The imaging of subsurface structure using conventional seismic reflection methods is problematic across areas where high-velocity basaltic rocks are intercalated with sedimentary layers of low velocity. In this study we use an approach that combines wavefield inversion of both normal-incidence and wide-aperture seismic data to constrain velocity structure within and beneath the basalt. Our field data are a two-ship long-offset profile acquired in the Faeroe Basin. A conventional traveltime inversion of the wide-angle data is performed to obtain a starting model for the wavefield inversion. Synthetic tests are used to explore resolution and to determine a strategy for inversion of the field data. Our final velocity model shows a high-velocity basaltic layer underlain by an intermediate-velocity layer that is presumably sedimentary. The basalts appear highly heterogeneous in velocity, and the degree of heterogeneity increases significantly with depth within the layer. A prestack depth migration, using the final velocity model, reveals a number of new features. Despite the velocity heterogeneity within the basalts, strong reflections are seen within and immediately beneath the basaltic section, and these reflectors are more clearly imaged on the final depth-migrated section than hitherto. The transition from sediments to basalt does not appear to be sharp, uniquely defined, or locally subhorizontal. The data suggest that velocity heterogeneity, and the complexity of the transition from basalt to sediment, may explain the difficulties of imaging beneath basalts west of Britain. Wavefield tomography can resolve this complexity and hence improve both imaging and confidence of interpretation within and beneath basalts.