The classical problem of scattering of a high-frequency wave from a point source in an elastic medium by an arbitrary smooth nonconvex free boundary surface of the elastic body is studied in view of possible multiple reflections. The analysis is based on estimates of multiple diffraction integrals by the multidimensional stationary phase method. We obtain closed-form expressions for the leading term in the asymptotics of the displacement amplitudes in reflected waves for various possible combinations of reflection and transformation of longitudinal and transverse waves by nonconvex parts of the boundary surface.
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