Up-down resolution in ocean acoustic tomography

Abstract

In a recent experiment ( The Ocean Tomography Group, Nature, 299, 121–125, 1982) the sound-speed field (and hence temperature) within an ocean volume was computed from acoustic travel times through the volume along many diverse ray paths, using inverse theory. Here we consider the limits on vertical resolution imposed by the fundamental character of the ocean sound channel. For a standard case we take an axial transmitter and receiver separated by 1000 km, with layers determined by the turning depths of double-looped rays. This gives an underdetermined system of 10 layers and six rays, with a forbidding up-down ambiguity between ‘conjugate’ layers (two layers with equal sound speed above and beneath the sound axis). The ambiguity can be reduced (but not eliminated) by including rays with an extra upper (or lower) loop, and can be removed by going to a coarse vertical grid. The results apply to the ‘agnostic’ case where nothing is prescribed; if it can be assumed that the disturbances are N( z) weighted according to WKBJ theory, then the standard 10-layer case is adequately resolved in the upper and axial ocean. If one can prescribe that the disturbance is associated with only the gravest few modes (as found during the MODE expedition), then the results are favourable at all depths. We consider tomography with reciprocal transmissions for obtaining the fields of both particle velocity and sound speed, and we assume that the density perturbations are adequately determined by the sound field using an average T-S relation. The thermal-wind equation relates the vertical velocity gradient to the horizontal density gradient and can be used to impose a constraint on the inversion process, which significantly improves the determination of both fields. The procedure leads to a formalism for objectively separating barotropic and baroclinic velocity fields.