Sound propagation in shallow water is highly dependent on the interaction of the sound field with the bottom. In order to fully understand this problem, it is necessary to obtain reliable estimates of bottom geoacoustic properties that can be used in acoustic propagation codes. In this thesis, perturbative inversion methods and exact inverse methods are discussed as a means for inferring geoacoustic properties of the bottom. For each of these methods, the input data to the inversion is the horizontal wavenumber spectrum of a point-source acoustic field. The main thrust of the thesis work concerns extracting horizontal wavenumber content for fully three-dimensionally varying waveguide environments. In this context, a high-resolution autoregressive (AR) spectral estimator was applied to determine wavenumber content for short aperture data. As part of this work, the AR estimator was examined for its ability to detect discrete wavenumbers in the presence of noise and also to resolve closely spaced wavenumbers for short aperture data. As part of a geoacoustic inversion workshop, the estimator was applied to extract horizontal wavenumber content for synthetic pressure field data with range-varying geoacoustic properties in the sediment. The resulting wavenumber content was used as input data to a perturbative inverse algorithm to determine the sound speed profile in the sediment. It was shown using the high-resolution wavenumber estimator that both the shape and location of the range-variability in the sediment could be determined.
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