ARRIVAL-TIME PERTURBATIONS OF BROAD-BAND TOMOGRAPHIC SIGNALS DUE TO SOUND-SPEED DISTURBANCES - A WAVE-THEORETIC APPROACH

The problem of arrival-time perturbations due to perturbations of the sound-speed profile is studied on the basis of full-wave equation modeling of the direct problem. Arrival times are analytically modeled as the time instants corresponding to the significant maxima (peaks) of the arrival pattern, in full agreement with measurement practice. In this framework the identification of actual (measured) arrivals as ray or modal ones is not required. An elegant perturbation formula is derived for the arrival times, containing the background arrival times, time derivatives of quantities associated with the background field, and also the functional derivative of the background field with respect to the sound-speed profile. This formula is of a system-theoretic nature and can be applied to any kind of environment, either range-dependent or range-independent. The restriction to the range-independent environment permits further elaboration of the perturbation formula since, in this case, the functional derivative of the acoustic-channel transfer function can be analytically expressed, e.g., in terms of normal modes. The performance of the proposed approach is demonstrated by studying two test cases: the linear- and the canonical-profile waveguide. The agreement between actual arrival times, obtained by numerically solving the direct propagation problem, and the arrival times predicted by means of the perturbation formula is very satisfactory. Since the proposed scheme can predict arrival-time perturbations even in cases that the arrival times cannot be identified as ray or modal ones, it is expected to be helpful in extending the applicability of ocean acoustic tomography. © 1995, Acoustical Society of America. All rights reserved.