A physical model for aftershocks triggered by dislocation on a rectangular fault (original) (raw)
Related papers
2007
We compute the static displacement, stress, strain and the Coulomb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the source. The time-dependent rate of triggered earthquakes is estimated by a rate-state model applied to a uniformly distributed population of faults whose equilibrium is perturbated by a stress change caused only by the first dislocation. The rate of triggered events in our simulations is exponentially proportional to the shear stress change, but the time at which the maximum rate begins to decrease is variable from fractions of hour for positive stress changes of the order of some M P a, up to more than a year for smaller stress changes. As a consequence, the final number of triggered events is proportional to the shear stress change. The model predicts that the total number of events triggered on a plane containing the fault is proportional to the 2/3 power of the seismic moment. Indeed, the total number of aftershocks produced on the fault plane scales in magnitude, M , as 10 M. Including the negative contribution of the stress drop inside the source, we observe that the number of events inhibited on the fault is, at long term, nearly identical to the number of those induced outside, representing a sort of conservative natural rule. Considering its behavior in time, our model does not completely match the popular Omori law; in fact it has been shown that the seismicity induced closely to the fault edges is intense but of short duration, while that expected at large distances (up to some tens times the fault dimensions) exhibits a much slower decay.
Shear and normal load perturbations on a two-dimensional continuous fault: 2. Dynamic triggering
[1] We study the consequences of temporal stress perturbations on earthquake nucleation in a continuous fault model. Using a two-dimensional (2-D) quasi-dynamic model of a strike-slip fault governed by a rate-and-state friction law with depth variable properties, we show that dynamic triggering (due to stress pulses or wave packets), although allowed by our results, is an exception rather than a rule and should be limited to understressed areas such as areas of high pore pressures or to faults at the very end of their earthquake cycle. When periodic stress perturbations are sensitive, the response of the fault is frequency-independent for periods lower than a period T 0 but strongly depends on the frequency for periods larger than T 0. We demonstrate that the crossover period T 0 is equal to the time left until the earthquake instability. According to our model, high frequencies are demonstrated to have a higher triggering potential than low ones, which makes tidal triggering very unlikely before the end of the cycle due to the very low amplitudes of the stress perturbations involved. INDEX TERMS: 7209 Seismology: Earthquake dynamics and mechanics; 7215 Seismology: Earthquake parameters; 7260 Seismology: Theory and modeling; KEYWORDS: earthquake triggering, dynamic triggering, Coulomb stress change, rate and state friction laws, clock advance/delay Citation: Perfettini, H., J. Schmittbuhl, and A. Cochard, Shear and normal load perturbations on a two-dimensional continuous fault: 2.
Geophysical Research Letters, 2008
1] We perform a numerical experiment with quasidynamic continuous 3D fault model governed by a laboratory derived rate-and-state friction law. We test several cases in which the Coulomb stress (CS) increases either on the whole fault or only on its part. For the partial stressing we find that if the triggering is almost instantaneous (within 1 -2 months), the nucleation takes place in the strike extent of the CS increase area. On the contrary, if the earthquake does not occur within these few months, it can nucleate anywhere on the fault, and even later than without the positive CS load. These features represent new findings which are unique for 3D model and cannot be explained by 1D spring-slider models. The finding might find applications in the aftershock (time-dependent) seismic hazard assessment. Citation: Gallovič, F. , Heterogeneous
Aftershocks due to property variations in the fault zone: A mechanical model
Tectonophysics, 2013
Studies of many large strike-slip earthquakes have shown that the seismicity rate increases in quadrants in which the Coulomb stress is increased by the earthquake rupture. This mechanism explains the concentration of aftershocks near the tips of the fault rupture, but cannot explain the aftershocks on the sides of the rupture zone, where the aftershocks are commonly abundant. We suggest that these aftershocks may be induced by variations of fault-zone properties not included in the previous models. In a finite-element model that treats the rupture plane as a zone with heterogeneous physical properties, as suggested by field observations and laboratory experiments, the Coulomb-stress changes triggered by the mainshock no longer uniformly decrease on the sides of the rupture zone, but show complex patterns of negative and positive changes. These results may explain some of the aftershocks on the sides of the mainshock rupture.
