Plate-boundary rifting between transform faults is opening the Imperial Valley of southern California and the rift is rapidly filling with sediment from the Colorado River. Three 65-90 km long seismic refraction profiles across and along the valley, acquired as part of the 2011 Salton Seismic Imaging Project, were analyzed to constrain upper crustal structure and the transition from sediment to underlying crystalline rock. Both first arrival travel-time tomography and frequency-domain full-waveform inversion were applied to provide P-wave velocity models down to 7 km depth. The valley margins are fault-bounded, beyond which thinner sediment has been deposited on preexisting crystalline rocks. Within the central basin, seismic velocity increases continuously from 1.8 km/s sediment at the surface to >6 km/s crystalline rock with no sharp discontinuity. Borehole data show young sediment is progressively metamorphosed into crystalline rock. The seismic velocity gradient with depth decreases approximately at the 4 km/s contour, which coincides with changes in the porosity and density gradient in borehole core samples. This change occurs at 3 km depth in most of the valley, but at only 1.5 km depth in the Salton Sea geothermal field. We interpret progressive metamorphism caused by high heat flow to be creating new crystalline crust throughout the valley at a rate comparable to the 2 km/Myr sedimentation rate. The newly formed crystalline crust extends to at least 7-8 km depth, and it is shallower and faster where heat flow is higher. Most of the active seismicity occurs within this new crust.