Surface Motion for P-Wave Scattering by an Arbitrary-Shaped Canyon in Saturated Half-Space

This paper obtained a semianalytical solution for the P-wave scattering problem by an arbitrary-shaped canyon in a saturated half-space by using Biot’s theory, the wave function expansion method, and the moments method. Firstly, based on the Biot fluid-saturated porous media theory and the wave function expansion method, the wave potentials which automatically satisfy the zero-stress boundary condition on the surface of the half-space are obtained. Then, the boundary value problem is transformed into an algebraic problem by the method of moments according to the boundary conditions, and then solved numerically by truncation. By adjusting the parameters, the saturated medium in the original model approximately degenerates into a single-phase elastic medium, and the correctness of the proposed method is verified by comparing it with published results. Finally, the effects of the canyon shape, the porosity of the soil, and the incidence angle and frequency of the incident wave on the amplitude of ground surface motion are investigated. The results show that the incidence angle has a significant effect on the ground surface motion, while the porosity of the soil has little influence on the amplitude of surface motion. The influence of canyon shape on surface motion is mainly reflected in the shielding effect on the incident wave. Although P-wave scattering by a canyon is a traditional problem, most of the analytical solutions are limited to solving the scattering of seismic waves in geometric regular canyons. However, the actual shape of the canyon is not regular, which limits the application of closed analytical solutions in practical engineering. In this paper, the scattering of P-waves in arbitrary-shaped canyons is successfully solved by using a semianalytical method combined with a numerical method-moments method, which provides a possibility for engineering application.