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A simple method of image solution for a sphere of constant electrical potential in a conducting half-space; implications for the applied potential method

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doi: 10.1111/1365-2478.12506
Authors:Butler, S. L.
Author Affiliations:Primary:
University of Saskatchewan, Department of Geological Sciences, Saskatoon, SK, Canada
Volume Title:Geophysical Prospecting
Source:Geophysical Prospecting, 65(6), p.1680-1686. Publisher: Blackwell on behalf of the European Association of Geoscientists & Engineers (EAGE), Houten, Netherlands. ISSN: 0016-8025
Publication Date:2017
Note:In English. 25 refs.; illus.
Summary:The applied potential, or mise-à-la-masse, method is used in mineral exploration and environmental applications to constrain the shape and extent of conductive anomalies. However, few simple calculations exist to help gain understanding and intuition regarding the pattern of measured electrical potential at the ground surface. While it makes intuitive sense that the conductor must come close to the ground surface in order for the lateral extent of the potential anomaly to be affected by the dimensions of the conductor rather than simply by the depth, no simple calculation exists to quantify this effect. In this contribution, a simple method of images solution for the case of a sphere of constant electrical potential in a conducting half-space is presented. The solution consists of an infinite series where the first term is the same as the method of images solution for a point current source in an infinite half-space. The higher order terms result from the interaction of the constant potential sphere with the no-flux boundary condition representing the ground surface and cause the change in the shape of the potential anomaly that is of interest in the applied potential method. The calculation is relevant to applied potentials when the conductive anomaly is limited in all three space dimensions and is highly conductive. Using the derived formula, it is shown that, while the electrical potential at the ground surface caused by the sphere is affected even when the sphere is quite deep, the ratio of the potential to the current, a quantity that is more relevant to the applied potential method, is not affected until the centre of the sphere is within two radii of the ground surface. An expression for the contact resistance of the sphere as a function of depth is also given, and the contact resistance is shown to increase by roughly 45% as the sphere is moved from great depth to the ground surface. Abstract Copyright (2017), European Association of Geoscientists & Engineers.
Subjects:Electrical anomalies; Electrical conductivity; Electrical currents; Electrical methods; Equations; Geophysical methods; Half-space; Imagery; Numerical models; Potential field; Resistivity
Record ID:809535-18
Copyright Information:GeoRef, Copyright 2021 American Geosciences Institute. Reference includes data from John Wiley & Sons, Chichester, United Kingdom
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