ABSTRACT
The problem of low frequency scattering of harmonic plane waves by a rough topographic irregularity is studied. Both soft and hard conditions are assumed on the rough surface boundary. Mathematically, these conditions translate into Dirichlet and Neumann boundary conditions on the surface z = f(x). The slope of surface roughness is arbitrary over a finite length. A low frequency asymptotic solution in terms of small parameter is sought, where λ is the wave length of the incident wave. The matched asymptotic expansions are used between far field and near field solution to derive the far field solution in terms of small parameter both for the Dirichlet and Neumann condition up to order . The scattering cross-section for various kinds of mountain arc and valley and limiting cases of line crack and circle are obtained.
