含有圆形夹杂的双相介质半空间对SH波的散射与地震动

采用复变函数和Green函数方法，对双相介质界面附近含有圆形弹性夹杂的无限半空间在稳态入射SH波作用下的地表运动问题进行研究。首先，利用“虚设点源”的方法构造所需Green函数，即在四分之一空间自由表面上任意一点作用点源函数时位移基本解答；其次，利用界面“契合”技术和“镜像”的思想建立含有无穷未知力系的第一类Fredholm积分方程组，通过有效截断方法求解该方程组；最后，建立地表位移幅值表达式并给出其分布的具体算例分析。结果显示：入射角度、入射波数和圆形夹杂到自由表面的距离以及双相介质界面的距离均对地表位移幅值有一定程度的影响。

The Ground Motion and Scattering of SH Waves for Bi-material Half Space Including Circular Inclusion

The analysis for the problems of the ground surface motion in infinite half space including a circular elastic inclusion near bi-material interface impacted steady incident SH waves is studied by using the methods of complex function and Green function. Firstly, the Green function needed for the problem is constructed with the aid of the “image a point source load” method, which is an essential solution of displacement function for a quarter space impacted a point source load at any point of the its free boundary. Secondly, a series of the first kind of Fredholm integral equations containing infinite unknown forces are contained by using the technology of interfacial “conjunction” and the idea of “image”. Then the equations are solved with aid of an effective truncation. Finally, some examples for the amplitude of the ground surface displacement are given in detail. Numerical examples demonstrate that the distribution of the amplitude of ground surface displacement is influenced to some degree by the incident angles, incident wave numbers, the distance between the circular inclusion and the free surface and the distance between the circular inclusion and the bi-material interface and so on.