Sound transmission in a channel with bilinear sound speed and environmental variations

Abstract

The effects in a bounded channel of a bilinear sound-speed profile on ray geometry, travel time, and spreading loss are examined. General equations are derived. The case of bottomed source and receiver is considered in detail. Appropriate approximations are made and properties of the ray geometry, travel time, spreading loss, and the total acoustic field at the receiver are deduced. It is shown that the gross characteristics of observed phase variations off Bermuda may be generated by changes in sound speed associated with Rossby waves and tidal effects. The addition to the model of tidal depth variation leads to intensity variation which accounts for 80% of the range of intensity variations observed near Bermuda.

Target-depth estimation in active sonar: Cramer–Rao bounds for a bilinear sound-speed profile

“…For SSPs with multiple constant gradients, the ray propagation from the source to the target position was realized by computation of successive ray arches. 15 The next two partial derivatives, @T=@r and @T=@z, are derived analytically from the equations system that connects the one-way travel time (i.e., sonar target, target array) to the target parameters in the bilinear SSP case, which was introduced by Baer and Jacobson, 16 and is given as r ¼ Gðu; zÞ;…”

TMA from bearings and multipath time delays

“…Using the framework of the ray theory in a stratified medium where the sound speed is no longer constant, the expressions of T p and T q are much more complicated and also depend on both the type of each eigenray and the SVP, as explained in appendix A for the bilinear case [9].…”

“…More precisely but beneath observability theory and manipulating (9), the source range is expandable in terms of the noiseless time-delay measurement ¿ and the actual depths Z p , Z q without approximation 1…”

“…We detail the analytical computation of the two functions G and H introduced in Section II, the following equations and notations being largely borrowed from [9]. Denoting by c, c O , c 1 , c 2 , c 3 the sound speed, respectively, at the source depth z, the observer depth z O , the sea surface depth z 1 = 0, the minimum of celerity depth z 2 , and at the bottom depth z 3 (assuming c 1 > c 3 > c 2 , otherwise exchange the bottom and the surface, and z positive downwards), and by g 1 , g 2 the algebraic gradients of celerity in the surface layer and in the deep layer (note that these gradients are taken positive in [9], thus introducing minor changes of sign in the sequel), one recalls the expressions obtained in [9] for the eigenrays…”

The overtone structure of acoustic fluctuations due to harmonic variations in sound speed (L)

“…The effect of geostrophic flow on sound speed and thereby on the intensity and phase of acoustic transmission has been analyzed by Jacobson et al [1][2][3][4] These authors used ray theory, and considered long range transmission in the deep ocean over times of typically days. Intensity variations due to tidal depth changes found by Baer 3 are similar to those discussed below for shallow water.…”