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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。
The analytical solution of the SH wave to the elliptical inclusion scattering near the vertical interface is given by the complex function method and the Green function method. First, the half-space model to be solved is divided into two right-angle regions I and II along the vertical boundary. By using the method of conformal mapping, the outcrops of elliptic inclusions in region I are mapped to the outliers of the unit circle, and the scattering wave fields that satisfy the right-angle boundary conditions in the two regions and the Green function are constructed by using the image method. Secondly, Based on the idea of convergence, an infinite algebraic equation system satisfying the continuous displacement and stress conditions at the interface is established by adding an additional force system at the interface, and the finite-term equations are truncated. Finally, a concrete example for solving the displacement of the surface is given. The results show that the incident wave number, incident angle, inclusion location, vertical interface and material parameters have an impact on the distribution of the amplitude of surface displacement.