Direct interpretation of geoelectric measurements by the use of linear filter theory

Abstract

In a recent paper Lee and Green (1973) worked out a method for direct interpretation of electrical soundings made over a fault or dike (see Figure 1). They computed the kernel function using the method developed by Meinardus (1970). However, Koefoed (1968), while dealing with direct interpretation of electrical measurements made over a horizontally layered earth, showed that the relative variations in the apparent resistivity were not of the same order of magnitude in the corresponding kernel curve; thus, any method based on the determination of this function as the intermediate step would lead to a loss of information and hence to incorrect interpretation. Koefoed (1970) introduced a function T(λ) called the resistivity transform (a function related to the kernel function) as an intermediate step. Ghosh (1971) used linear filter theory and gave a simple and quick procedure to obtain the T(λ) function from the apparent resistivity field curve. He cited the properties of the T function as, (1) it is solely determined by the layer distribution; (2) it is an unambiguous representation of the ρ_a function; and (3) for small and large values of 1/λ it approaches the ρ_a curves.