We present a frequency domain inversion in which the observed earthquake strong ground motions are used to constrain the space-time dependence of slip on a fault. Green's functions are numerically evaluated and the parameters describing the rupture are the local slip, rupture time and rise time. These parameters are simultaneously evaluated without additional constraints. This procedure allows for large variation in the local rupture velocity. The June 28, 1992 Landers earthquake (MW=7.3) offers an exceptional opportunity to apply this technique to a major strike-slip event. We model the rupture evolution, including local differences in slip durations and variations in rupture velocity. Our final results are in good agreement with other inversion studies, geodetic and surface observations. The main discrepancies occurred at depth and at the end of the Johnson Valley fault. We show that a relatively low resolution could be an explanation for these differences. Rupture velocity and slip are extremely heterogeneous, both along strike and with depth. A moment of 0.90¿1020 N m was found. The slip distribution shows that this event consists of a series of regions of high slip (subevents) separated by regions or relative low slip. Approximately 50% of the moment was released on the Homestead Valley fault; in this region of large slip, the rupture velocity inferred by our inversion is well constrained and is equal to 3.0 km/s at depth and 2.5 km/s near the surface. Our inversion favors the hypothesis that the duration of the slip at each point of the fault is of the order of the duration of rupture of each subevent. ¿ American Geophysical Union 1995