All large earthquakes are followed by an increase of seismicity ("aftershocks"), likely triggered by the static stress change induced by the mainshock. Aftershock rate decays approximately as the inverse of the time since the mainshock. This property can be explained by the seismicity model of Dieterich [1994], based on the rate-and-state friction law. We have introduced heterogeneity of the stress change in this model. This new model explains why most aftershocks are located on or close to the mainshock rupture, where the stress has decreased on average after the mainshock. Stress heterogeneity also modifies the temporal decay of aftershocks, compared to the case of a uniform stress step [Dieterich 1994]. We can thus estimate the stress distribution from the aftershock rate.
However, some aftershock sequences have a faster temporal decay than expected by this model. This suggests that postseismic stress relaxation is not negligible, or that the friction law should be modified.