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