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Range dependent tomography of internal tides with relative arrivals

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

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Ref.: Proc. of ICCES' 2004, (ISBN:0-9657001-6-X), p.1747-1752, Madeira (Portugal), June 2004.

Abstract : Travel time based inversion is a technique of Ocean Acoustic Tomography, which allows to estimate a field of sound speed perturbation,  c, by inverting a system of linear equations, relating travel time and  c, through the so-called observation matrix. Such matrix can be calculated by representing the waveguide as a layered system, with  c being estimated at each layer. For practical purposes, the parameterization of  c on a basis of orthogonal func-tions can be more advantageous. For instance, the inversion developed in  introduces an expansion of  c on a basis of two-dimensional plane waves, whose amplitudes are estimated in order to map the temporal evolution of the environmental field in a complex bathymetry, through the usage of several sources and a significant amount of receivers. Theoretical modes can be used also as a basis for the estimation of  c(r, z). For a reduced amount of receivers the vertical structure of the field can be expanded on the modes, while the range dependence can be constrained using horizontal plane waves. Such choice of basis significantly reduces the number of parameters to be estimated, but its reliability depends on plane wave propa-gation along range, which is only a particular case. Furthermore, travel time inversion requires the synchronization between the emitted and received signals, so the instant of emission can be taken as the origin of the time axis for the arrivals. Otherwise, the technique has to be modified in order to develop the inversion. In the discussion presented in relative-time inversion is developed, by expanding  c on a basis of empirical modes, and optimizing the match between observed and modeled arrivals within the search space of mode amplitudes. Although the validity of such approach depends on the uniqueness of the solution, the corresponding estimates of depth-averaged tempera-tures provided a good agreement with independent observations. The approach discussed in this paper reconsiders the parameterization of  c on a basis of theoretical modes, without imposing particular analytical constraints to their amplitudes, except that their variation is sufficiently smooth along range. Thus, wave propagation is not restricted to plane waves. Further, the system of equations is rewritten in order to relate modal amplitudes to relative arrivals. The performance of this approach is discussed using environmental and acoustic data from the INTIMATE 96 experiment.

ACKNOWLEDGMENT: this work was partially supported by INTIMATE, ATOMS and NUACE projects from FCT - Portugal.