RAYLEIGH-WAVE DIFFRACTION AT A WEAK DISCONTINUITY IN THE BOUNDARY-CONDITIONS .1.

Rayleigh wave diffraction at the boundary between free and weakly load ed parts of a surface is considered. To find the scattered field, we s olve the matrix functional equation of Riemann's problem. An approxima te technique for solving this equation is proposed and rigorously subs tantiated in the scalar case. The technique is based on the Laurents s eries expansion of the functional equation kernel taking into account the higher order terms. The scattered field is found by quadratures, a nd its asymptotic expansion is calculated.