In this thesis, acoustic inversion methods are employed to estimate array element locations and the geoacoustic properties of the seabed using measured acoustic data consisting of noise from a surface ship in the Gulf of Mexico. The array element localization utilizes relative travel-time information obtained by cross-correlating the recorded time series of ship noise received at spatially separated hydrophones. The relative travel-time data are used in an inversion, based on the regularized least-squares method and the acoustic ray tracing equations, to obtain improved estimates of the receiver and source positions and their uncertainties. Optimization and Bayesian matched-field inversion methods are employed to estimate seabed geoacoustic properties and their uncertainties in the vicinity of a bottom-moored vertical line array using the recorded surface ship noise. This study is used to test the feasibility of matched-field methods to detect temporal changes in the geoacoustic properties of the seabed near a known gas hydrate mound in the Gulf of Mexico. Finally, a synthetic study is performed that demonstrates how ignoring environmental range dependence of seabed sound speed and water depth in matched-field inversion can lead to biases in the estimated geoacoustic parameters. The study considers the distributions of optimal parameter estimates obtained from a large number of range-independent inversions of synthetic data generated for random range-dependent environments. Range-independent Bayesian inversions are also performed on selected data sets and the marginal parameter distributions are examined. Both hard- and soft-bottom environments are examined at a number of scales of variability in sound speed and water depth.