Computation of the time-domain response of a polarizable ground

Abstract

Computation of the theoretical time-domain response of a polarizable ground on the basis of a frequency-domain model of relaxation, e.g., a Cole-Cole or any other model that involves a fractional power of the complex frequency variable, runs into difficulties either because the Laplace transform can only be written as a very slowly converging summation or because it cannot be written in closed computable form. A clear way around this is to use a digital linear filter. A filter is presented in this paper that has been designed specifically to work well with complex impedance functions that tend asymptotically to real values at both extremes of the frequency variable, the magnitude descending monotonically from the low-frequency asymptote to the high frequency asymptote. This filter produces the step response from the real part of the impedance-versus-frequency function with reasonable accuracy for all impedance functions that one may like to represent by models of electrical relaxation for a polarizable ground, but it does not work for functions containing sharp resonances or discontinuities.