Resistivity sounding computations with any array using a single digital filter

Abstract

Theoretical resistivity sounding graphs over layered structures can be rapidly computed by the method of digital convolution. Through a series of substitutions it is possible to obtain similar forms of the convolution integral for all of the commonly used four-electrode arrays (Wenner, Schlum-berger, bipole-bipole, dipole-dipole), such that a single monopole resistivity filter function is involved. In this paper we derive a 34 point filter, sampled at (1n 10)/6, which is considered accurate for resistivity contrasts as high as 1000 : 1.