Ocean acoustic tomography: Travel time biases

The travel times of acoustic rays traced through a climatological sound-speed profile are compared with travel times computed through the same profile containing an eddy field. The exact travel time difference is compared with its constituent terms, one of which is linearly related to the deviation of the sound speed (referenced to the climatological profile) and the others which are nonlinearly related to the deviation. At ranges that are much greater than the eddy scale and for eddy fields whose range-averaged temperature anomaly is small, the numerical results are: (1) the values of the nonlinear terms are insensitive to changes in the positions of the eddies and (2) the nonlinear terms are approximately proportional to the range between the source and receiver and to the square of the eddy anomaly. At a 1084-km range in the east Atlantic at 24 °N (36 °N) the nonlinear terms can account for 17% (90%) of the exact travel time change where the temperature anomalies associated with the eddies are typically ±0.5 °C (±1 °C). Linearized inversions (based on the linear estimator of the travel time difference) which use the exact travel time differences for data should yield biased results since the average values of the nonlinear terms are not zero. If an a priori knowledge of the eddy spectrum is known, the nonlinear terms could be computed for each ray and subtracted from the exact travel time change. It may then be beneficial to use the corrected set of travel time differences in a linear inversion which would require no iteration.