Ray Theory Results and Ray Wavefront Diagrams for the Hyperbolic Cosine Propagation Sound-Speed Profile

In this paper, we provide a complete geometrical treatment of classical rays emanating from an underwater point source and propagating in an unbounded medium where the speed of sound has a hyperbolic cosine dependence on the depth coordinate (z). General results are derived exclusively from Snell's law and are not limited to the case in which the ray emitting source is located at a point on the minimum propagation speed plane. Explicit relations are provided for the following: 1) the ray depth coordinate (z) expressed as a function of the ray horizontal range (ρ) and the ray source angle (θ
₀
); 2) all the relations among the ray source angle (θ
₀
), the ray receiver angle (θ), and the travel time (τ) to reach an arbitrary position of the receiver from an arbitrary position of the source; and 3) the classical wavefront coordinates (ρ,z) along a ray expressed as a function of the ray source angle (θ
₀
) and travel time (τ). From the wavefront coordinates (ρ,z), we construct and display ray/wavefront diagrams for a varying source depth (z
₀
) relative to the minimum propagation speed plane. We also derive the time-averaged acoustic energy flux carried along classical ray tubes.