Scattering of plane elastic waves on a small inhomogeneity lying inside an elastic layer

The problem of diffraction of the elastic plane wave of the horizontal polarization (SH-wave) on a small inhomogeneity lying in a layer is investigated. The layer is situated on the stress-free boundary of the half-space. The inhomogeneity is supposed to be a circular cylinder, radius of which is small in comparision with the length of the falling wave. The insident wave is polarized in parallel to the axis of the cylinder.
It is proved that the small inhomogeneity radiates as a point source, the intensity of which is proportional to area of the cross-section inhomogeneity and the jumps of the squared velocities in the layer and in the inhomogeneity.