  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.
