Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on aver age in contrast to a plane. Backscattering from such a surface is considere d based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of sca ttering by small roughness (assumed to be Local) and the propagation of inc ident and scattered fields over a smooth large-scale concave surface. In co ntrast to the 'two-scale' scattering model, the zero-order unperturbed wave field is not assumed to be specularly reflected from the local tangent plan e to the smooth surface, but it is a solution of a corresponding diffractio n problem. Two particular cases of smooth surfaces are considered: first, t he inner surface of a concave cylinder with a constant radius and finite an gular pattern. and second, a compound surface that consists of a coupled ha lf-plane and the cylindrical surface mentioned above. In a geometrical opti cs limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) held are obtained for these two cases in th e form of a series over multiple specular reflected fields. It is shown tha t these non-local processes lead to the essential increase in the backscatt ering cross section in comparison with the two-scale model and tangent-plan e approach.