Kirchhoff approximation for scattering from solid spheres at flat interfaces: Improved description at large grazing angles

Abstract

The Kirchhoff approximation has previously been used to model scattering from partially exposed elastic spheres breaking through a flat interface, with variable exposure level, grazing angle, and frequency [J. Acoust. Soc. Am. 136, 2087 (2014)]. The limits of the Kirchhoff integral are determined by the boundaries of illumination on the sphere for each scattering path. Recent adaptations to the methods of boundary determination within the Kirchhoff approximation have yielded faster numerical integration algorithms and higher similarity of results when compared to experimental scattering data and the exact solution at half exposure [J. Acoust. Soc. Am. 140, 3582-3592 (2016)]. Additional steps have been taken to account for the partial blocking of the interface by the partially exposed sphere, through inclusion of a new correction term. This correction is largest at high grazing angles, low frequencies, and low target exposures, and drastically improves the Kirchhoff approximation within these limits. [Work supported by ONR.]