ASA 126th Meeting Denver 1993 October 4-8

4aPA11. Wavelet representation of the three-dimensional anisotropic elastodynamic Green's function.

Vinod K. Tewary Christopher M. Fortunko

Mater. Reliability Div., NIST, 325 Broadway, Boulder, CO 80303

A detailed knowledge of waveforms is required for nondestructive ultrasonic characterization of anisotropic materials. The waveforms can be calculated in terms of the elastodynamic Green's function of solids. The traditional Fourier/Laplace transform methods are computationally inefficient for three-dimensional anisotropic solids since they require four-dimensional numerical integration in the wave vector and the frequency space. A representation of the Green's function has been developed in terms of highly localized Huygens-type wavelets in which the Green's function is expressed in the space of slowness vectors rather than that of wave vectors and frequency. The wavelet representation requires only a one-dimensional numerical integration of simple functions and thus saves computational (CPU) time by a factor of about 1000 compared to the Fourier transform method. A solution of the tensorial elastodynamic Cauchy problem and calculation of the retarded Green's function will be described in terms of these wavelets. Results will be presented for pulse propagation in anisotropic solids.