Scattering on a small nonhomogeneities in an elastic medium

The problems of diffraction of a flat elastic wave (transversal or longitudinal), scattered on the cylinder, are investigated. The radius $a$ of the cylinder is small ($\operatorname{ka}\ll1$, where $k$ is the wave frequency). The waves of the horizontal polarization (SH-waves) are scattered similarly to the electromagnetic waves of the appropriate polarization. The small nonhomogeneity is proved to radiate as a point source, the potency of which is proportional to magnitudes of jumps of the Lame parameters $\mu_1$, $\mu_2$ and the square of the nonhomogeneity cross-section.
The scattering of the flat waves of the vertical polarization submits to the more complicated law of radiation, because of the problem is vectorial and the components of displacement vector are expressed by means of scalar and vectorial potentials. However, the scattering on the small nonhomogeneity is the same asymptotic behavior as in the case of the SH-waves.