SH-wave scattering problem of an arbitrary shaped hill using the boundary integral quadrature method

Abstract

In this paper, the SH-wave scattering problem of an arbitrary-shaped hill is solved by using the boundary integral quadrature method (BIQM). By adopting the adaptive exact solution, the singular integral in the boundary integral equation can be determined skillfully. The adaptive exact solution is required to fulfill the same governing equation and the continuity conditions across the boundary. In this way, calculating the solid angle is also not required. After using the parametric representation for the boundary contour and Gaussian quadrature for the contour integral, the boundary integral equation is nothing more than an algebraic equation. Therefore, the BIQM is a meshless method. For solving the SH-wave scattering problem with a convex hill, an artificial interface is required to introduce at the bottom of the hill. The original problem is decomposed into a half-plane problem and an interior problem. By using the image method for the half-plane problem, the traction free boundary condition on the ground surface can be automatically satisfied. The collocation point located on the ground surface to satisfy the traction free boundary condition is not required. The numerical results show the influence of the incident frequency and incident angle for the displacement amplitude on the ground surface. Finally, the focusing phenomenon is also observed. Significant amplification of the displacement amplitude is observed in a specific local region. This localized amplification has important implications for seismic safety assessments.