ERCIM News No.22 - July 1995 - FORTH

# Inversion Algorithms for Ocean Acoustic Tomography

by Michael Taroudakis

Ocean acoustic tomography was introduced in the physical sciences several years ago, by Munk and Wunsch, as a tool for monitoring the sea environment. Since then, many experiments have been held in the sea for the validation of the concept itself and the data inversion schemes. The Institute of Applied and Computational Mathematics of FORTH has made an important contribution in the field, through the development of inversion algorithms for acoustic data inversion and their successful application with actual field data.

The concept of Ocean Acoustic Tomography is based on the assumption that acoustic signals recorded in the water column and which are, due to a known acoustic source, placed at a long distance from the receiver, can be used for the estimation of the properties of the water column in the region between the source and the receiver. The problems associated with ocean acoustic tomography, besides the design and realisation of the field experiment, are related to the initial processing of the measured acoustic data and their subsequent inversion for the estimation of the sea water parameters. The sound speed and current velocities are the principal parameters that can be directly recovered by ocean acoustic tomography schemes. From the mathematical point of view, the problem of using tomographic data for sea parameter estimation is an inverse problem. The data (measurement) vector consists of measurable acoustic field quantities, such as modal or ray arrivals, modal phase structure, or even local maxima of the tomographic signal as it is recorded in the receiver location. When the sea currents are neglected, the parameter vector of the simplest inverse problem consists of the sound velocity structure at discrete points in the water column.

The problem can be treated as one dimensional with respect to the sea parameter spatial dependence, i.e. the sound speed is recovered as a function of a single variable (depth), two dimensional when the sound velocity is considered a function of range and depth, or even three dimensional when the sound velocity is a function of a third spatial variable also (azimuth angle). Currently, IACM-FORTH is involved in one and two dimensional problems. In this context, main research activities at IACM-FORTH involve the definition of the function relating the measurable acoustic quantities with the sea parameters, the treatment of the inverse problem thus defined, as well as the study of the linear behaviour of the observables (acoustic measurements) with respect to variations of the water parameters.

Three alternative schemes have been developed and tested by synthetic data, each one based on the assumption that either modal phase, modal travel time or peak arrival times are measurable and linearly related to the unknown parameters. All of them lead to inverse problems that fall within linear inverse theory. Advanced numerical codes solving the direct problem are used in the definition of the inverse problem. Singular Value Decomposition techniques are being used for the solution of the linear system, resulting from the numerical modelling of the inverse problem through the appropriate vector function, while tracking algorithms have been developed for the inter-association of the field observables (e.g. peak tracking).

IACM-FORTH participates in a European consortium working in Ocean Acoustic Tomography in the Western Mediterranean basin. In this context, two large scale experiments have been conducted in this area, funded by the European Commission within the framework of the MAST programme. Several moorings containing two different kinds of tomographic sources which emit BPSK signals of 250 and 400 Hz central frequency have been deployed. The sources were continuously transmitting over two distinct periods of several months each and simultaneous acoustic measurements were made and recorded. Initial processing of the data after the recovery of the moorings was done by IFM/Kiel (Germany), IFREMER (France) and IACM-FORTH. In addition, IACM-FORTH has applied the inversion algorithms based on peak arrivals measurements for a successful recovery of the average sound velocity structure in the area over long periods of the year.

Current activities at IACM-FORTH involve the study of non-linear effects associated with the direct problem and the signal structure formation, so as to modify existing algorithms and extend the range of their applicability.