Semi‐Analytical Solution for Topographic Amplification of SH Waves on Rocky Ridges With Multi‐Level Asymmetric Slopes

ABSTRACT The geometric irregularity of topographic interfaces induces prominent reflection and scattering of seismic waves during propagation. In particular terrain configurations, constructive interference among incident, reflected, and scattered waves can result in substantial topographic amplification. This study addresses the SH‐wave scattering problem in elastic half‐spaces with geometrically complex slope ridges, proposing a series solution method based on complex function method and wave function expansion method. By employing multi‐region matching technique and introducing two semi‐circular auxiliary boundaries, the scattering problem of multi‐slope complex protrusions is effectively resolved. The half‐space is divided into three sub‐regions, and a domain‐function construction is developed for asymmetric geometries. Complex‐variable theory handles the coordinate transformation between these functions and simplifies the analysis. The results demonstrate that this method exhibits good applicability and computational efficiency in addressing symmetric or asymmetric geometric protrusion SH‐wave scattering problems. Finally, numerical results are utilized to analyze the influence of protrusion geometric characteristics, incident wave frequency, and angle of incidence on ground motion, providing benchmarks for numerical method validation and offering significant implications for seismic site selection and engineering protection.