Refracted/Reflected Ray Propagation in a Channel with Horizontal and Vertical Sound-Speed Gradients

Abstract

The sound-speed gradient is assumed to be a vector of constant magnitude and direction that has both horizontal and vertical components. Ray geometry, travel time, and spreading loss are derived for refracted/bottom-reflected rays having an arbitrary initial direction at a bottom-mounted point source and experiencing multiple bottom reflections in a horizontal channel. Rays intercepting a bottom-mounted receiving point after traversing a given number of lobes are isolated and studied. It is found that the changes in travel time and spreading loss caused by the presence of the horizontal gradient are approximately proportional to the component of the horizontal gradient in the direction of the receiving point. With the receiving point placed in the direction of the horizontal gradient, a calculation is made of the total field due to a CW source as a function of the magnitude of the horizontal gradient. Substantial changes from the values when the gradient is purely vertical are found in both intensity and phase. An approximate formula shows that the change in phase is also proportional to the component of the horizontal gradient in the receiving-point direction.