Rays, modes, wavefield structure and wavefield stability

Sound propagation is considered in range-independent environments and environments consisting of a range-independent background on which a weak range-dependent perturbation is superimposed. Recent work on propagation of both types of environment, involving both ray- and mode-based wavefield descriptions, have focused on the importance of $\alpha $, a ray-based ``stability parameter,'' and $\beta ,$ a mode-based ``waveguide invariant.'' It is shown that, when $\beta $ is evaluated using asymptotic mode theory, $% \beta =\alpha .$ Using both ray and mode concepts, known results relating to the manner by which $\alpha $ (or $\beta $) controls both the unperturbed wavefield structure and the stability of the perturbed wavefield are briefly reviewed.