“…The waveguide invariant has been used for a wide range of applications such as: passive range estimation [58,56,62], matched field processing [59,23], active sonar [49,27,25], array processing [37,57,66], time-reversal mirrors [32,54,38,39], and more (See Appendix A for a complete review of the waveguide invari-ant literature). Despite its many uses, the waveguide invariant is not well studied compared to other ocean-acoustic phenomena.…”