We investigate the finite rupture processes of two M > 5 earthquakes in the 2012 Brawley swarm by joint inversion of nearby strong motion and high-rate GPS data. Waveform inversions up to 3 Hz were made possible by using a small event (Mw3.9) for path calibration of the velocity structure. Our results indicate that the first (Mw5.3) event ruptured a strong, concentrated asperity with offsets of ~20 cm centered at a depth of 5 km. The subsequent Mw5.4 event occurred 1.5 h later with a shallower slip distribution that surrounds and is complementary to that of the earlier event. The second event has a longer rise time and weaker high-frequency energy release compared to the Mw5.3 event. Both events display strong rupture directivity toward the southwest and lack of very shallow (<2 km) coseismic slip. The hypocenters for these events appear to be near or in the bedrock, but most of the slip is distributed at shallower depths (<6 km) and can explain a large part of the GPS offsets for the swarm. The complementary slip distributions of the two events suggest a triggering relationship between them with no significant creep needed to explain the various data sets.