Propagation over an inhomogenous irregular surface

Abstract

A new integral equation has been obtained for the attenuation factor of a radio wave launched by an elevated element, as the wave propagates over a radially inhomogeneous surface of varying height, with an elevated current element as a receiver. In the analysis use is made of the vector form of compensation theorem, using the concept of a real surface impedance on the irregular surface together with that of an equivalent normalized surface impedance in air, at points which follows the contour of the irregular surface. The new integral equation generalises previous work to treat arbitrary terrain, so that both gradual and sharp changes of terrain height, such as a cliff and a knife edge are considered. The validity of the integral equation has been tested theoretically by comparison with alternative solutions for particular cases, and also by experiment.