Low-frequency rolloff in the response of shallow-water channels

Abstract

Propagation in a shallow-water channel of constant sound speed, overlying a homogeneous viscoelastic half-space with frequency-independent loss factors, is examined as a function of range, frequency, water depth, and a parameter representing the initial rate of increase of bottom reflection loss with increasing grazing angle. Particular attention is focused on the ‘‘transition’’ frequency below which the transmission loss increases rapidly. It is found to separate a ray-theoretical domain, where the directional spectrum of transmitted sound is quasicontinuous, from a modal domain where, in fact, only the first mode carries significant energy. A simple algebraic formula is derived for this transition frequency that also yields good estimates of both the ‘‘optimum frequency’’ of Jensen and Kuperman [J. Acoust. Soc. Am. 73, 813 (1983)] and the low-frequency rolloff observed in some data.