Experimental determination of modal depth functions from covariance matrix eigenfunction analysis

Abstract

A low-frequency sound field in a shallow-water duct is usually represented by a set of discrete normal modes, each of which is characterized by a unique vertical pressure amplitude depth function. In many applications, such as matched-field signal processing, it is important to have accurate determinations of these depth functions, which are usually calculated from normal-mode models. By using a densely populated vertical array spanning the water column and a large time-bandwidth test signal, in some circumstances the normal-mode functions of the duct may easily be obtained by diagonalizing the cross-spectral density function of the received signal. The condition required for using this technique is that, over the bandwidth used, the fields of individual modes must be mutually incoherent so that the cross-spectral density matrix is the sum of individual modal diads, making the modal depth functions the same as the matrix eigenfunctions. Experimentally determined mode functions of orders 1 through 4 are compared with theoretical results.