Low frequency electromagnetic scattering from an island

Adopting a simple model, a formulation is presented for the scattering from a circular island surrounded by an otherwise smooth sea. Both the surface impedance and the height profile of the island are functions of the radial distance. Employing the electromagnetic compensation theorem, an expression for the mutual impedance between two small ground-based vertical antennas is derived. To simplify the analysis these antennas are assumed to be located at distances that are large compared with the radius of the island. It is shown that the relative importance of the surface impedance and the height profile will depend on the scattering angle subtended, at the island center, by the direction to the source and receiving antennas. The results are relevant to the propagation of electromagnetic waves in the earth-ionosphere waveguide at very low frequencies (VLF)