The two-dimensional theory of electromagnetic induction in thin sheets with applications to the earth
Date
1978
Authors
Green, Victor Richard
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Abstract
In this thesis, a method for studying problems of electromagnetic induction in local regions of the Earth where the principal conductivity anomalies are confined to a thing surface layerhas been developed using the thin sheet approximation. A two-dimensional model is used in which the Earth is represented by a uniformly conducting half-space covered by an infinitely thin sheet of variable integrated conductivity. A quasi-static magnetic source field, in both E-polarization and B-polarization, is considered.
With the aid of the well-known boundary conditions for thin sheets, the horizontal electric field at the surface of the Earth is shown to satisfy a simple one-dimensional integral equation in both E- and B-polarizations. The method of reducing these integral equations to a linear system of algebraic equations for numerical solution is discussed in detail. The final (discrete) expressions for the fields are presented in a form suitable for programming. (A complete listing of the Fortran program is included in the appendix).
Results obtained by this method agree well with those obtained analytically by Nicoll and Weaver (1977) (B-polarization case). When comparing results with those obtained numerically by Fischer et al. (1978a, 1978b) (E-polarization), some differences do occur. However, the similarity of our results and those obtained from an analytical solution of Weidelt (1971) and from the finite-difference formulation of Brewitt-Taylor and Weaver (1976) indicates that our results are indeed accurate.
To illustrate the method, field values are calculated for two simple models in which the integrated conductivity changes (i) abruptly and (ii) gradually from one value to another. A more complex model depicting a cross-section through Vancouver Island is also considered.