Recent Progress in Modeling Bottom-Interacting Sound Propagation With Parabolic Equations

In 1973 Tappert introduced the parabolic equation (PE) into underwater acoustics, along with an efficient Fourier transform method for solving the equation. His method has been widely used to model sound propagation in the ocean. Where sound interacts weakly with the bottom, the method is fast and accurate, but in cases where bottom interaction is strong, the method is considerably slower and less accurate. Consequently, new PE methods have been developed that efficiently and accurately account for strong bottom interaction. This paper discusses two important improvements: the first improvement is a more accurate approximation for the phase of bottom-interacting sound, and the second is accurate treatment of boundary conditions in the bottom. PE calculations with and without these improvements have been compared with exact benchmark results for test cases with strong bottom interaction. The improved calculations are in excellent agreement with the exact results whereas the unimproved calculations show only marginal agreement.