The Rayleigh wave scattering on a rectangular lattice of the solid roughness discontinuities

The problem of the surface acoustic Rayleigh wave scattering on a deterministic three-dimensional roughness, occupying a finite size rectangular region of an isotropic solid free surface, is solved in the Rayleigh-Born approximation of the perturbation theory in a roughness amplitude. Formula for the displacement field in the scattered Rayleigh wave at a big distance from the roughness, as compared to rough region sizes L1,2 along the x1,2- axes respectively, and asymptotic formulas for this displacement field in the Bragg, i.e. short-wavelength λ≪ L1,2 limit, where λ is the wavelength, are derived. The new laws of scattering are obtained. They are caused by a strong modulation of scattering by the roughness form. They exceed the fundamental physical conception, that a wave scattering in the short-wavelength limit takes place on a medium discontinuities, by the statement, that a wave strongly senses the structure of a medium in the near vicinity of discontinuities as well as the form-factor of the discontinuities lattice. This form-factor is a dependence of the discontinuity amplitude, i.e. of a difference of the left and right limit values of a roughness non-zero derivative, including one of zero order, in coordinate at a point of discontinuity, on a number of this discontinuity in a lattice. This exceeded physical conception violates the classical Laue-Bragg-Wulff laws of scattering.