Rigorous ray tracing for frequency-dependent, stratified media

Abstract

The equations of motion for rigorous ray tracing for a frequency-dependent, horizontally stratified media are the same as those for simply a horizontally stratified media. In the Hamilton-Jacobi representation, both time and range are still cyclic variables. The behavior of the motion of cyclic variables can be determined by Routh's procedure, and so the trajectory of the ray path in the vertical plane is described by the equations of motion of rigorous ray tracing. The concept of “group velocity” may be shown in a Hamilton-Jacobi representation to be an application of Routh's procedure where the velocity is explicitly dependent upon the momentum conjugate to time (i.e., frequency). As a by-product, since the effective velocity of rigorous ray tracing is dependent upon the momentum conjugate to horizontal range, the relationship between rigorous ray tracing and classical ray tracing is analogous to the relationship between “group velocity” and “phase velocity.”