On the Use of Simple Mathematical Models to Predict SOFAR Propagation Effects

Abstract

A major feature of pulsed sound transmission between points on the SOFAR axis is the abruptly terminated crescendo associated with the decreasing time separation of purely refracted arrivals. Of the nonreflected paths, the first to be received corresponds to a comparatively large horizontal angle at the source, whereas the last is the axial or zero-angle arrival. Ray calculations, using simple analytic functions to represent the sound-channel velocity profile, however crudely, have been thought to describe the principal characteristics of SOFAR propagation, at least qualitatively. Thus, for example, the small-angle solution of Goodman and Duykers [J. Acoust. Soc. Am. 34, 960 (1962)] for a locally parabolic profile predicts the existence of equally spaced convergence zones along the axis. It is shown, however, that their approach fails to give even approximately the observed relationship between arrival velocity and ray angle at the source. Examination of other models of the velocity profile tentatively suggests that those which do yield semirealistic travel time results do not exhibit pronounced convergence effects. In addition, smoothing of convergence peaks is to be expected in broadband pulse transmission from the fact that the ranges at which focusing occurs are dependent on frequency, as revealed by normal-mode calculations. [This work was supported by the Bureau of Ships, U. S. Navy.]