Abstract
The duct model used here is that of Kahan and Eckart. It has a discontinuous drop of the otherwise constant relative permittivity at the upper duct boundary. The earth is assumed to be a perfect conductor and an ideal plane. The source of the electromagnetic field is taken to be a vertical magnetic dipole, in the upper surface layer, with an arbitrary time-varying moment. The method used for solution is essentially based on the application of two functional transforms. Starting with the wave equation of the electric field strength and applying a Laplace transform in time, one then finds a two-dimensional Fourier transform in the horizontal coordinates in space leading to an integral representation of the solution of the wave equation in transform space, considering initial, boundary, and transition conditions. Having chosen a horizontal polarization of the primary source, one can determine the transient behaviour of the electric field strength at any distance above the duct.
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