Marine seismic data from the Blake Outer Ridge offshore Florida show strong ``bottom simulating reflections'' (BSRs) associated with methane hydrate occurrence in deep marine sediments. We use a detailed amplitude versus offset (AVO) analysis of these data to explore the validity of two models regarding the origin of bottom simulating reflectors. After careful preprocessing steps including source wavelet deconvolution, nonlinear trace interpolation, amplitude and moveout traveltime calibration, and velocity analysis, we estimate the P and S impedance contrasts at all subsurface positions. This is done by applying a least-squares elastic parameter inversion method to the preprocessed CMP gathers. Our results suggest that the Blake Outer Ridge BSR is compatible with a model of methane hydrate in sediment, overlying a layer of free methane gas-saturated sediment.