Nai-chyuan Yen
Phys. Acoust. Branch, Naval Res. Lab., Washington, DC 20375-5320
In observing the scattering phenomena from an isolated elastic object, one would like to understand the composition of the scattered waves so the characteristic structure of the scatterer can be estimated. This paper reviews such an inverse scattering problem in terms of wave packet decomposition. Particularly, the focus is on a heuristic approach that has been developed from the study of acoustic scattering. The basic scheme of this approach is to examine the coherence property of the wave signature of the scattered waves and to compute its energy distribution in a joint time and frequency representation. Also shown is how to apply signal synthesis techniques to determine the dominant components, namely wave packets, expressed as the natural frame (basis), the building block for the formulation of the scattered wave. The magnitude and the phase of each wave packet are evaluated by algorithms that treat them as the independent nonorthogonal components from a set of linear equations. Examples of the response of the scattered waves from shell type elastic objects are used to illustrate the physical implication of this decomposition method in resolving the inverse scattering problem. It is concluded that the wave packet decomposition by means of the natural frame (basis) can be considered as a generalized Gabor and/or wavelet transform. Their relationships are discussed through the fundamentals of linear functional analysis.