The normal modes of acoustic propagation in the shallow ocean are extracted from sound recorded on a vertical line array (VLA) of hydrophones as a source travels nearby, and the extracted modes are used to invert for the environmental properties of the ocean. The mode extraction is accomplished by performing a singular value decomposition (SVD) of individual frequency components of the signal's temporally-averaged, spatial cross-spectral density matrix. The SVD produces a matrix containing a mutually orthogonal set of basis functions, which are proportional to the depth-dependent normal modes, and a diagonal matrix containing the singular values, which are proportional to the modal source excitations and mode eigenvalues. The extracted modes exist in the ocean at the time the signal is recorded and thus may be used to estimate the sound speed profile and bottom properties. The inversion scheme iteratively refines the environmental parameters using a Levenberg-Marquardt algorithm such that the modeled modes approach the data-extracted modes Simulations are performed to examine the robustness and practicality of the mode extraction and inversion techniques. Experimental data measured in the Hudson Canyon Area of the New Jersey Shelf are analyzed, and modes are successfully extracted at the frequencies of a towed source. Modes are also extracted from ambient noise recorded on the VLA during the experiment. Using data-extracted modes, inverted values of the water depth, the thickness of a thin first sediment layer, and the compressional sound speed at the top of the first layer are found to be in good agreement with historical values. The density, attenuation, and properties of the second layer are not well determined because the inversion method is only able to obtain reliable values for the parameters that influence the mode shapes in the water column.
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