Wave Propagation Lab./NOAA/Environmental Res. Labs., Boulder, CO 80303
Using long vertical arrays (LVAs) in ocean acoustics enables one to measure an S matrix describing transformations of modes in inhomogeneous waveguides. The S matrix allows one not only to calculate the sound field for any configuration of sources and receivers but also to proceed to the solution of the inverse problem (IP)---retrieving inhomogeneities from acoustical data. The wave-type IP is studied for the 1-D case, which differs significantly from the multidimensional situation. For instance, in the 2-D case, the IP can be solved based only on the submatrix describing forward scattering as a function of frequency. The 2-D irregularities in the acoustic waveguide could be reconstructed as in the 1-D problem with the help of the layer-peeling algorithm via backscattering data. But this approach is of little practical use because backscattering is usually weak. Practical formulation of the deterministic IP in ocean acoustics should exploit some final-dimensional description of the media and use all available data about the S matrix. For example, using phases of diagonal elements measured at only two close frequencies leads to the Munk--Wunsch scheme of modal ocean tomography. In the general case, a numerical-evolution-type algorithm is proposed to solve this nonlinear problem in the spirit of the invariant imbedding approach. [Work supported by NRC and PPSIO of Russia.] [sup a)]On leave from the P. P. Shirshov Institute of Oceanology, Moscow, Russia.