Shear and normal load perturbations on a two-dimensional continuous fault: 1. Static triggering
The influence of normal and shear stress static perturbations on a strike-slip fault is addressed on the basis of a two-dimensional continuous and quasi-dynamic model. Friction along the fault plane is described using a rate-and-state friction law with depth variable properties. Normal and shear stress perturbations result in similar effects in terms of earthquake triggering if Át À m * Ás is constant, Át and Ás being the amplitude of the shear and normal stress fluctuations, respectively, and m * being a constant which can be interpreted as the static friction coefficient on the fault in a Coulomb failure model. Therefore the Coulomb stress change ÁCFF = Át À m * Ás is a useful tool to account simultaneously for normal and shear stress variations in our model. We also show that when estimating the clock advance or clock delay of an earthquake, the simple Coulomb failure model is at first order in good agreement with our results during the first 90% of the earthquake cycle. However, it differs significantly during the last 10% due to the sharp velocity increase predicted by the rate-and-state friction law before rupture. This suggests that as long as static variations of stress are concerned, realistic fault models using rich, laboratory-based, friction laws like rate-and-state friction laws may lead to predictions fairly close to the ones made using one of the simplest failure model, i.e., the Coulomb failure model. This may explain why Coulomb stress change computations, although often based on drastic approximations, have been able in many occasions to explain earthquake triggering sequences. INDEX TERMS: 7209 Seismology: Earthquake dynamics and mechanics; 7215 Seismology: Earthquake parameters; 7260 Seismology: Theory and modeling; KEYWORDS: earthquake triggering, static triggering, Coulomb stress change, rate and state friction laws, clock advance/delay Citation: Perfettini, H., J. Schmittbuhl, and A. Cochard, Shear and normal load perturbations on a two-dimensional continuous fault: 1. Static triggering,
Quasi-static and quasi-dynamic modeling of earthquake failure on a large discrete fault system
Egs Agu Eug Joint Assembly, 2003
We present a model for earthquake failure at intermediate scales (space: 100 m-100 km, time: 100 m/v shear -1000's of years). The model consists of a segmented strike-slip fault embedded in a 3-D elastic solid as in the framework of . The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of the regions around the fault, static/ kinetic friction laws with possible gradual healing, and stress transfer based on the solution of CHINNERY (1963) for static dislocations in an elastic half-space. As a new ingredient, we approximate the dynamic rupture on a continuous time scale using a finite stress propagation velocity (quasi-dynamic model) instead of instantaneous stress transfer (quasi-static model). We compare the quasi-dynamic model with the quasi-static version and its mean field approximation, and discuss the conditions for the occurrence of frequency-size statistics of the Gutenberg-Richter type, the characteristic earthquake type, and the possibility of a spontaneous mode switching from one distribution to the other. We find that the ability of the system to undergo a spontaneous mode switching depends on the range of stress transfer interaction, the cell size, and the level of strength heterogeneities. We also introduce time-dependent log ðtÞ healing and show that the results can be interpreted in the phase diagram framework. To have a flexible computational environment, we have implemented the model in a modular C++ class library. some parameters empirical values are available, while others can be used to tune the model dynamics towards an expected behavior. The model of of a fault in a 3-D elastic half-space appears to meet these criteria. Using this model, several observed frequency-size and temporal statistics could be explained in terms of structural properties of a given fault.
A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences
Geophysical Journal International, 2000
It is common practice to refer to three independent stages of creep under static loading conditions in the laboratory: namely transient, steady-state, and accelerating. Here we suggest a simple damage mechanics model for the apparently trimodal behaviour of the strain and event rate dependence, by invoking two local mechanisms of positive and negative feedback applied to constitutive rules for time-dependent subcritical crack growth. In both phases, the individual constitutive rule for measured strain e takes the form e(t)=e 0 [1+t/mt]m, where t is the ratio of initial crack length to rupture velocity. For a local hardening mechanism (negative feedback), we find that transient creep dominates, with 0<m<1. Crack growth in this stage is stable and decelerating. For a local softening mechanism (positive feedback), m<0, and crack growth is unstable and accelerating. In this case a quasi-static instability criterion e 2 can be defined at a finite failure time, resulting in the localization of damage and the formation of a throughgoing fracture.
