Geologists have been collecting, for decades, information from historical and paleoearthquakes that could contribute to the formulation of a “big picture” of the earthquake engine. Observations of large earthquake ruptures, unfortunately, are always going to be spotty in space and time, so the extent to which geological information succeeds in contributing to a grander view of earthquakes is going to be borne not only by the quantity and quality of data collected but also by the means by which it is interpreted. This article tries to understand geological data more fully through carefully tailored computer simulations of fault ruptures. Dogtails and rainbows are two types of fault rupture terminations that can be recognized in the field and can be interpreted through these models. Rainbows are concave down ruptures that indicate complete stress drop and characteristic slip. Rainbow terminations usually coincide with fault ends or strong segment boundaries. Dogtails are concave up ruptures that indicate incomplete stress drop and noncharacteristic slip. Dogtail terminations can happen anywhere along a fault or fault segment. The surface slip pattern of the magnitude 6.6, 1979 Imperial Valley, California, earthquake shows both dogtail and rainbow terminations. The rainbow confirms the presence of a strong fault segment boundary 6 km north of the international border that had been suggested by Sieh (1996). The dogtail implies that the displacement observed in 1979 is not characteristic. By combining paleoseismic information with the surface slip patterns from this event and the magnitude 7.1, 1940 Imperial Valley earthquake, I develop a quantitative Imperial fault model with northern, central, and southern segments possessing 50, 110, and 50 bar strength, respectively. Both the 1940 and 1979 events caused 1-m amplitude dogtailed ruptures of the northern segment; however, characteristic slip of the segment is more likely to be about 3 m. To illustrate the full spectrum of potential rupture modes, models were run forward in time to generate a 2000 year rupture “encyclopedia.” Even with well-constrained segmentation and strengths, modest changes in two friction law parameters produce several plausible histories. Further discrimination awaits analysis of the extensive paleoseismic record that geologists believe exists in the shore deposits of the intermittent lakes of the Salton Trough.