Very low‐frequency electromagnetic response of a perfectly conducting half‐plane in a layered half‐space

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Abstract
Following Dmitriev (1961), a rigorous theoretical solution for the problem of scattering by a perfectly conducting inclined half‐plane in a layered half‐space in a plane‐wave field has been obtained. The solution is in the form of a Fredholm integral equation of the second kind, where the unknown is the Laplace transform of scattering current in the half‐plane. The integral equation is solved numerically by the method of successive approximations. The scattered fields at the surface of the half‐space are found by integrating the half‐space Green’s function over the transform of the scattering current. The effects of depth of burial and inclination of the half‐plane, conductivity contrast between the overburden and the substratum, and thickness of the overburden are studied in some detail. As expected, the tangent of the tilt angle and the ellipticity of the ellipse of magnetic polarization decrease rapidly with increasing depth of burial, conductivity contrast, and thickness. Inclination introduces asymmetry in the anomaly profile besides affecting its magnitude. Depth of exploration is greater for the ellipticity than for the tilt angle. A target depth equal to half of the skin depth in the substratum is the limiting depth of detection in the very low‐frequency, electromagnetic (VLF-EM) method. An interpretation scheme for VLF-EM field data is presented, based on peak‐to‐peak separation and difference between peaks of the two polarization parameters.

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