Dynamical rupture process on a three-dimensional fault with non-uniform frictions and near-field seismic waves

Summary. Dynamical rupture process on the fault is investigated in a quasi-three-dimensional faulting model with non-uniform distributions of static frictions or the fracture strength under a finite shearing pre-stress. The displacement and stress time functions on the fault are obtained by solving numerically the equations of motion with a finite stress—fracture criterion, using the finite difference method.
If static frictions are homogeneous or weakly non-uniform, the rupture propagates nearly elliptically with a velocity close to that of P waves along the direction of pre-stress and with a nearly S wave velocity in the direction perpendicular to it. The rise time of the source function and the final displacements are larger around the centre of the fault. In the case when the static frictions are heavily non-uniform and depend on the location, the rupture propagation becomes quite irregular with appreciably decreased velocities, indicating remarkable stick-slip phenomena. In some cases, there remain unruptured regions where fault slip does not take place, and high stresses remain concentrated up to the final stage. These regions could be the source of aftershocks at a next stage.
The stick—slip faulting and irregular rupture propagation radiate high-frequency seismic waves, and the near-field spectral amplitudes tend to show an inversely linear frequency dependence over high frequencies for heavily non-uniform frictional faults.     

Earthquake sequences on a frictional fault model with non-uniform strengths and relaxation times

Summary. The space and time characteristics of earthquake sequences, including a main shock, aftershocks and the recurrence of major shocks in a long time range, are investigated on a frictional fault model with non-uniform strengths and relaxation times, which is subjected to a time-dependent shear stress. Aftershocks with low stress drop take place successively in spaced regions so as to fill the gaps which have not yet been ruptured since the main shock, while those with high stress drop occur in and around the regions left unruptured during the main faulting. The frequency decay of aftershocks with time follows a hyperbolic law with the rates p consistent with observations. There are good linear relations in logarithmic scales for source area versus frequency and seismic moment versus frequency of the generated aftershocks. The b -value obtained in the present experiments appears slightly larger than that for observations. It was found that more heterogeneous distribution of the fault strength give smaller p and larger b -values. The recurrence of major shocks, particularly of very large shocks with high stress drop, is often preceded by a completely silent period of activity or very low activity with a small number of foreshocks. The major shocks take place successively in adjacent unruptured regions and sometimes show slow-speed migrations. These results provide explanations to various observations of earthquake sequences.     

Dynamic nucleation process of shallow earthquake faulting in a fault zone

Two distinct phases are commonly observed at the initial part of seismograms of large shallow earthquakes: low-frequency and low-amplitude waves following the onset of a P wave ( P ₁) are interrupted by the arrival of the second impulsive phase P₂ enriched with high-frequency components. This observation suggests that a large shallow earthquake involves two qualitatively different stages of rupture at its nucleation.
We propose a theoretical model that can naturally explain the above nucleation behaviour. The model is 2-D and the deformation is assumed to be anti-plane. A key clement in our model is the assumption of a zone in which numbers of pre-existing cracks are densely distributed; this cracked zone is a model for the fault zone. Dynamic crack growth nucleated in such a zone is intensely affected by the crack interactions, which exert two conflicting effects: one tends to accelerate the crack growth, and the other tends to decelerate it. The accelerating and decelerating effects are generally ascribable to coplanar and non-coplanar crack interactions, respectively. We rigorously treat the multiple interactions among the cracks, using the boundary integral equation method (BIEM), and assume the critical stress fracture criterion for the analysis of spontaneous crack propagation.
Our analysis shows that a dynamic rupture nucleated in the cracked zone begins to grow slowly due to the relative predominance of non-coplanar interactions. This process radiates the P₁ phase. If the crack continues to grow, coalescence with adjacent coplanar cracks occurs after a short time. Then, coplanar interactions suddenly begin to prevail and crack growth is accelerated; the P₂ phase is emitted in this process. It is interpreted that the two distinct phases appear in the process of the transition from non-coplanar to coplanar interaction predominance.     

Estimating rupture scenario likelihood based on dynamic rupture simulations: the example of the segmented Middle Durance fault, southeastern France

The Middle Durance fault system, southeastern France, is a slow active fault that produced moderate-size historical seismic events and shows evidence of at least one   M _w ≳ 6.5  event in the last 29 000 yr. Based on dynamic rupture simulation, we propose earthquake scenarios that are constrained by knowledge of both the tectonic stress field and of the 3-D geometry of the Durance fault system. We simulate dynamic rupture interaction among several fault segmentations of different strikes, dips and rakes, using a 3-D boundary integral equation method. 50 combinations of reasonable stress field orientations, stress field amplitudes and hypocentre locations are tested. The probability of different rupture evolutions is then computed. Each segment ruptures mainly as a single event (44 per cent of the 50 simulations test in this paper). However, the probability that an event triggers simultaneously along three segments is high (26 per cent), leading to a potential rupture length of 45 km. Finally, 2 per cent of the simulations occur along four adjacent segments, producing the greatest total rupture length of 55 km. The simulation results show that the southernmost segment is most easily ruptured (40 per cent), because of its favourable orientation with respect to the tectonic stress and of its favourable location for interaction with the other segments. South-bound unilateral propagation is slightly preferable (41 per cent), compared to north-bound unilateral and bilateral propagation modes. Although, these rupture scenarios cannot be directly translated into probabilities of occurrence, they do provide a better insight as to which rupture scenarios are more likely, an important element to better estimate near-field strong ground motion and seismic hazard.