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.