One-step analysis of non-linear traveltime data in ocean acoustic tomography

A new approach based on statistical estimation is proposed for the analysis of tomographic traveltime data in cases of significant nonlinear dependence of the traveltimes on the sound-speed variations. Traditional tomography schemes based on linear perturbative inversions about a single, a priori fixed background state cannot properly handle such cases since the linearized model relations will lead to considerable inversion errors, depending on the extent of nonlinearity. In contrast, the background state is considered here as a variable unknown quantity to be estimated from the traveltime data, simultaneously with the peak identification function and the sound-speed perturbation. Using the maximum likelihood approach and the Gaussian assumption, the statistical estimation problem reduces to a weighted least squares problem to be solved simultaneously for the three unknown quantities. A posteriori inversion-error estimates are derived accounting also for uncertainties in the background selection and the peak identification. The proposed method is applied to nine-month-long traveltime data from the Thetis-2 experiment, conducted from January to October 1994 in the Western Mediterranean Sea, where the variability of the ocean environment gives rise to significant nonlinear dependencies between sound-speed and traveltime variations. The recovered temporal variability and stratification compare well with independent XBT observations.