An analytical approach to scattering of cylindrical SH waves by a circular-arc hill: Near-source topographic effects

Abstract

A circular-arc hill is a prevalent feature on Earth's landscape. This distinctive convex terrain can significantly affect seismic waves, leading to notable amplification of ground motions. This paper investigates the near-source topographic effects on a circular-arc hill in an elastic half-space using a line source of cylindrical shear horizontal (SH) waves as excitation. By combining wavefunction expansion and mirror image techniques, the wavefields within two distinct subregions, characterized by unknown coefficients, are independently established. These coefficients are resolved through traction-free boundary, stress continuity, and displacement continuity conditions. Based on a comprehensive parametric analysis, the near-source topographic effects of convex topography are systematically studied from the perspectives of both the frequency and time domains. The findings reveal that the extent of amplification or reduction of surface ground motions is substantially influenced by the source location, wave frequency, and hill height. Subsurface displacements further exhibit a distinct focusing effect of the circular-arc hill, contrasting with surface motion patterns.