Theoretical Resistivity Sounding Results Over a Transition Layer Model *

Abstract

An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σv (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σv. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis.

Direct current electric potential computation in an inhomogeneous and arbitrarily anisotropic layered earthl

“…Bhattacharya and Patra (1968) have discussed the dipping anisotropy of a halfspace (see also Negi and Saraf 1989;Pal and Mukherjee 1984). Many workers have studied the effects of anisotropy on the direct current potential measurements with the help of numerical modelling (Asten 1974;Niwas and Upadhyay 1974;Bhattacharya and Sen 1981 ;Eloranta 1988). However, these publications only address transverse isotropy with the principal axes of anisotropy parallel to and perpendicular to the earth's surface.…”

Resistivity Sounding on a Horizontally Stratified Multi‐layered Earth*

“…Recently there has been a great revival of resistivity sounding for the horizontally stratified earth with conductivity varying as a function of depth. Since the work of Mallick and Roy (1968), many papers (for example, Jain 1972, Niwas and Upadhyay 1974, Koefoed 1979 have appeared on this subject. Stoyer and Wait (1977) considered first the conductivity varying exponentially with depth under homogeneous overburden.…”

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

“…They considered a threelayered earth model in which the transitional layer has a linear variation of conductivity with depth. Sri Niwas and Upadhyay (1974) derived an expression for apparent resistivity for a three-layered earth with inhomogeneous and anisotropic interstratum. They introduced the inhomogeneity effect by inserting the depth dependence function in the coefficient of anisotropy f , but the theoretical apparent resistivity sounding curves they obtained show large negative values and seem to be incorrect, as has been pointed out by Jain (1976).…”