Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity

In this paper, the scattering of SH-wave by a semi-cylindrical hill above a subsurface cavity in half-space is studied based on the idea of match up, by using complex functions and multi-polar coordinates. During the solution, we divide the solution domain into two. The first one is a circle domain, including the boundary of the hill, and the second one consists of all of the rest parts. A solution is constructed in the circle domain, where the solution satisfies the condition that stress is zero at the hill edge and arbitrary at the other part. In the second domain, including a semi-cylindrical canyon and a subsurface cavity in the half-space, the scattered wave function is constructed, which satisfies the condition of stress free at the horizontal surface. Then, by using the moving coordinate method, the two solutions are matched up on the junction interface, satisfying the boundary condition at the subsurface cavity edge. The problem can be reduced to solve a set of infinite linear algebraic equations. Finally the computational results of surface displacement are presented together with a discussion.