Influence of friction and fault geometry on earthquake rupture

We scale the various parameters de ning a 3D fault model (i.e. characteristic distance and time of a state friction law, size and aspect ratio of the fault, medium impedance) and derive two dimensionless parameters governing the typical dynamics of the fault through single or multiple ruptures. The di erent faulting regimes are illustrated by a series of numerical simulations. As the parameters are varied the model crosses over from a regime which exhibits narrow, self-healing slip pulses, to one which exhibits broad, crack-like solutions that only heal in response to edge e ects. In the crack-like regime we observe periodic systemwide events. For self-healing pulses, the system exhibits self-roughening which leads to dynamical complexity. The behavior also changes from periodicity o r quasi-periodicity t o m o re complex time sequences as the total fault size or the length to width ratio are increased. Our results are in good qualitative agreement with analogous results which we obtain for a one dimensional Burridge{Knopo model, where the variations in the sti ness of the transverse spring are related to variations in the width of an equivalent two dimensional fault, and radiation e ects are approximated by viscous dissipation.

1998

We propose a fourth-order staggered-grid finite-difference method to study dynamic faulting in three dimensions. The method uses an implementation of the boundary conditions on the fault that allows the use of general friction models including slip weakening and rate dependence. Because the staggered-grid method defines stresses and particle velocities at different grid points, we preserve symmetry by implementing a two-grid-row "thick" fault zone. Slip is computed between points located at the borders of the fault zone, while the two components of shear traction on the fault are forced to be symmetric inside the fault zone. We study the properties of the numerical method comparing our simulations with well-known properties of seismic ruptures in 3D. Among the properties that are well modeled by our method are full elastic-wave interactions, frictional instability, rupture initiation from a finite initial patch, spontaneous rupture growth at subsonic and supersonic speeds, as well as healing by either stopping phases or rate-dependent friction. We use this method for simulating spontaneous rupture propagation along an arbitrarily loaded planar fault starting from a localized asperity on circular and rectangular faults. The shape of the rupture front is close to elliptical and is systematically elongated in the inplane direction of traction drop. This elongation is due to the presence of a strong shear stress peak that moves ahead of the rupture in the in-plane direction. At high initial stresses the rupture front becomes unstable and jumps to super-shear speeds in the direction of in-plane shear. Another interesting effect is the development of relatively narrow rupture fronts due to the presence of rate-weakening friction. The solutions for the "thick fault" boundary conditions scale with the slip-weakening distance (Do) and are stable and reproducible for Do greater than about 4 in terms of 2T,//.t × Ax. Finally, a comparison of scalar and vector boundary conditions for the friction shows that slip is dominant along the direction of the prestress, with the largest deviations in slip-rate direction occurring near the rupture front and the edges of the fault.

Physics of the Earth and Planetary Interiors, 1990

. Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys. Earth Planet. Inter., 64: 1-20.

Journal of Geophysical Research, 2011

We address the problem of modeling dynamic rupture on multiscale heterogeneous faults in 3D. Under the assumption of slip-weakening friction, we numerically construct effective friction laws that integrate the effects of small-scale heterogeneity during the rupture. This homogenization process is based on the description of the initial phase of the rupture by the dominant unstable spectral mode. Its dynamics is influenced by the geometry of the fault, the static friction heterogeneities and the friction law. We first define a periodic small-scale heterogeneous model, introducing heterogeneity in the distribution of the static friction coefficient. We then describe a method for constructing this effective friction law. Applying this new law homogeneously on the fault permits to reproduce the dynamic evolution of the heterogeneous fault. Furthermore, we show that the effective friction law can be used to replace small-scale heterogeneities in two-scale heterogeneous models, while preserving their effects. We study three kinds of two-scale models, with growing complexity: first periodic at both scales, then periodic only at small scale, and finally irregular at both scales. This homogenization method can be adapted to the case where the heterogeneity is introduced in the initial stress rather than in the static friction value. Finally, we show in a simple example that the effective friction law permits to reproduce the transition between subshear and supershear rupture propagation, originally produced by heterogeneities on the fault.

