Travel times of acoustic ray paths are computed between a source and a receiver placed at mid-depth at a range of 1000 km. The times are computed for a smooth reference profile and for a profile containing a mesoscale eddy field. The differences between the travel times for the reference and ''eddy-populated'' fields are used to iterate a linearized model (Wiener filter) of the sound-slowness field. The model is iterated until it fits the data. The final iterate, however, is statistically inconsistent with the correct result according to error bars computed from linear theory. At long ranges the travel times are biased by the eddy field. The bias is small (but not insignificant) compared with the travel time fluctuations arising from climatological fluctuations of the ocean. A correction for the bias is used to compute a model that fits the data and is statistically consistent with the correct result. In addition, a numerical technique is described that significantly reduces the computation required for the Wiener filter in this application.