Multiple scattering of sound by correlated monolayers

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Abstract
Earlier results for scattering by random uncorrelated planar distributions, and by doubly periodic planar configurations of relatively arbitrary obstacles, are generalized to pair-correlated nonsymmetrical monolayers. The existing development for parallel cylinders in terms of the Zernike–Prins one-dimensional pair function p(x), is extended to analogous two-dimensional distributions specified by p(R) for aligned impenetrable disks. We obtain the average multiple scattered transmitted and reflected waves, and an energy conserving approximation of the differential scattering cross section per unit area. Simplified forms are developed to facilitate determing p by inverting measured data. Closed form low-frequency results are derived for identical ellipsoids aligned nonsymmetrically to the plane of centers, and the array multipole-coupling processes are discussed in terms of functions of p and their approximations.

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