Recent exploration activity in the peripheral regions of the Shetland-Faeroe Basin, offshore northwest Scotland, has led to the discovery of some of the largest oil reserves on the United Kingdom (UK) continental shelf. We present results from two ocean-bottom seismometer profiles acquired by Mobil North Sea Ltd. across the center of the Shetland-Faeroe Basin. These data provide a powerful tool for delineating long-wavelength velocity variations and thus have potential for reducing the nonuniqueness associated with conventional seismic exploration methods. Analysis of the first-arrival traveltime data using both forward and inverse ray-based techniques produces a well constrained velocity-depth model of the basin fill. We estimate that the uncertainty in the velocity structure is + or -5% from a series of trial and error perturbations applied to the final models. The velocity structure of the Faeroe Basin has three principal layers: (1) a near-surface layer with velocities in the range 1.6 to 2.2 km/s. (2) a 3.0-3.2 km/s layer which is characterized by a northwards structural pinch out in the center of the basin, and (3) a deeper laterally heterogeneous layer with velocities in the range 3.8 to 4.2 km/s. In the northwestern portion of the basin, a high velocity (5.0 km/s) basaltic layer is imaged dipping toward the southeast at a depth of 2-3 km. The basement is mapped at a depth of 7-9 km in the center of the basin. Gravity modeling provides independent corroboration of our models through the application of a velocity-density relationship obtained from a synthesis of physical property measurements. Reflections from the Moho indicate a crustal thickness of 18+ or -3 km, suggesting that the basin is underlain by highly attenuated continental crust, but the velocities in the basement are closer to those of the Faeroe Islands basalts than the expected Lewisian gneiss, suggesting that it may be highly intruded.