### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 1pNS7. A numerical approach to scattering by many scatterers of various
sizes.

**Matthias G. Imhof
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*MIT Earth Resources Lab., E34-370, 42 Carleton St., Cambridge, MA
02142-1324
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A numerical method is derived for solving wave fields in the presence of
many scatterers with different sizes. Three different scattering regimes are
distingished: a<<(lambda), a<(lambda), and a>(lambda), where (lambda) denotes
the wavelength and a is the maximal diameter of the particular scatterer. In the
case of a<<(lambda), the Rayleigh approximation can be used where the scattered
wave field hardly depends on the geometry of the scatterer. For a>(lambda) the
scattered fields are calculated using MMP expansions [M. G. Imhof, J. Acoust.
Soc. Am. 97, 754--763 (1995)], which yields the full waveform solution by
evaluating the boundary conditions. Scatterers with a<(lambda) are too large for
the Rayleigh approximation to hold or for the scattered field to be independent
of the geometry. On the other hand, the scatterers are too small to justify the
MMP approach. Thus, the scattered fields are expanded into a series of Hankel
functions where only the first few orders are used. Their weights are found in
the least-squares sense by Galerkin's method. As an example, results are
presented for many elliptical scatterers of different sizes.