Application of perturbation techniques to the problem of low-frequency electromagnetic wave scattering from an air-ground interface

The two-dimensional problem of horizontally polarized wave scattering from an air-ground interface is considered. The diffraction problem is formulate d by means of the extinction theorem, leading to a system of two simultaneo us surface integral equations. Three perturbation techniques, namely the sm all-perturbation method, the phase perturbation method, and the small-slope approximation, have been applied to this system. Iterative relations for t he terms of arbitrary order are obtained for each perturbation series. For the sinusoidal surface a benchmark solution, which remains stable near the points of Wood's anomalies, is developed. It is used to establish the area of validity of each perturbation technique by means of numerical comparison .