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POTENTIAL FIELD OF A STATIONARY ELECTRIC CURRENT USING FREDHOLM'S INTEGRAL EQUATIONS OF THE SECOND KIND *
Author(s) -
ELORANTA E.H.
Publication year - 1986
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1986.tb00498.x
Subject(s) - integral equation , fredholm integral equation , electric field , mathematical analysis , electric potential , electric field integral equation , piecewise , electrical resistivity and conductivity , discontinuity (linguistics) , mathematics , isotropy , physics , optics , quantum mechanics , voltage
An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the ‘second kind’ developed for the potential of the electric field. In this method the discontinuity‐surfaces of electrical conductivity are divided into ‘sub‐areas’ that are so small that the value of their potential can be regarded as constant. The equations are applied to 3‐D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise‐a‐la‐masse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite.