Matthias G. Imhof
MIT Earth Resources Lab., E34-370, 42 Carleton St., Cambridge, MA 02142-1324
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.