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The electric field in the conductive half space as a model in mining and petroleum prospecting. (English) Zbl 0693.65088
Starting from Maxwell’s equation, the authors derive a mathematical model which can be used for computing the propagation of the electric field in the substratum provided that the source current and the electromagnetic characteristics of the material are known.
The medium under investigation is actually a union of two half spaces: (i) a homogeneous nonconductive half space, the air; (ii) a non homogeneous conductive half space, the substratum. In the mining and petroleum prospecting a knowledge of the electric field in the conductive half space substratum is required. Thus to avoid the computation of the solution in the air, the homogeneous non-conductive half space is substituted by a non-local boundary condition.
For this purpose the classical integral equation technique is used. A variational formulation of the problem whose solution is the electric field in the substratum is given. Finally the standard finite element method is used for computing the numerical solution. The numerical results are presented graphically.
Reviewer: K.N.Srivastava

MSC:
65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35R30 Inverse problems for PDEs
78A55 Technical applications of optics and electromagnetic theory
86A20 Potentials, prospecting
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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