In this paper, the method of combining indirect boundary element method (IBEM) with the region-matching technique is used to solve the seismic responses of a three-dimensional (3D) hill in a layered half-space subjected to spherical P, SV, and SH waves. The direct stiffness method and Hankel transform method are used to solve the free field of spherical wave source field, and the scattering field is constructed by Green's function in half-space. The correctness and accuracy of this method are verified by comparing with the results of several literatures. This method can be used to deal with arbitrary-shaped hill topography, and has the advantages of wide applicability, high accuracy and fast convergence. Taking Gaussian hill topography as an example, the scattering phenomenon of hill under the incidence of spherical P, SV and SH waves is studied, and the influences of hill topography, source location and frequency on site seismic responses are explored. The results show that: Existence of the hill topography has evident focusing effect, which significantly enlarges the seismic response on the hill surface, and the hill has evident isolation effect in the process of energy propagation; With higher frequency of the incident wave, the fluctuation amplitude of displacement on the hill surface increases; The fluctuation amplitude of horizontal displacement on the hill surface is SV wave > SH wave > P wave, and the vertical displacement is P wave > SV wave.

本文将间接边界元法（IBEM）与区域匹配技术相结合的方法用于求解层状半空间中受球体P，SV约束的三维（3D）小山的地震响应和SH波。用直接刚度法和汉克尔变换法求解球面波源场的自由场，利用格林函数在半空间中构造散射场。通过与一些文献的结果进行比较，验证了该方法的正确性和准确性。该方法可用于处理任意形状的山丘地形，具有适用性广，精度高，收敛速度快等优点。以高斯山地形为例，球面P入射下山体的散射现象，研究了SV波和SH波，并探讨了山丘地形，震源位置和频率对现场地震响应的影响。结果表明：山体地形的存在具有明显的聚焦作用，显着扩大了山体表面的地震反应，山体在能量传播过程中具有明显的隔震作用；随着入射波频率的增加，在山地表面位移的波动幅度增大；坡面上水平位移的波动幅度为SV波> SH波> P波，垂直位移为P波> SV波。显着扩大了山体表面的地震反应，山体在能量传播过程中具有明显的隔震作用；随着入射波频率的增加，在山地表面位移的波动幅度增大；坡面上水平位移的波动幅度为SV波> SH波> P波，垂直位移为P波> SV波。显着扩大了山体表面的地震反应，山体在能量传播过程中具有明显的隔震作用；随着入射波频率的增加，在山地表面位移的波动幅度增大；坡面上水平位移的波动幅度为SV波> SH波> P波，垂直位移为P波> SV波。