Examination of coherent surface reflection coefficient (CSRC) approximations in shallow water propagation

The parabolic wave equation (PE) code of Rosenberg [J. Acoust. Soc. Am. 105, 144–153 (1999)] is used as a benchmark to study acoustic propagation in an ocean waveguide with a rough air/water interface. The PE results allow a close examination of the ability of a ray code [i.e., Gaussian RAy Bundle (GRAB)] to accurately estimate coherent field propagation using a coherent reflection coefficient derived from scattering theory. Comparison with PE implies that the Beckmann–Spizzichino model, as given within the GRAB software package, does not give accurate predictions of the coherent field at long ranges. Three other coherent reflection coefficient approximations are tested: the perturbation, the small slope, and the Kirchhoff approximations. The small slope approximation is the most accurate of the models tested. However, the Kirchhoff approximation is perhaps accurate enough for some purposes and would be simpler to implement as a module within GRAB.