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 (θ₀); 2) all the relations among the ray source angle (θ₀), 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 (θ₀) and travel time (τ). From the wavefront coordinates (ρ,z), we construct and display ray/wavefront diagrams for a varying source depth (z₀) relative to the minimum propagation speed plane. We also derive the time-averaged acoustic energy flux carried along classical ray tubes.