Scattering of Rayleigh waves by a shallow circular alluvial valley: High-frequency solution

A high-frequency analytical solution for scattering of Rayleigh waves by a shallow circular alluvial valley was derived using wave function expansion method, and the solution was utilized to analyze the effects of incident frequency, width of the valley, and depth of the valley, etc, on the wave scattering. Numerical results showed that, because of the alluvial valley, the distribution of surface displacement at the side where wave arrives becomes relatively complicated, but the displacement amplitude is not large; the distribution of the surface displacement at far side is relatively simple, but the displacement amplitude is relatively large, and in most cases the amplitude is larger than that at the alluvium.