A study on the direct interpretation of resistivity sounding data measured by Wenner electrode configuration

Chan, Siew Hung (1970) A study on the direct interpretation of resistivity sounding data measured by Wenner electrode configuration. Geophysical Prospecting, 18 (2). pp. 215-235. ISSN 0016-8025

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Official URL: https://doi.org/10.1111/j.1365-2478.1970.tb02104.x

Abstract

This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation (Formula Presented.) where K1(λ) is the kernel and B1(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least‐squares method. The least‐squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions. Copyright © 1970, Wiley Blackwell. All rights reserved

Item Type: Article
Additional Information: Chan, S.H. Department of Geology, University of Malaya, Kuala Lumpur, Malaysia.
Uncontrolled Keywords: Electric; geophysics; GPPRA; GSU
Subjects: Q Science > Q Science (General)
Q Science > QE Geology
Divisions: Faculty of Science > Dept of Geology
Depositing User: Mr Jasny Razali
Date Deposited: 22 Mar 2021 05:04
Last Modified: 22 Mar 2021 05:04
URI: http://eprints.um.edu.my/id/eprint/24517

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