The effect of the inhomogeneities on the propagation of elastic waves in isotropic bodies

A new method is introduced for estimating the effects of the inhomogeneities on the propagation of the elastic waves in isotropic bodies. The method is based on the Kirchhoff electromagnetic potentials. It is applied here for estimating the effect of a static density inhomogeneity, either extended or localized, on the elastic waves propagating in an infinite, or a semi-infinite (half-space) body. For a semi-infinite body the method leads to coupled integral equations, which are solved. It is shown that such a density inhomogeneity may renormalize the waves velocity, or may even produce dispersive waves, depending on the geometry of the body and the spatial extension of the inhomogeneity. The method can be extended to other types of geometries or inhomogeneities, as, for instance, those occurring in the elastic constants.