We present results from a combined multichannel seismic reflection (MCS) and wide-angle onshore/offshore seismic experiment conducted in 1996 across the southeast Greenland continental margin. A new seismic tomographic method is developed to jointly invert refraction and reflection travel times for a two-dimensional velocity structure. We employ a hybrid ray-tracing scheme based on the graph method and the local ray-bending refinement to efficiently obtain an accurate forward solution, and we employ smoothing and optional damping constraints to regularize an iterative inversion. We invert 2318 Pg and 2078 PmP travel times to construct a compressional velocity model for the 350-km-long transect, and a long-wavelength structure with strong lateral heterogeneity is recovered, including (1) ~30-km-thick, undeformed continental crust with a velocity of 6.0 to 7.0 km/s near the landward end, (2) 30- to 15-km-thick igneous crust within a 150-km-wide continent-ocean transition zone, and (3) 15- to 9-km-thick oceanic crust toward the seaward end. The thickness of the igneous upper crust characterized by a high-velocity gradient also varies from 6 km within the transition zone to ~3 km seaward. The bottom half of the lower crust generally has a velocity higher than 7.0 km/s, reaching a maximum of 7.2 to 7.5 km/s at the Moho. A nonlinear Monte Carlo uncertainty analysis is performed to estimate the a posteriori model variance, showing that most velocity and depth nodes are well determined with one standard deviation of 0.05--0.10 km/s and 0.25--1.5 km, respectively. Despite significant variation in crustal thickness, the mean velocity of the igneous crust; which serves as a proxy for the bulk crustal composition, is surprisingly constant (~7.0 km/s) along the transect. On the basis of a mantle melting model incorporating the effect of active mantle upwelling, this velocity-thickness relationship is used to constrain the mantle melting process during the breakup of Greenland and Europe. Our result is consistent with a nearly constant mantle potential temperature of 1270--1340 ¿C throughout the rifting but with a rapid transition in the style of mantle upwelling, from vigorous active upwelling during the initial rifting phase to passive upwelling in the later phase. ¿ 2000 American Geophysical Union