Rigorous Gaussian‐beam modeling of source functions for acoustic radiation and propagation

Abstract

Gaussian beam functions have favorable properties for propagating acoustic wavefields through complicated ocean environments. Use of these functions in propagation algorithms requires a decomposition of the actual or induced source distribution into a superposition of Gaussian beams. In implementations of the “Gaussian beam method” so far, the decomposition is not unique because of freely assignable parameters in the beam stack. This causes difficulties with a priori predictability [Lu et al., Geophys. J. R. Astron. Soc. (1987); Niver et al., J. Acoust. Soc. Am. Suppl. 1 81, S9 (1987)]. The source representation problem can be addressed rigorously by performing the decomposition on a lattice in a discretized (configuration‐spatial wavenumber) phase space. The formulation of this discretization scheme [Bastiaans, Opt. Eng. 20, 594 (1981)] is reviewed and then applied to radiation from a cosine aperture test field distribution. It is shown how successive addition of individual displaced and (or) rotated beams with narrow, wide, or “matched” waists systematically homes in on the independently calculated reference solution, although each selection strategy emphasizes different regions in the phase space. The utility of the various options is discussed, as are the implications for synthesis of aperture fields from measured farfield data.