Automaton models of seismic fracture: Constraints imposed by the magnitude‐frequency relation

Lomnitz-Adler, J.

doi:10.1029/93jb01390

Cited by 58 publications

(25 citation statements)

References 34 publications

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“…It has been shown that complex features of observed natural seismicity such as the occurrence of the Gutenberg‐Richter (GR) statistics and aftershock pattern cannot be generated by rate‐ and state‐controlled models in the continuum limit with homogeneous frictional properties [e.g., Tse and Rice , 1986; Rice , 1993; Ben‐Zion and Rice , 1997; Lapusta et al , 2000], but by inherently discrete model realizations [e.g., Burridge and Knopoff , 1967; Langer et al , 1996; Carlson and Langer , 1989; Bak et al , 1987; Ito and Matsuzaki , 1990; Lomnitz‐Adler , 1993; Ben‐Zion , 1996; Zöller et al , 2005]. Cochard and Madariaga [1996], Nielsen et al [2000], and Shaw and Rice [2000] confirmed that generation of slip complexity on a homogeneous fault requires special choices of constitutive and model parameters.…”

Section: Discussionmentioning

confidence: 99%

Stability regimes of a dilatant, fluid‐infiltrated fault plane in a three‐dimensional elastic solid

Hillers

Miller

2006

J. Geophys. Res.

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[1] We investigate in a systematic parameter space study dilatant effects on slip evolution of a fluid-infiltrated fault in the continuum limit. The fault is governed by rate-and state-dependent friction and an empirical law for porosity evolution. We focus on the response of systems as a function of fluid-related parameters, such as the degree of overpressurization, dilatancy and diffusivity. This study emphasizes the exploration of the parameter space for homogeneous along-strike properties to investigate the evolution of spatiotemporal slip depending on hydromechanical processes. Three types of responses emerge. First, system-wide unstable stick-slip develops for drained conditions, and for undrained conditions if mechanisms leading to an increase in pore space are less effective. The critical stiffness depends on hydraulic diffusivity and dilatancy, which is shown to correspond with interevent times of simulated stick-slip events. During instabilities the evolution of hydraulic variables differ significantly between drained and undrained conditions. Second, stable creep is a result of dilatant processes. Third, systems situated in transitional stability regimes develop nonuniform slip pattern in space and time, revealing a possible explanation for rupture termination and observed stable afterslip. Although these patterns are produced by models located in transition zones of the parameter space, the occurrence of heterogeneous slip evolution is persistent for an extensive range of parameter values. Since transition zones contain an broad range of plausible conditions in the crust, they do not represent extreme cases.Citation: Hillers, G., and S. A. Miller (2006), Stability regimes of a dilatant, fluid-infiltrated fault plane in a three-dimensional elastic solid,

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Section: Discussionmentioning

confidence: 99%

Stability regimes of a dilatant, fluid‐infiltrated fault plane in a three‐dimensional elastic solid

Hillers

Miller

2006

J. Geophys. Res.

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“…RICE (1993, 1995) and BEN-ZION (1996) examined this issue in terms of stress concentration and strength heterogeneities in elastic solids. LOMNITZ-ADLER (1999), STEACY and MCCLOSKEY (1999) and others studied the same with cellular automata models. HAINZL and ZO¨LLER (2001) studied this question in terms of stress concentration and spatial disorder in a spring-block model.…”

Section: Introductionmentioning

confidence: 99%

The Role of Heterogeneities as a Tuning Parameter of Earthquake Dynamics

Zöller

Holschneider

Ben‐Zion

2005

Pure appl. geophys.

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We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity (''quasidynamic model''). The model produces a ''brittle-ductile'' transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: (1) high stress drop barriers in near-vertical directions and (2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations.

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“…The cellular automatum model, percolation theory, and some other statistical physics models have also been applied to study the FM relation (cf. Chelidze 1986;Sornette et al 1991;Ito 1992;Lomnitz-Adler 1993;and Main 1996). Based on a quasi-dynamic elastic model, Ben-Zion and Rice (1995) stated that FM statistics are approximately self-similar for small events, with b = 1.2, but strongly enhanced with respect to self-similarity for events larger than a critical size.…”

Section: Relation Of Frequency Versus Magnitude As Well As Energymentioning

confidence: 99%

One-Dimensional Dynamical Modeling of Earthquakes: A Review

Wang

2008

Terr. Atmos. Ocean. Sci.

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3. This relation is commonly considered to hold up for a wide range of events (Hanks 1977). However, for Japanese earthquakes, Shimazaki (1986) AbstrActStudies of the power-law relations of seismicity and earthquake source parameters based on the one-dimensional (1-D) Burridge-Knopoff's (BK) dynamical lattice model, especially those studies conducted by Taiwan's scientists, are reviewed in this article. In general, velocity-and/or state-dependent friction is considered to control faulting. A uniform distribution of breaking strengths (i.e., the static friction strength) is taken into account in some studies, and inhomogeneous distributions in others. The scaling relations in these studies include: Omori's law, the magnitude-frequency or energy-frequency relation, the relation between source duration time and seismic moment, the relation between rupture length and seismic moment, the frequency-length relation, and the source power spectra. The main parameters of the one-dimensional (1-D) Burridge-Knopoff's (BK) dynamical lattice model include: the decreasing rate (r) of dynamic friction strength with sliding velocity; the type and degree of heterogeneous distribution of the breaking strengths, the stiffness ratio (i.e., the ratio between the stiffness of the coil spring connecting two mass elements and that of the leaf spring linking a mass element and the moving plate); the frictional drop ratio of the minimum dynamic friction strength to the breaking strength; and the maximum breaking strength. For some authors, the distribution of the breaking strengths was considered to be a fractal function. Hence, the fractal dimension of such a distribution is also a significant parameter. Comparison between observed scaling laws and simulation results shows that the 1-D BK dynamical lattice model acceptably approaches fault dynamics.

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Automaton models of seismic fracture: Constraints imposed by the magnitude‐frequency relation

Cited by 58 publications

References 34 publications

Stability regimes of a dilatant, fluid‐infiltrated fault plane in a three‐dimensional elastic solid

Stability regimes of a dilatant, fluid‐infiltrated fault plane in a three‐dimensional elastic solid

The Role of Heterogeneities as a Tuning Parameter of Earthquake Dynamics

One-Dimensional Dynamical Modeling of Earthquakes: A Review

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