Multipole expansion technique for wave scattering by buried objects in an elastic half-space

A conceptually simple technique is proposed to solve the problem related to the elastic scattering by buried objects. The scattered fields are expanded with the basis functions in integral forms. These integrals consist of the wave emitting from the multipole sources, which may be called generalized Weyl integral, and the corresponding waves reflected at the planar ground surface, which satisfy the radiation condition at infinity. Thus the scattering problem reduces to the determination of expansion coefficients by matching the boundary conditions at the object itself. The method is very similar to that of separation of variables for the scattering problem in an infinite space. As an example, the scattering of a plane wave by a spherical cavity in half-space is analyzed and the results are presented with figures.