A constitutive law for rate of earthquake production and its application to earthquake clustering

Seismicity is modeled as a sequence of earthquake nucleation events in which the distribution of initial conditions over the population of nucleation sources and stressing history control the timing of earthquakes. The model is implemented using solutions for nucleation of unstable fault slip on faults with experimentally derived rate‐ and state‐dependent fault properties. This yields a general state‐variable constitutive formulation for rate of earthquake production resulting from an applied stressing history. To illustrate and test the model some characteristics of seismicity following a stress step have been explored. It is proposed that various features of earthquake clustering arise from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and interprets aftershock parameters in terms of stress change and stressing rate. Earthquake data appear to support a model prediction that aftershock duration, defined as the time for rates to return to the back‐ground seismicity rate, is proportional to mainshock recurrence time. Observed spatial and temporal clustering of earthquake pairs arises as a consequence of the spatial dependence of stress changes of the first event of the pair and stress‐sensitive time‐dependent nucleation. Applications of the constitutive formulation are not restricted to the simple stress step models investigated here. It may be applied to stressing histories of arbitrary complexity. The apparent success at modeling clustering phenomena suggests the possibility of using the formulation to estimate short‐ to intermediate‐term earthquake probabilities following occurrence of other earthquakes and for inversion of temporal variations of earthquake rates for changes in driving stress.