Three-dimensional ocean acoustics: Techniques and examples

Abstract

The method of matched asymptotics can be used to solve scattering problems involving a compact object in a waveguide [M. D. Collins and M. F. Werby, J. Acoust. Soc. Am. 85, 1895–1902 (1989)]. This approach involves different asymptotic limits in different regions. In the inner region near the object, the Green’s function can be approximated by either the free-space or half-space Green’s function depending on the vertical location of the object. The inner problem is therefore the free-space or half-space scattering problem. The outer solution satisfies the three-dimensional parabolic equation. When horizontal variations in the waveguide are sufficiently gradual, the solution is asymptotic to a specular point source for ka=O(1). This approximation can be improved by including a vertical dipole correction. The three-dimensional parabolic equation has been applied to free-space scattering problems by solving the exterior problem for the scattered field directly [M. F. Levy and A. A. Zaporozhets, J. Acoust. Soc. Am. 103, 735–741 (1998)]. This approach is also useful for some waveguide scattering problems. [Work supported by ONR.]