Complexity of seismicity due to highly rate-dependent friction

We study a simple antiplane fault of finite length embedded in a homogeneous, isotropic, elastic solid in order to understand the origin of seismic source heterogeneity in the presence of nonlinear rate-dependent friction. All the mechanical properties of the medium and friction are assumed to be homogeneous. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for more than 20,000 events, in some cases. The style of seismicity produced by this model is determined by a control parameter which measures the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction seismicity becomes slightly nonperiodic but most events are still characteristic earthquakes. When friction is highly rate-dependent, seismicity is completely irregular and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process, producing premature healing of slip and partial stress drop. Premature healing causes rupture to take the form of narrow, propagating slip episodes, the so-called Heaton's [1990] pulses. Partial stress drop produces large variations in the state of stress which, in turn, produce earthquakes of different sizes. We make the conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.