垂直界面附近椭圆形夹杂对SH波的散射与地震动研究

利用复变函数法和Green函数法给出了SH波对垂直界面附近椭圆形夹杂散射问题的解析解答。首先，将待求的半空间模型沿垂直边界分割为区域Ⅰ和区域Ⅱ两个直角域。通过保角映射的方法将区域Ⅰ内椭圆形夹杂的外域映射为单位圆外域，并利用镜像方法构造出两个区域内满足直角域边界条件的散射波场及适用的Green函数；其次，利用界面契合思想，通过在界面处添加附加力系的方法建立起满足界面处位移和应力连续条件的无穷代数方程组，并截断有限项求解；最后，给出了求解地表位移幅值的具体算例。结果表明，入射波数、入射角度、夹杂位置、垂直界面以及材料参数都对地表位移幅值的分布有影响。

Study of scattering of SH-waves by a buried elliptic inclusion near a vertical interface and ground surface vibration

The methods of complex variable function and Green’s function are applied to derive analytical solutions to the scattering of SH-waves induced by a buried elliptic inclusion near a vertical interface in the elastic half space. Firstly, the analytical model to be solved is divided into two rectangular domains along the vertical interface. The conformal mapping method was used to map the outer boundary of the elliptic inclusion into a unit circle in the domain I. Moreover, in these two domains, the method of images is applied to construct scattering wave fields and an applicable Green’s function satisfying boundary conditions of rectangular domains. Secondly, with the aid of interface ‘conjunction’ technique, infinite algebraic equations are established by adding an additional system of forces at the interface and then solved by truncation, which meets the displacement and stress continuity conditions at the interface. Finally, some specific examples are given to estimate surface displacement amplitudes. Numerical results show that incident wave, incident angle, the position of inclusion, material properties and vertical interface to some extent affect the distribution of ground surface displacement.