Some of the gross characteristics of the rupture processes for the 1966 Parkfield, 1979 Imperial Valley, and 1980 Mexicali Valley earthquakes are determined by waveform inversion of near‐source data employing a steady state dislocation model in a layered half‐space. The forward model involves a piecewise‐linear rupture front moving with a constant horizontal rupture velocity on a fault of infinite length and finite width. The inferred shapes for the rupture front and for the distribution of slip as a function of depth are consistent with previous results obtained by use of more general models. The results obtained show that a strong velocity pulse observed in the nearsource region can be modeled as the passage of the rupture front phase and that the supershear propagation of the rupture front in the sedimentary layers of the medium provides a mechanism for the generation of the observed large ampli