By comparing synthetic particle velocities with the near-source strong motion data we have constructed, by trial and error, a faulting model for the 1979 Imperial Valley earthquake. The calculation of the synthetic seismograms takes into account the vertical inhomogeneity of the elastic parameters in the Imperial Valley and the spatial variation of the slip rate parameters on the fault plane. The independent slip rate parameters are (1) the strike-slip rate amplitude. (2) the dip-slip rate amplitude, (3) the duration that slip rate is nonzero (the rise time of the slip function) and (4) the rupture time, which determines when the slip rate is initiated. Our faulting model has the following principal features: (1) Faulting occurred on the Imperial fault and on the Brawley fault, rupture on the Brawley fault being triggered by rupture on the Imperial fault. (2) The Imperial fault is a plane 35 km long and 13 km wide with a strike of 323¿, measured clockwise from north, and a dip of 80¿ NE. The Brawley fault is a 10 km long and 8 km wide plane with a strike of 360¿ and a dip of 90¿. (3) Faulting on the Imperial fault is primarily right-lateral strike slip with a small component of normal dip slip in the sediments at its northern end. The larger strike-slip rates are generally confined between depths of 5 and 13 km with maximum values of about 1.0 m/s. The duration varies on the fault with a maximum of 1.9 s, which is considerably shorter than the total time for the rupture to take place. (4) The rupture velocity on the Imperial fault is highly variable. Locally, it exceeds the shear wave velocity and, in one instance, the compressional wave velocity. The average rupture velocity, though, is less than the shear wave velocity. (5) Although the slip on the Brawley fault contributes only about 4% of the total moment, it greatly affects the ground motion at nearby stations. (6) The total seismic moment is 6.7¿1018 N m where the Imperial fault contributes 6.4¿1018 N m and the Brawley fault contributes 2.7¿1017 N m. In the process of trying almost 300 faulting models, we found that given the elastic parameters of the medium, the synthetic seismograms were most sensitive to the specification of the rupture time. Although the slip rate amplitudes are linearly related to the data, the rupture time and the duration are not. The parameterization of the nonlinear variables has a strong effect on the generation of synthetic seismograms from a finite fault.