Elastic wave propagation in general transversely isotropic media. I. Green's functions and elastodynamic holography

The formalism of plane-wave spectral decomposition of elastic wave fields to derive a simple method for solving the inverse scattering problem, which can also be regarded as a basis for further imaging techniques. For trasnversely isotropic materiasl like fiber composites, but also, e.g., unidirecttionally grain-structured austenitic steels, the elastodynamic dyadic and triadic Green's function are derived in form of their two-dimensional space-time spectral representations. The results are particularly useful for extension to the case of layered material.The formulation of Huygen's principle for a source-free half-space provides the socalled elastodynamic holography in form of an integral representation for the displacement vector. This representation is evaluated with respect to space and time via fast Fourier trasnforms, the effectiveness of the resulting imaging algorithm is demonstrated in comparison with the conventional isotropic algorithm used so far.