3-D Finite-Difference Modeling of the Magnetic Field in Geoelectromagnetic Induction
J. T. Weaver, A. K. Agarwal, X. H. Pu, 1999. "3-D Finite-Difference Modeling of the Magnetic Field in Geoelectromagnetic Induction", Three-Dimensional Electromagnetics, Michael Oristaglio, Brian Spies
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A versatile finite-difference program has been developed for solving 3-D magnetotelluric problems in which the inducing field is uniform and horizontal. Finite-difference equations for the magnetic-field components are obtained by integrations over rectangular volume elements surrounding each node of the grid. This procedure avoids the ambiguity about whether to define weighted average conductivities or resistivities at the nodes of the numerical grid. The algorithm can handle an anomalous thin sheet at the surface of the general 3-D structure, thereby modeling both near-surface and deep-seated conductivity anomalies for certain ranges of period. The anomalous structure is allowed to approach different 2-D configurations at infinity in all four horizontal directions, with the result that both E-polarization and B-polarization solutions arise as boundary conditions on the grid. Integral boundary conditions on the surface of the Earth and at the top of the basement half-space (of uniform conductivity) reduce the overall size of the grid by eliminating the air and basement layers from the numerical solution. Recent developments include an automatic grid generator designed for geoelectromagnetic induction problems, the treatment of difficulties that can occur when the 2-D E-polarization problems on the side boundaries of the grid are solved in terms of the magnetic field, and a new method for calculating the electric-field components.