Mathematical formulation and type curves for induced polarization

Abstract A basic mathematical formulation is developed for overvoltage and other induced polarization phenomena. Starting from the fundamental representation of a volume dipolar distribution, one is led to the concept of a change in apparent conductivity due to polarization effects. The mathematical solution of induced polarization phenomena, therefore, reduces to the appropriate solution of Laplace's equation for the same geometry and conductivity distribution ignoring polarization, followed by partial differentiation of the apparent resistivity function so determined. The dielectric constants of the media are not involved in the solution. As examples of the use of the representation, the response of a polarizable sphere and of a polarizable lower layer in a typical two-layer case are presented. Actual field results are shown illustrating the use of the latter solution.