Seismicity simulation with a mass-spring model and a displacement hardening-softening friction law

Dieterich simulated aftershocks numerically, using a one-dimensional mass-spring model with a time-dependent friction law. But an important precursory phenomenon called ‘quiescence’ cannot be produced by this model unless, as Mikumo and Miyatake showed with a three-dimensional continuum model, a somewhat arbitrary bimodal distribution of frictional strength is assumed. Here we used the friction law proposed by Stuart, which is a displacement hardening-softening model, and simulated the quiescence. By varying the parameters of the friction law in our mass-spring model, we found a variety of seismicity patterns. When we choose extremely large critical displacement we get a recurrent sequence of creep followed by mainshock without small earthquakes. But when we choose a critical displacement in the same order of magnitude as the slip-weakening critical displacement estimated by Papageorgiou and Aki from strong motion data, we get a normal seismicity pattern, including quiescence before large events. This simple model points to a promising approach for the interpretation of the rupture process during an earthquake by the same physical model.