Travel time bias at sound reflection from an uneven surface: Implications for ocean remote sensing

Travel time is the acoustic quantity which is most frequently used to infer physical properties of the ocean or its bottom from acoustic measurements. Ocean boundaries typically have a complicated shape with smaller-scale features normally described as random roughness. The roughness translates into fluctuations of reflected acoustic arrivals. In this paper, statistical properties of acoustic travel time are considered in homogeneous and a vertically-stratified 3-D ocean with rough boundaries and interfaces. On average, the rough surfaces can be either horizontal planes, corresponding to the ocean surface, or deterministic curved surfaces, corresponding to the sea floor or interfaces within the ocean bottom. It is shown that mean acoustic travel time differs from the travel time in an average medium. In particular, in agreement with Fermat’s principle, small cross-range slopes of the reflecting surface always decrease ray travel time. The travel time bias is studied using the ray and the adiabatic normal mode theories. Implications are analyzed of the travel time bias on interpretation of measurements made with echo sounders, inverted echo sounders, and tomography systems employing surface- and/or bottom-reflected arrivals. [Work supported by ONR.]