Resistivity Sounding on a Three‐layer Transitional Model*

Abstract

The expression for the potential due to a point source of current, placed on the surface of a horizontal three‐layer earth, has been derived when conductivity in the second layer varies linearly with depth and changes abruptly at the boundaries. Master curves for Wenner and Schlumberger configurations have been presented for an insulating basement and for one value of conductivity gradient in the second layer.

The electrical resistivity method

“…The log records resistivity from 20 m depth. While Mallick and Roy (1968) and Jain (1972) consider the intermediate layer with linearly transitional conductivity, Koefoed (1979b) considers linearly transitional resistivity which is more common. The resistivity of formations underlying the saprolite upto 40 m depth increases gradually and not in steps The increase or decrease in resistivity over a certain depth range i.e., within the intermediate layer, could be linear or exponential (Fig.…”

Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth*

“…Moreover, a number of investigators in this field considered the variation of conductivity in vertical direction only in different types of earth models. Among them are Paul andBanerjee (1970), La1 (1970), Jain (1972), Sampaio (1976), Stoyer and Wait (1977), Patella (1977Patella ( , 1978, Koefoed (1979), Mallick and Jain (1979), Banerjee, Sengupta andPal (1980a, 1980b), Sato and Sampaio (1980), Pal (1982Pal ( , 1983.…”

Theoretical Resistivity Sounding Results Over a Transition Layer Model *

“…In recent years, some realistic representative earth models have been considered in which the effect of conductivity variation with depth is analyzed (cf. Mallick and Roy 1968, Jain 1972, Naidu 1970. Mallick and Roy (1968) considered the conductivity variation in a transitional boundary (zone of weathering) for a two layer earth model.…”

“…Mallick and Roy (1968) considered the conductivity variation in a transitional boundary (zone of weathering) for a two layer earth model. Jain (1972) took up the study of a similar model and obtained the effect of conductivity jump at the two boundaries in a three layer earth model. On the base of his previous transition model (1968), Mallick (1970) worked out results for magneto-telluric sounding.…”

“…Examples of conductivity variation are quite common in nature and have been exemplified in investigation by Mallick and Roy (1968) for peninsular India. We consider in this paper a combination of situations taken in the theoretical models of Mallick and Roy (1968), Jain (1972) and Naidu (1970). Specifically we take a layered earth model embedding a transition (anisotropic inhomogeneous) layer.…”