable, the masking effect involves both "dilution" and "distortion" of the intrinsic complex resistivity of the adjacent formation.