Abstract:

A method is developed for extracting the depth-dependent mode functions from single-frequency measurements on a vertical line array as a source moves out in range. A matrix of the complex pressure field versus receiver depth and source range is formed, and the cross-spectral density matrix (CSDM) is computed. A singular value decomposition (SVD) is performed on the CSDM to obtain the orthonormal eigenvectors and the eigenvalues. Rearrangement of the normal mode equations reveals that under ideal conditions, the eigenvectors correspond to the mode functions and the eigenvalues are proportional to the modal source excitation and wave number. When two or more eigenvalues are nearly equal, the eigenvectors are not unique, and the correct mode functions are linear combinations of the eigenvectors. Other complications arise when the pressure field is not sampled adequately in depth or range. The procedure is applied to simulated data for a Pekeris waveguide and a realistic geoacoustic profile. Extracted mode functions from sources of opportunity are intended to be used for geoacoustic inversion of the sound-speed profile and bottom properties. [Work supported by the U. S. Army Research Office, AASERT Grant No. DAAH04-95-1-0486, and ONR.]