Simple model for scattering of VLF modes from a circular island

It is well known that the finite conductivity of the ground will modify the attenuation and phase velocity of VLF propagation in the Earth-ionosphere waveguide. Most analyses, however, do not deal explicitly with the case where the Earths surface is inhomogeneous. A case of particular interest is when the radio great-circle path, over the sea, passes around or over an island including the case of a floating ice sheet. The author treats an idealized patch of anomalous conductivity on the bottom surface of the Earth-ionosphere waveguide for widely separated source and observer locations. The formulation bears some similarity to that employed in mixed path ground wave propagation theory.<>