The electromagnetic response of an inhomogeneous layered earth—A general one‐dimensional approach

Abstract

The electromagnetic response is studied for a model three‐layer earth formed by constant conductivity in the first and the third layers and conductivity varying with depth in the second layer (i.e., the inhomogeneous transition layer). A generalization to the case of many constant or variable conductivity layers is presented, too. The model problem is addressed by numerically solving an initial value problem for an ordinary differential equation for the inhomogeneous transition layer. The applicability of the procedure proposed, which is limited by the numerical method used, is discussed. As an illustration, the computed apparent resistivities and phases are compared with the results of Kao and Rankin (1980). The technique presented is applied to the computation of the response in the very‐low frequency (VLF) method. Application to other methods employing the plane wave is similar.

An Application of Fast Algorithms to Numerical Electromagnetic Modeling*

“…1). The boundary condition (8) (which replaces (3)) has been determined from the corresponding 1-D problem (Bezvoda and Segeth 1985). The numerical experiments showed that the sizes of the rectangles used are sufficient and cannot influence the results.…”

“…Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case. Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case.…”

“…Further we put u(0) = 1. Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case.…”