The seismic cycle and the difference between foreshocks and aftershocks in a mechanical fault model
Geophysical Research Letters, 2003
1] We examine the evolution of and the exchange between two forms of elastic energies stored in the quasistatic fault model of Ziv and Rubin [2003]. The first, E tect , is due to the integrated slip deficit accumulated between the plate boundaries and the fault surface, and the second, E fault , is the result of differential slip along the fault surface. The results of our analysis reveal cyclic exchange between the two energies. On a E fault versus E tect plot, the seismic cycle has a triangular shape with the large earthquakes occurring at the top corner of the triangle (where E fault is maximum), and the foreshocks and the aftershocks occupying the right side and left side, respectively. While both foreshocks and aftershocks dissipate tectonic energies, the cumulative effect of the foreshocks is to increase the potential elastic energy along the fault plane and the cumulative effect of the aftershocks is to reduce it. INDEX TERMS: 3210 Mathematical Geophysics: Modeling; 7209 Seismology: Earthquake dynamics and mechanics; 7230 Seismology: Seismicity and seismotectonics; 8168 Tectonophysics: Stressesgeneral. Citation: Ziv, A., and J. Schmittbuhl, The seismic cycle and the difference between foreshocks and aftershocks in a mechanical fault model, Geophys.
Nucleation and early seismic propagation of small and large events in a crustal earthquake model
Journal of Geophysical Research: Solid Earth, 2003
Earthquake nucleation and early seismic propagation are studied in a two-dimensional strike-slip fault model with depth-variable properties. The fault is governed by the Dieterich-Ruina rate and state friction law. We use an efficient and rigorous numerical procedure for elastodynamic analysis of earthquake sequences on slowly loaded faults developed by Lapusta et al. [2000]. We find that for decreasing values of the characteristic slip distance of the friction law, small events appear at the transition from the locked to creeping behavior toward the bottom of the seismogenic zone. Small and large events have very similar nucleation phases in our simulations. Here, by ''nucleation phase'' we mean gradually accelerating aseismic slip in a small slowly expanding zone before the breakout of the dynamic, seismically detectable event. Moment acceleration (to which velocity seismograms are proportional) in early stages of seismic propagation exhibits irregular fluctuations, in the form of speedups and slowdowns in the moment release rate, consistently with observations as reported by Ellsworth and Beroza [1995]. Our simulations show that such irregular moment acceleration can, at least in part, be due to the heterogeneous stress distribution imprinted on the fault by the arrest of previous small events and by stress concentrations at the borders of creeping regions and to partial arrest of the rupture in velocity-strengthening fault regions which inhibit seismic slip.
Journal of Geophysical Research: Solid Earth, 2003
1] It has been recently suggested that moderate and large earthquakes can be triggered by similarly sized events at very long range. Here we study the main characteristics of earthquake triggering by determining its correlation length, time dependence, and directionality. The problem is examined at a global level, by using the Harvard centroid moment tensor catalogue. Our results show that the correlation lengths depend only weakly on the magnitude thresholds involved. No significant systematic triggering is observed for distances greater than the lithospheric thickness (100-150 km), and the correlation length magnitude is similar to the seismogenic thickness (10-20 km). The mean triggering distance and correlation length both increase with time very slowly compared with what would be expected from a normal diffusion process. This is consistent with a clock advance on the failure time based on the constitutive rules for subcritical crack growth following a transient change in the loading stress. The power law scaling disappears after a few months. A functional form for the probability of triggering as a function of time and distance is proposed on the basis of the properties of near critical point systems. The model fits the data well and could be used to calculate conditional probabilities for time-dependent seismic hazard due to earthquake triggering. An apparent directionality effect that was observed in the data set can be attributed to an artefact of poor depth determination. These results do not preclude individual long-range triggering with a potential directionality effect, but they do rule out a statistical correlation at distances much greater than the thickness of the lithosphere.