Amplification of ground vibration on a non-symmetric triangular hill under SH waves

Surface irregularities, such as hills and ridges, can significantly amplify ground motion caused by earthquakes. Therefore, in this study, we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves. Firstly, based on the development of wave functions and regional matching techniques, we introduce a semi-circular artificial auxiliary boundary, dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region. Secondly, we derive the domain function form applicable to solving asymmetric problems. Utilizing the theory of complex variables, we establish a well-posed matrix for solving domain functions within the same coordinate system. Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence. Additionally, the frequency of the incident wave also has a certain degree of impact on the displacement amplitude. This study elucidates the scattering mechanism of SH waves by complex boundaries, providing a theoretical reference for building site selection and seismic design. In practical problems, the asymmetric assumption is more applicable than the symmetry assumption.