Abstract: Topography plays a crucial role in shaping the propagation paths and energy distribution of seismic waves. To investigate the modulation effect of topography on seismic wave propagation, the dynamic response of isosceles triangular mountain subjected to horizontal shear wave (SH wave) in a homogeneous semi-infinite medium was studied by the wave function expansion method. Based on the existing frequency-domain scattering solution, the topographic ground motion transfer factor was introduced, and the time-domain analytical solution of mountain displacement was obtained by combining Laplace and Fourier transform. The spatiotemporal and energy distribution characteristics of mountain ground motion under the interaction of SH wave and triangular topography were studied. This solution allows for a comprehensive study of the spatiotemporal and energy distribution characteristics of ground motion when SH waves interact with triangular topography. The results show that: (1) Under SH wave incidence, the surface points of the mountain exhibit significantly greater fluctuations compared to flat ground points, with a stronger influence from frequency components. At specific frequencies, notable amplification and attenuation effects are observed. The incident angle has a significant impact on the resonance frequency and the amplitude of the topographic ground motion transfer factor. (2) Seismic waves undergo multiple reflections and refractions at the mountain’s boundaries and apex, forming a complex interference wave field. Under vertical incidence, the displacement amplitude at the mountain apex reaches 2.65. As the incident angle increases, the maximum displacement amplitude decreases and shifts from the apex to the right slope, with a maximum value of 2.12 under horizontal incidence. (3) The interaction between the triangular mountain topography and seismic waves causes energy to focus on specific areas of the mountain. Under vertical incidence, energy is concentrated near the apex and slopes. Under oblique and horizontal incidence, energy tends to be distributed more on the right side of the mountain. The geometric focusing effect is more pronounced under oblique and horizontal incidence, leading to more significant energy convergence in localized areas.

Key words: topographic effect, triangular mountain topography, wave function expansion method, spatiotemporal distribution of ground motion, energy distribution