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

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