Focusing effects due to solitons: 3D Gaussian beam modeling

Abstract

As is well known, the SOFAR channel in deep water reduces spherical spreading, to cylindrical spreading, allowing sound to propagate to enormous distances. Similarly, soliton packets can produce channels in shallow water, forming acoustic corridors, their walls consecutive solitons. As the solitons pass over a propagation path they can generate dramatic focusing and defocusing effects. Acoustic modeling of such phenomena is challenging in that 3D (horizontal refraction) effects are clearly important (Nx2D approaches fail here). The geotime evolution is equally important—we must model a series of frozen oceans as the soliton packet passes by. Gaussian beam tracing models are ideally suited for such 4D modeling. We have developed a MATLAB Gaussian beam-tracing model to address these problems. It includes capabilities for a variety of useful beam options, from ‘‘geometric beams’’ to the most formal beam theory based on paraxial approximations. The latter is implemented using a novel ‘‘reduced delta-matrix formulation’’ that greatly simplifies the algorithms. The new model also allows for broadband calculations, 3D bathymetry, and 3D oceanography. We will discuss a variety of applications, with particular emphasis on the effects of solitons.