Elastodynamic long wavelength phase

Abstract

The phase of the elastodynamic scattering amplitudes (both longitudinal and transverse) varies linearly with frequency in the long wavelength limit for scatterers of finite extent. In this Paper it will be shown that the linear phase variation has the same magnitude but opposite sign when the directions of incidence, scattering and polarization of the transmitter and receiver are reversed. Hence, the coefficient of the linear phase variation can be shown to be zero for a variety of special cases. First, the linear phase variation is shown to be zero for scattering in the forward direction if there is no change in polarization. Second, the long wavelength phase variation is shown to be zero for scatterers which possess various spatial symmetries with an appropriate choice for the origin of co-ordinates. Finally, it is shown that if the material properties are self-similar and the elastic constants in the region of scattering differ only slightly from those of the host, an origin of coordinates can be found such that the linear phase variation always vanishes.