### ASA 125th Meeting Ottawa 1993 May

## 1pNS2. Application of multiresolution decomposition to scattering.

**John J. McCoy
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*School of Eng., Catholic Univ. of America, Washington, DC 20064
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**Ben Zion Steinberg
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*Tel-Aviv Univ., Tel-Aviv 69978, Israel
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The theory of multiresolution decomposition, using orthogonal wavelets,
has received considerable attention as a tool for signal processing and more
recently for developing efficient numerical algorithms for the solution of a
class of integral equations. Relatively few studies have been reported of its
use to investigate fundamental physics of the across-length-scale coupling that
is a critical component for understanding the response of complex dynamical
systems. In the context of the scattering of acoustic signals by a complex
subscale heterogeneity in an elastic plate, the accommodation of the subscale
heterogeneity in prediction models for the full-scale response, via a precisely
defined operator, is demonstrated. This operator is seen to be invariant under
changes in either the problem forcing or in the full-scale geometry of the
plate system.