Seismic attributes such as traveltimes and reflection amplitude variation with offset contain information on the elastic parameters of subsurface rocks. The aim of generalized inversion of seismic data is to estimate values of the elastic parameters such as P-wave velocity, S-wave velocity and density for lithology discrimination and direct detection of hydrocarbons. My dissertation research comprises two parts: development of a method to improve the least-squares and the preconditioned conjugate gradient algorithm, and estimation of detailed velocity structure of gas hydrate-bearing sediments offshore Oregon from Ocean-bottom seismometers (OBS) and multi-channel streamer (MCS) data. I developed a new nonlinear inversion algorithm for estimating velocities from fully stacked reflection data with application to a field data set consisting of well logs from Ocean Drilling Program (ODP) Leg 170 and multi-channel seismic reflection (MCS) data offshore Costa Rica. Inversion of post-stack seismic data generally yields reflection coefficients or impedance as a function of two-way reflection time. In this experiment, fully stacked seismic data and density logs at selected locations along a 2-D seismic line are inverted to estimate seismic velocities. Mathematically, generalized inversion provides the best estimate of earth model parameters by minimizing the so-called cost (or misfit between observed and computed seismic data) function, which is a function of the data covariance matrix CD and the a priori model covariance matrix CM. Matrices CD and CM (generally approximated by scalars od and om) introduce stability to the process and robustness and thus have strong influence on the quality of the final inversion solution. Based on the least-squares and the preconditioned conjugate gradient algorithm, I have developed a 2-step procedure to solve this nonlinear inverse problem by first determining the two matrices CD and CM using the two-step procedure that involves mapping the sensitivity of model smoothness and data error to the parameters od and om .I found that there always exits an area in the dm plane in which the low values of the cost function lie, and hence a large 2-dimensional search space can be reduced to a significantly smaller search region. This led to the easy application of this method. The results from this experiment show that almost every identified reflector of seismic data is very well matched by final synthetic seismograms and the density from borehole log data, which confirms that my estimates of velocities are reliable. Combination of the inverted velocity and density profiles allows identification of major stratigraphic boundaries. The improved inversion method is extended to the inversion of pre-stack seismic data, which is applied to estimate seismic velocities of gas hydrate-bearing sediments, offshore Oregon. Gas hydrates are recognized as a target for major future energy reserves, are believed to be a potential source of an important greenhouse gas, and are considered to be a possible cause of submarine geo-hazard. A simple indicator of gas hydrate is a bottom-simulating reflector (BSR), which marks the transition between hydrate-bearing sediments with high Vp above free gas with low Vp. A 3-D streamer and ocean bottom seismometer (OBS) survey in the Hydrate Ridge, offshore Oregon was conducted to image structures controlling the migration of methane-rich fluid and free gas and to map the gas-hydrate distribution. Preliminary Vp and Vs profiles obtained from OBS data by interactive analysis are used as a starting model to estimate Vp from the streamer data. The results of my inversion and interpretation study in Hydrate Ridge are summarized below: Both 3-D streamer and OBS data show a strong BSR indicating the presence of gas hydrate above and free gas below. Interactive P- and S-wave velocity analysis of OBS data allows us to identify the presence of a "conversion surface" in the gas hydrate-bearing sediments. The conversion surface separates the overlying low P-wave velocity layer and underlying high P-wave velocity layer. Inverted velocity profiles show a low-velocity layer existing below the sea floor and above the normal gas hydrate, suggesting a new geological model of gas hydrates. Two types of hydrate fabrics, massive and porous hydrates, observed by deep-towed video survey, were identified in the P-wave velocity profiles. Three main layers of gas hydrate-sediments separated by the conversion surface and BSR are distinguished. Below the free gas is the normal sedimentary section. The profiles reflecting the physical properties of sediments, such as the P-wave velocity, acoustic impedance and Poisson's ratio profiles, are able to map the distribution of gas hydrates and show very similar trends of lateral variation of the main layers.