We propose a new procedure for estimating the critical slip weakening distance, Dc, by evaluating the spatio-temporal distribution of the apparent stress calculated from the spatio-temporal distribution of the slip velocity function on the fault plane obtained from a kinematic inversion of the earthquake source. The idea is based on the fact that the apparent stress can be related to the difference between the earthquake average stress and the frictional dynamical stress on the fault plane during the rupture process. From the cumulative slip-apparent stress relationship we estimate the critical slip, Dc, of the 1992 Landers earthquake. We find that the critical slip weakening plays an important role in controlling the rupture velocity. In the case of the Landers earthquake the very low rupture velocity in the central segment could be explained by the large Dc-value obtained for the main asperity on that segment. ¿ 2000 American Geophysical Union