When continents break apart, the rifting is sometimes accompanied by the production of large volumes of molten rock. The total melt volume, however, is uncertain, because only part of it has erupted at the surface. Furthermore, the cause of the magmatism is still disputed-specifically, whether or not it is due to increased mantle temperatures. We recorded deep-penetration normal-incidence and wide-angle seismic profiles across the Faroe and Hatton Bank volcanic margins in the northeast Atlantic. Here we show that near the Faroe Islands, for every 1 km along strike, 360-400 km(3) of basalt is extruded, while 540-600 km(3) is intruded into the continent-ocean transition. We find that lower-crustal intrusions are focused mainly into a narrow zone approximately 50 km wide on the transition, although extruded basalts flow more than 100 km from the rift. Seismic profiles show that the melt is intruded into the lower crust as sills, which cross-cut the continental fabric, rather than as an 'underplate' of 100 per cent melt, as has often been assumed. Evidence from the measured seismic velocities and from igneous thicknesses are consistent with the dominant control on melt production being increased mantle temperatures, with no requirement for either significant active small-scale mantle convection under the rift or the presence of fertile mantle at the time of continental break-up, as has previously been suggested for the North Atlantic Ocean.