Performance bounds for acoustic tomography in a vertical ocean slice

Reciprocal travel-time data along acoustic multipaths between transceivers in the ocean sound channel can be inverted to form estimates of sound speed and horizontal current in the vertical plane of the transceiver pair. We investigate the quality of such estimates in a range-independent environment. Since most of the information gathered along an acoustic path is concentrated near its turning depths, inversions are characterized by strong sidelobe contamination. Estimates at depths in the upper ocean are contaminated by fields in the lower ocean and vice versa. Therefore estimates can be improved by use of a priori knowledge of contaminating fields at the position of the sidelobe. The Backus-Gilbert method is adapted to allow for use of a priori knowledge and three measures of system performance are defined, viz., resolution length, stochastic error, and ratio of sidelobe to primary lobe acceptance. Trade-off relations among these quantities are calculated for 17 eigenrays in a Munk canonical profile for various orders of a priori knowledge. The limit of perfect knowledge gives an absolute bound on system performance. Numerical examples indicate poor performance in the lower ocean; but good estimates of sound speed and acceptable estimates of horizontal current are feasible in the upper ocean.