Bounds on performance in tomographic estimates of currents

Abstract

Measurements of travel time anomalies along the acoustic ray paths of a tomographic configuration can be inverted to obtain estimates of the ocean sound velocity profile. Estimates of current component profiles can also be obtained directly from measured data, without use of an intermediate step, such as one relating sound velocity, geostrophy, and satellite altimetry data. While direct estimates of current profiles are theoretically possible, their usefulness will depend on their accuracy in a practical context. This question is now being studied. The Backus-Gilbert theory provides a format in which performance bounds related to such estimates can be conveniently formulated in terms of resolution length, bias error, and variance. Statistical errors, such as those due to clock error, mooring motion, nonreciprocity, and microscale fluctuations, enter the analysis of performance bounds through the covariance matrix of the measured quantities. An example of this covariance matrix has been developed and applied to the configuration used in the 1981 tomography experiment in the MODE area [B. Cornuelle, J. Acoust. Soc. Am. Suppl. 1 70, S38 (1981)].