A numerically efficient global matrix approach to the solution of the wave equation in stratified environments

Abstract

Solution of wave propagation problems in horizontally stratified environments arises in many fields, including underwater acoustics, seismology, and ultrasonics. When the environment is considered range‐independent the wave equation can be separated in depth and range by standard integral transform techniques. The depth‐dependent solution is then found by matching boundary conditions at horizontal interfaces, and the field as a function of range is found by evaluating the inverse integral transforms. Several numerical methods have been developed for this purpose, in underwater acoustics known as the fast‐field technique and in seismology as full wave field and reflectivity methods. These methods have generally been based on propagator matrix solutions for the multilayer Green's function. In contrast to these techniques, the use of a global matrix approach to solve the depth‐separated wave equation automatically yields the possibility of treating problems with several sources and receivers without requirin...