On the invariance of the waveguide invariant

Abstract

Constructive and destructive interference between different acoustic ray paths or modes is a common feature of propagation in the ocean waveguide. Russian investigators first distilled these interference effects into a single quantity, the so-called waveguide invariant. Over the last two decades, investigators have incorporated the waveguide invariant into signal processing algorithms for applications including localization, tracking, and environmental inversion. An important caveat is that a specific numerical value for the waveguide invariant sometimes applies for only a subset of all propagating modes; different numerical values can apply for different subsets. Under appropriate conditions, the waveguide invariant can appear to bifurcate with acoustic data simultaneously showing traits from both values. In the present work, a derivation is sketched that emphasizes what is actually invariant about the waveguide invariant. The proposed approach permits a more ready integration of the waveguide invariant into signal processing algorithms. Examples are presented for both deep- and shallow-water scenarios.