Theoretical Model of Differential Acoustic Travel Times in a Deep Stratified Lake

We have been developing the lacustrine application of Coastal Acoustic Tomography (“CAT”) at Lake Biwa, Japan. We are targeting reliable measurement of ray path-averaged currents by differential travel time. As the largest lake in Japan, Biwa supplies water to 14 million; it has a mean depth in its main “Northern Basin” of 41 m and is stratified from May through December. This work theoretically models the “differential travel time” (DTT) between transducers deployed near the bottom of the lake, at ranges exceeding 5 km under stratified conditions. Notably, we investigate the importance of including the influence of current shear on the ray paths, an effect that is usually neglected when computing DTT. Our model is designed with reference to conditions from a field experiment in the North Basin of Lake Biwa, Japan, in November 2018, for which the thermocline lay at a depth of about 30 m. Deep water is taken to be motionless and to have a constant sound speed. Within the “internal reflection” zone at the thermocline, both current and sound speed are assumed to increase linearly upward, at rates typical of our field experiments. Under these assumptions, the rays are straight in the deep water, and circular in the thermocline. Accordingly, one can easily construct an eigenray from one bottom reflection to the next, with or without account for the effect of current shear on the paths of eigenrays, which allows us to evaluate this influence on computation of DTT.