Space wave field produced by a vertical electric dipole above a rough surface

Abstract

The present diffraction problem is solved by means of a perturbation calculus in the transition conditions and by repeated application of the method of steepest descent to two-dimensional Fourier integrals. We obtain a reflection coefficient for the rough surface resulting in a geometrical-optics approximation for the space wave field strength. In the case of a periodic roughness profile the application of the method of steepest descent in the transform space can be avoided and we get the electromagnetic field through differentiation of the Bromwich potentials. The numerical results of the two methods are discussed in the case of a one-dimensional cosine profile. We show that the influence of the earth's roughness increases with increasing receiver heights and fixed receiver distance. On the other hand, we point out that the geometric optical approach is a rather good approximation for the space wave field strength.