Low-angle radiation from vertically polarized antennas over radially heterogeneous flat ground

A theory is presented giving far-field radiation patterns and surface-wave behavior for vertically polarized antennas located at zero height over flat ground, with a surface impedance which can be discontinuous along a radius from the antenna. The theory is based on the radiation from the surface electric and magnetic currents as determined by the Sommerfeld attenuation function. Both sky-wave and surface-wave solutions are obtained simultaneously, with applications to ground screens, recovery phenomena, Fresnel zones, and similar engineering problems discussed with examples. In general, the results agree with those obtained using the compensation theorem.