Construction of Approximations to Acoustic Green's Functions for Nonhomogeneous Oceans Using Transmutation

摘要

Transmutation can map the solutions of one equation into solutions of another equation. Recent applications of transmutation in underwater acoustics have involved the Helmholtz equation that governs the propagation of sound in the ocean and the Sturm-Louiville problem that governs the depth dependent normal modes of the ocean. In all of these cases, the goal was to find solutions corresponding to depth dependent indices of refraction from knowing solutions for a constant index of refraction because the latter solutions are much easier to find. In the present paper the authors again use transmutation from constant to variable indices, but emphasize finding and using approximate solutions corresponding to variable indices of refraction.