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An analysis is given for scattering of a plane wave from a two‐layer conducting medium where the upper layer is homogeneous but where the lower layer or substrate is characterized by a periodically varying surface impedance. The exact solution obtained is expressed in terms of continued fraction expansions that converge rapidly for most cases of physical interest. The motivation was to provide understanding of how electromagnetic waves can be used to determine the thickness of a layer of coal that is backed by a relatively highly conducting region of slate. It is shown that, if the slate varies sufficiently slowly in the horizontal direction, the observed surface impedance and wave tilt at the air/coal interface is related directly to the local properties at the point of measurement.
Wait et al. (Mon,) studied this question.