Scattering of cylindrical SH waves by a concentric semi-circular discontinuity and hill

Abstract

Seismic wave propagation is significantly influenced by discontinuities and topographic undulations; however, the interactive effects of these factors on wave scattering remain underexplored. Utilizing the displacement discontinuity model, this study constructs a theoretical model for the scattering of cylindrical SH waves by a concentric semi-circular discontinuity and hill within an elastic half-space. A series solution is derived employing the wave function expansion method, and its precision and convergence are verified, which demonstrates its high accuracy and reliability. Through parametric analysis, the research systematically examines the impact of discontinuity stiffness, incident wave frequency and angle, source distance, and the ratio of discontinuity to hill radius on ground and underground motion distribution patterns under steady-state wave conditions. Notably, the study simulates transient wave action using a Ricker wavelet, revealing how scattering field characteristics change significantly under different conditions. The findings show that discontinuities have a particularly significant impact on seismic wave propagation when their stiffness is low.