The significance of the choice of basis functions in the problems of acoustic tomography of the ocean

Abstract

Different approaches to the parametric description of the ocean inhomogeneities of both refraction and kinetic types are discussed in the context of the inhomogeneity reconstruction with the use of tomographic techniques. In addition to bases commonly known and widely used in oceanological problems (such as specification of the inhomogeneity parameters at the grid nodes or in nonoverlapping shapes compactly covering the region of interest), a new nonorthogonal and redundant basis consisting of a set of overlapping bands (and, presumably, more convenient for solving tomographic problems) is considered. The abilities of different bases to reconstruct the ocean inhomogeneities are compared with the use of special theoretical approach. The quality of reconstruction on the band and cell bases is investigated against the relationship between the number and composition of the basis elements. Examples of the reconstruction of ocean inhomogeneities with the use of the aforementioned basis functions are given together with the results of comparison.