A numerical marching scheme to compute scattering in the ocean

In the study of underwater propagation of sound in an ocean environment, much effort has been expended in considering energy propagating in a designated direction. In a range-dependent ocean environment, scattering in all directions will occur, but in some ocean environments the all-direction scattering is weak and often can be ignored. For long-range propagation, keeping the cumulative weak scattering can be important. Numerical treatment of this type of scattering in a very long range presents two computational problems: (1) the required memory storage, and (2) the required computation time. In this paper, a marching technique is developed to handle the cumulative scattering, thus alleviating the memory storage problem, and an efficient numerical solution is introduced which reduces the computation time. When using a marching technique to solve this problem, one usually encounters the problem of well-posedness. In the context of the development of the numerical scheme, an approximation is made which suppresses the instability associated with the well-posedness question. Additionally, in the scheme, at large distances from the source a continuation process is employed (essentially a PE) to continue the solution, thereby modeling an actual physical environment without scattering. The theoretical formulation of a representative scattering equation and the development of the scheme for solving this equation will be discussed. Moreover, a realistic problem with weak scattering is presented to demonstrate the validity of this treatment.