Dynamics of a fault model with two mechanically different regions

Abstract

We consider a fault containing two regions with different mechanical behaviours: a strong, velocity-weakening region (asperity) and a weak, velocity-strengthening region. The fault is embedded in a shear zone subject to a constant strain rate by the motions of adjacent tectonic plates. The fault is modelled as a discrete dynamical system whose state is described by two variables expressing the slip deficits of the two regions. Because of plate motion, the asperity accumulates stress and eventually releases it, producing an earthquake, when a frictional threshold is exceeded. The weak region is subject to a very slow creep during interseismic intervals and may slip at a higher rate (afterslip) as a consequence of coseismic stress imposed by the asperity failure. The evolution equations of the system are solved analytically for the interseismic intervals, the asperity slip and the afterslip in the weak region. It is found that the amount of afterslip is proportional to the seismic slip of the asperity, in agreement with observations. The model shows that afterslip is a natural consequence of seismic slip in a fault containing a velocity-strengthening region. Afterslip may have any duration, according to the intensity of velocity strengthening, thus accounting for the wide range of observed durations. The model is applied to the fault of the 2011 Tohoku-Oki earthquake. The results suggest that the first four months after the event were dominated by afterslip, while the subsequent postseismic deformation was probably due to viscoelastic relaxation in the asthenosphere.

Reply to the Short Comment

“…We now consider the perturbations of the state of the fault caused by the coseismic slip on surrounding faults. Following Dragoni and Piombo (2015), we assume that (1) the perturbations occur during an inter-seismic interval; (2) the stress transfer takes place over a time interval negligible with respect to the duration of the inter-seismic interval; and (3) at the time of the perturbation, the state of the fault is sufficiently far from the failure conditions and the stress transfer is small enough that the onset of motion of either asperity is not achieved immediately.…”

“…In a number of recent works, modelling of different mechanical phenomena in a two-asperity fault system has been addressed, such as stress perturbations due to surrounding faults (Dragoni and Piombo, 2015) and the radiation of seis-mic waves (Dragoni and Santini, 2015). In these models, the fault is treated as a discrete dynamical system with four dynamic modes: a sticking mode, corresponding to stationary asperities, and three slipping modes, associated with the separate or simultaneous failure of the asperities.…”

Complex interplay between stress perturbations and viscoelastic relaxation in a two-asperity fault model

“…In a number of recent works, modelling of different mechanical phenomena in a two-asperity fault system has been addressed, such as stress perturbations due to surrounding faults (Dragoni and Piombo, 2015) (Dragoni and Santini, 2015). In these models, the fault is treated as a discrete dynamical system with four dynamic modes: a sticking mode, corresponding to stationary asperities, and three slipping modes, associated with the separate or simultaneous failure of the asperities.…”

“…The aim of the present paper is to discuss the combined effects of viscoelastic relaxation and stress perturbations on a two-asperity fault in the framework of a discrete fault model. In order to deal with such a problem, we base our work on the results achieved by Dragoni and Piombo (2015) and Dragoni and Lorenzano (2015). In the former work, the authors considered a two-asperity fault with purely elastic rheology and discussed the effect of stress perturbations due to earthquakes on neighbouring faults.…”

“…In the latter work, viscoelastic relaxation on the fault was dealt with by adding a third state variable, the variation in the difference between the slip deficits of the asperities during inter-seismic intervals. In the present paper, we introduce stress perturbations as modelled by Dragoni and Piombo (2015) in the framework of the two-asperity fault considered by Dragoni and Lorenzano (2015). Accordingly, the present work represents a three-dimensional generalization of the model devised by Dragoni and Piombo (2015).…”