3D scattering of plane SV waves by a circular-arc alluvial valley

The 3D scattering of plane SV waves by circular-arc alluvial valleys is studied.The circular surface assumption is used to simulate the half-space surface.The wave function expansion method and the finite item Fourier series expansion technique are used to give the analytical solution in the frequency domain.Based on the solution,the effects of the incident frequencies and incident angles of the plane SV waves on the dynamic response of circular-arc alluvial valleys are discussed.The study shows that the 3D scattering of plane SV waves by circular-arc alluvial valleys are more complicated than the 2D scattering problem.The simplified decomposition of separating the 3D scattering problem into two main planes may lead to error.Both the incident angles and the incident frequencies of the incident SV waves have important effects on the surface displacement amplitudes.