ELASTIC-WAVE PROPAGATION IN GENERAL TRANSVERSELY ISOTROPIC MEDIA .1. GREENS-FUNCTIONS AND ELASTODYNAMIC HOLOGRAPHY

The formalism of plane-wave spectral decomposition of elastic wave fie lds is used to derive a simple method for solving the inverse scatteri ng problem, which can also be regarded as a basis for further imaging techniques. For transversely isotropic materials like fiber composites , but also, e.g., unidirectionally grain-structured austenitic steels, the elastodynamic dyadic and triadic Green's functions are derived in form of their two-dimensional space-time spectral representations. Ba sed on a theory of plane-wave propagation in these media [M. Spies, J. Acoust. Sec, Am. 95, 1748-1760 (1994)], the resulting expressions app ear in a coordinate-free form and contain the orientation of the mater ials' fiber axis as an additional parameter. Thus the results are part icularly useful for extension to the case of layered material. The for mulation of Huygens' principle for a source-free half-space provides t he socalled elastodynamic holography, which allows forward-backward pr opagation of elastic wave fields in form of an integral representation for the displacement vector. This representation is evaluated with re spect to space and time via fast Fourier transforms, the effectiveness of the resulting imaging algorithm is demonstrated in comparison with the conventional isotropic algorithm used so far. The integral repres entation mentioned above is derived for given displacement in a refere nce plane (specimen surface), the derivation for the case of given sur face traction will follow in the second part of this presentation, pro viding an integral representation for the transducer field.