Anderson (1950) revisited

Abstract

The Anderson fluid sphere scattering model [J. Acoust. Soc. Am. 22, 426–431 (1950)] is reexamined to clarify three issues which have been the source of misunderstanding among underwater acousticians. First, the accuracy of the Morse large range approximation for the spherical Hankel functions is investigated. It is shown that the minimum range for use of the approximation is strongly mode number dependent, and should be carefully evaluated in short range and/or high frequency applications. Second, the precise characterization of the forward scatter region is studied. When the scattered field and the incident plane wave are combined, it is shown that little advantage is obtained in detection and localization applications by using forward scattering, rather than backscattering. Third, the translational response, or “rebound,” of the sphere under the action of the incident field is examined. By demonstrating that Anderson’s theory is a limiting case of Faran’s scattering model [J. Acoust. Soc. Am. 23, 405–418 (1951)] for an elastic sphere, which contains the rebound response, it is shown that the response is completely explainable within Anderson’s theory, and is consistent with a description which uses a normal mode expansion around a fixed origin.