Trefftz's method is applied to solve the diffraction of P, SV, and Rayleigh waves by surface irregularities in an elastic, isotropic and homogeneous half-space. The diffracted wave fields are constructed with linear combinations of solutions which form c-complete or T-complete (T after Trefftz) families for the wave equation. Boundary conditions are satisfied in the least-squares sense on the irregularity and on a finite interval of the half-space surface. Excellent agreement was found with the solution by Wong (1982).

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