  Several acoustic experiments show a surprising degree of stability in wave
fronts propagating over multi-megameter ranges through the ocean's sound
channel despite the presence of random-like, sound speed fluctuations. Previous
works have pointed out the existence of chaos in simplified ray models
incorporating structure inspired by the true ocean environment. A
``predictability horizon'' has been introduced beyond which stable wave fronts
cease to exist and point-wise, detailed comparisons between even the most
sophisticated models and experiment may be limited for fundamental reasons. We
find, by applying one of the simplified models, that for finite ranges, the
fluctuations of the ray stabilities are very broad and consistent with
lognormal densities. A fraction of the rays retain a much more stable character
than the typical ray. This may be one of several possible mechanisms leading to
greater than anticipated sound field stability. The lognormal ray stability
density may underlie the recent, experimentally determined, lognormal density
of wave field intensities [J. Acoust. Soc. Am. 105 (1999) 3202--18].
