Range-Dependent Regularization of Travel-Time Tomography based on Theoretical Modes

O.C. Rodríguez orodrig@ualg.pt
S.M. Jesus sjesus@ualg.pt
SiPLAB-FCT, Universidade do Algarve,
Campus de Gambelas,
PT-8005-139 Faro, Portugal.

Comments: download pdf file.
Ref.: Acta Acustica united with Acustica, vol. 88, pp.761-762, 2002.

Travel time inversion is a fundamental method of Ocean Acoustic Tomography, to estimate perturbations in sound speed. By discretizing the watercolumn into a system of layers, the method allows to introduce a system of linear equations, relating a known vector of perturbations in travel time, to an unknown vector of perturbations in sound speed, through the so-called ``observation matrix''. Inverting the system allows to estinate the perturbation in sound speed in each layer of the watercolumn. However, in most problems of practical interest, the number of unknowns (i.e. the perturbations in sound speed) is larger than the number of equations (i.e. the number of delays in travel time). Thus, inverting the sytem can be viewed as an ill-posed problem. The discussion presented in this paper illustrates an approach to the inversion problem, which is based on the usage of theoretical modes. Further, it is shown that for a range-dependent perturbation in sound speed, corresponding to a superposition of plane waves, the inversion problem can be regularized (i.e. the system can be written in order to deal with more equations than unknowns) by estimating only the amplitudes and phases of the linear waves. Particular examples are given for real data.