The extended-source modeling I have described to this point is purely kinematic. That is, these studies used seismic data to solve for the timing and distribution of fault slip, without considering the stresses that result. There have been several quasidynamic models of earthquake rupture that attempt to solve for dynamic parameters of faulting such as the dynamic stress drop and the strength excess, while still fitting the seismic data that are used to derive kinematic faulting models. Quin [1990] used the model derived by Archuleta [1984] for the 1979 Imperial Valley earthquake to develop a quasidynamic rupture model for that earthquake. It is interesting that despite the relatively short rise times relative to the overall rupture time in Archuleta's model, the rise times in Quin's dynamic model were shorter still. More recently Mikumo and Miyatake [1993] have iteratively solved for a model that successfully fits the seismic data from the Kita-Mino earthquake while maintaining dynamic feasibility.
By considering the dynamic stresses induced by rupture, Spudich [1992] described a method for determining absolute stress levels based on observations of variable slip direction (rake) during an earthquake. Vidale et al. [1994] found that a sequence of repeating earthquakes on the Calaveras fault had an increase in seismic moment with recurrence time, which is consistent with laboratory-derived, rate-dependent friction models.