Geophysical journal of the Royal Astronomical Society, 2009

The tearing and healing of a one-dimensional crack in a solid, in the presence of external tectonic forces, pre-stress, static friction, cohesion and dynamic friction is investigated. It is found that cohesive forces have a strong influence on the velocity of rupture; the velocity of rupture is always less than or equal to the velocity of sound. The extension of the crack ceases either when the crack enters a region with too high a cohesive force or when the difference between the tectonic stress and the dynamical shear stress becomes negative over a substantial region of space. For one simple model, a high displacement, high energy release event has been found, while in another model of the same fault length, a low displacement, low energy release event with the same stress drop takes place; the difference between the two models is in the mode of healing, and, in particular, whether the fault breaks out at the free surface of the Earth.

J. geophys. Res, 1997

The European Physical Journal Special Topics, 2010

Earthquake simulators become increasingly important with respect to seismic hazard assessment. It is, therefore, a crucial question whether the imposed simplifications, e.g. reducing fully dynamic to quasi-dynamic rupture propagation, may lead to unrealistic results. In the present study, we focus on the role of rupture velocity vr in an earthquake simulator governed by rate-and-state dependent friction as proposed by [8]. In particular, we investigate the range of possible values of vr within the model. As an end-member scenario, we consider the existence of a steady-state solution of a one-dimensional rupture front propagating with vr on an idealized two-dimensional fault of infinite dimension discretized into uniform cells. We find that, in principle, values of vr between 0 and ∞ are possible depending on the values of slip speedδ0 and pre-stress τ0 ahead of the rupture front. In this view, values ofδ0 close to the slip speed during an earthquakeδEQ lead to small values of the time-to-failure and can thus generate ruptures with unrealistic high values of vr, if the model is close to the steady-state conditions. These results are useful to provide constraints for the parameter space of a reasonable earthquake simulator.

Journal of Geophysical Research: Solid Earth, 2002

The initiation of frictional instability is investigated for simple models of fault zone using a linearized perturbation analysis. The fault interface is assumed to obey a linear slip‐weakening law. The fault is initially prestressed uniformly at the sliding threshold. In the case of antiplane shear between two homogeneous linearly elastic media, space‐time and spectral solutions are obtained and shown to be consistent. The nucleation is characterized by (1) a long‐wavelength unstable spectrum bounded by a critical wave number; (2) an exponential growth of the unstable modes; and (3) an induced off‐fault deformation that remains trapped within a bounded zone in the vicinity of the fault. These phenomena are characterized in terms of the elastic parameters of the surrounding medium and a nucleation length that results from the coupling between the frictional interface and the bulk elasticity. These results are extended to other geometries within the same formalism and implications fo...

Physica A: Statistical Mechanics and its Applications, 1998

Starting o from the relationship between time-dependent friction and velocity softening we present a generalization of the continuous, one-dimensional homogeneous Burridge-Knopo (BK) model by allowing for displacements by plastic creep and rigid sliding. The evolution equations describe the coupled dynamics of an order parameter-like ÿeld variable (the sliding rate) and a control parameter ÿeld (the driving force). In addition to the velocity-softening instability and deterministic chaos known from the BK model, the model exhibits a velocitystrengthening regime at low displacement rates which is characterized by anomalous di usion and which may be interpreted as a continuum analogue of self-organized criticality (SOC). The governing evolution equations for both regimes (a generalized time-dependent Ginzburg-Landau equation and a non-linear di usion equation, respectively) are derived and implications with regard to fault dynamics and power-law scaling of event-size distributions are discussed. Since the model accounts for memory friction and since it combines features of deterministic chaos and SOC it displays interesting implications as to (i) material aspects of fault friction, (ii) the origin of scaling, (iii) questions related to precursor events, aftershocks and afterslip, and (iv) the problem of earthquake predictability. Moreover, by appropriate re-interpretation of the dynamical variables the model applies to other SOC systems, e.g. sandpiles.

2000

Lapusta et al., 2000(2) have developed an efficient and rigorous numerical pro- cedure for elastodynamic analysis of earthquake sequences on slowly loaded faults. This is done for a general class of rate and state friction laws with positive direct velocity effect. We use the procedure to study the response of a 2-D strike-slip fault model with depth-variable properties. We find the fol- lowing (as partially reported by Lapusta et al., 2000(2)): Small events appear in increasing numbers for decreasing values of the characteristic slip distance of the friction law. The nucleation phase of small and large events is very similar. For a large event that is preceded by a small event (and hence hetero- geneous stress distribution), moment acceleration in the beginning of dynamic propagation exhibits "slow-downs" and subsequent "speed-ups", consistently with some observations. Insufficient time and space discretization qualita- tively changes the results. Incorporating ...