Variation of acoustic arrival patterns in the time domain due to sound-speed perturbations

The feasibility and efficiency of inversions in ocean acoustic travel-time tomography critically relies on the ability to accurately model and predict the reception of an acoustic source at a distant receiver in the time domain (arrival pattern), as well as its perturbations due to changes in the sound-speed distribution. The present work introduces an approximation method for wave-theoretic arrival-pattern predictions in general range-dependent ocean environments based on Born and Rytov approximations of the second order. The range-dependent ocean environment is considered as a perturbation of a range-independent reference state, for which the acoustic field of a point source in the frequency domain, i.e. the Greens function, is modelled using normal-mode theory. Then using the Born and Rytov approximations the perturbed Greens function, corresponding to the perturbed ocean environment, is expressed in terms of the unperturbed Greens function and the medium (sound-speed) perturbation for each frequency within the source bandwidth. Using the normal-mode representation for the unperturbed Greens function, closed-form expressions for the first and second Born and Rytov approximations are derived, generalizing previous results for Greens function perturbations in range-independent environments, and indicating that the effects of range dependence on the acoustic field in the time domain are of second order. To cope with the multi-modal nature of ocean acoustic propagation, a variation of the standard Rytov method is applied, proposed by J. Keller, according to which the Rytov approximation is applied to each modal component independently. Having calculated the perturbed Greens function in the frequency domain, the corresponding arrival pattern in the time domain is obtained through the inverse Fourier transform. A number of numerical examples demonstrate an advantage of the Rytov approximation (over the Born approximation) for time-domain and arrival-time calculations