A more stable transition matrix for acoustic target scattering by elongated objects.

Abstract

The transition (T) matrix of Waterman has been very useful for computing fast, accurate acoustic scattering predictions for axisymmetric elastic objects, but this technique is usually limited to fairly smooth objects that are not too aspherical unless complex basis functions or stabilization schemes are used. To ease this limitation, a spherical-basis formulation adapted from approaches proposed recently by Waterman [J. Acoust. Soc. Am. 125(1), 42-51 (2009)] and Doicu, Eremin, and Wriedt [Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, London, 2000)] is suggested. This is implemented by simply transforming the high-order outgoing spherical basis functions within standard T-matrix formulations to low-order functions distributed along the object's symmetry axis. A free-field T matrix is produced in a nonstandard form, but computations with it become much more stable for elongated aspherical elastic shapes. Some advantages of this approach over the approaches of Waterman and Doicu, Eremin, and Wriedt are noted, and sample calculations for a 10:1 Al prolate spheroid and a 10:1 Al superspheroid of order 10 are given to demonstrate the enhanced stability.