On violation of Rayleigh and Bragg laws of scattering

The problem of Rayleigh wave scattering by deterministic cylindrically symmetrical roughness occupying finite size region of isotropic solid surface is solved in Born (Rayleigh-Born) approximation of perturbation theory in roughness amplitude. Formula for displacement field in the scattered Rayleigh wave at big distance from roughness and asymptotic formulas for the mentioned displacement field in Rayleigh (long-wavelength) and in the short-wavelength limits are derived. The new laws of scattering violating Rayleigh law in the long-wavelength limit and Bragg law in the short-wavelength limit are obtained.