Where the seafloor consists of a highly backscattering surface covered with a drape of fine-grained sediment, and where the sediment does not contribute significantly to the backscattered signal, the sediment thickness can potentially be inferred from the amount of signal attenuation in the sediment layer. A first-order acoustical model is proposed in which the signal strength is reduced by an amount proportional to the sediment thickness and attenuation rate in the sediments. Data collected with Geological Long-Range Inclined Azdic (GLORIA) are used to develop and test this model. At an acoustic frequency of 6.5 kHz, the range of sediment thickness that the sonar can potentially recover is 0–20 m, a range that is often below the resolution of vertical profilers. In the first example, the signal variation with grazing angle over a uniformly buried surface is analyzed for attenuation, which is expected to increase toward shallow grazing angles and longer attenuating paths through the sediment layer. The surface is a lava flow north of Hawaii covered by 1–2 m of fine-grained sediments (Clague et al., 1990), and GLORIA data analyzed with the model suggest an attenuation coefficient of 0.2–0.4 dB/m, a value consistent with results from laboratory and field measurements of sediment attenuation. In the second example, a rocky surface is buried by varying amounts of sediment, which is analyzed at almost constant grazing angle. The surface is the volcanic basement of the Southeast Indian Ridge, and GLORIA data reveal the thickening of the sediment cover with distance away from the spreading center. This is used to derive an average sedimentation rate of 6 mm/ka, which is generally consistent with results from other studies and suggests that this technique may be used to study differences in sedimentation rates between different regions. Furthermore, the model is used to calculate, from image amplitude distributions, the sediment thickness distribution, which represents the accumulation of sediments in ponds and the exposure of abyssal hills. These sedimentary processes are also reflected in the standard deviation of sediment thickness which increases with seafloor age. I explore the various sources of error in estimating sediment thickness using this technique and propose a model for nonuniform sediment drapes (the first-order model assumes a uniform thickness at the subfootprint scale).