Mesh dependence and slip complexity in earthquake fault models

2010

No complete physically consistent model of earthquake rupture exists that can fully describe the rich hierarchy of scale dependencies and nonlinearities associated with earthquakes. We study mesh sensitivity in numerical models of earthquake rupture and demonstrate that this mesh sensitivity may provide hidden clues to the underlying physics generating the rich dynamics associated with earthquake rupture. We focus on unstable slip events that occur in earthquakes when rupture is associated with frictional weakening of the fault. Attempts to simulate these phenomena directly by introducing the relevant constitutive behaviour leads to mesh-dependent results, where the deformation localizes in one element, irrespective of size. Interestingly, earthquake models with oversized mesh elements that are ill-posed in the continuum limit display more complex and realistic physics. Until now, the mesh-dependency problem has been regarded as a red herringbut have we overlooked an important clue arising from the mesh sensitivity? We analyse spatial discretization errors introduced into models with oversized meshes to show how the governing equations may change because of these error terms and give rise to more interesting physics.

Communications Earth & Environment, 2022

The statistical properties of seismicity are known to be affected by several factors such as the rheological parameters of rocks. We analysed the earthquake double-couple as a function of the faulting type. Here we show that it impacts the moment tensors of earthquakes: thrustfaulting events are characterized by higher double-couple components with respect to strikeslip-and normal-faulting earthquakes. Our results are coherent with the stress dependence of the scaling exponent of the Gutenberg-Richter law, which is anticorrelated to the doublecouple. We suggest that the structural and tectonic control of seismicity may have its origin in the complexity of the seismogenic source marked by the width of the cataclastic damage zone and by the slip of different fault planes during the same seismic event; the sharper and concentrated the slip as along faults, the higher the double-couple. This phenomenon may introduce bias in magnitude estimation, with possible impact on seismic forecasting.

Earthquake source time functions carry information about the complexity of seismic rupture.

Journal of Geophysical Research, 2002

Finite-fault source inversions reveal the spatial complexity of earthquake slip over the fault plane. We develop a stochastic characterization of earthquake slip complexity, based on published finite-source rupture models, in which we model the distribution of slip as a spatial random field. The model most consistent with the data follows a von Karman autocorrelation function (ACF) for which the correlation lengths a increase with source dimension. For earthquakes with large fault aspect ratios, we observe substantial differences of the correlation length in the along-strike (a x) and downdip (a z) directions. Increasing correlation length with increasing magnitude can be understood using concepts of dynamic rupture propagation. The power spectrum of the slip distribution can also be well described with a power law decay (i.e., a fractal distribution) in which the fractal dimension D remains scale invariant, with a median value D = 2.29 ± 0.23, while the corner wave number k c , which is inversely proportional to source size, decreases with earthquake magnitude, accounting for larger ''slip patches'' for large-magnitude events. Our stochastic slip model can be used to generate realizations of scenario earthquakes for near-source ground motion simulations.

Pure and Applied Geophysics, 2005

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.

Geophysical Journal International, 2005

There has been debate on whether average slip D in long ruptures should scale with rupture length L, or with rupture width W . This scaling discussion is equivalent to asking whether average stress drop σ , which is sometimes considered an intrinsic frictional property of a fault, is approximately constant over a wide range of earthquake sizes. In this paper, we examine slip-length scaling relations using a simplified 1-D model of spatially heterogeneous slip. The spatially heterogeneous slip is characterized by a stochastic function with a Fourier spectrum that decays as k −α , where k is the wavenumber and α is a parameter that describes the spatial smoothness of slip. We adopt the simple rule that an individual earthquake rupture consists of only one spatially continuous segment of slip (i.e. earthquakes are not generally separable into multiple disconnected segments of slip). In this model, the slip-length scaling relation is intimately related to the spatial heterogeneity of the slip; linear scaling of average slip with rupture length only occurs when α is about 1.5, which is a relatively smooth spatial distribution of slip. We investigate suites of simulated ruptures with different smoothness, and we show that faults with large slip heterogeneity tend to have higher D/L ratios than those with spatially smooth slip. The model also predicts that rougher faults tend to generate larger numbers of small earthquakes, whereas smooth faults may have a uniform size distribution of earthquakes. This simple 1-D fault model suggests that some aspects of stress drop scaling are a consequence of whatever is responsible for the spatial heterogeneity of slip in earthquakes.

Geophysical Journal International, 2005

There has been debate on whether average slip D in long ruptures should scale with rupture length L, or with rupture width W . This scaling discussion is equivalent to asking whether average stress drop σ , which is sometimes considered an intrinsic frictional property of a fault, is approximately constant over a wide range of earthquake sizes. In this paper, we examine slip-length scaling relations using a simplified 1-D model of spatially heterogeneous slip. The spatially heterogeneous slip is characterized by a stochastic function with a Fourier spectrum that decays as k −α , where k is the wavenumber and α is a parameter that describes the spatial smoothness of slip. We adopt the simple rule that an individual earthquake rupture consists of only one spatially continuous segment of slip (i.e. earthquakes are not generally separable into multiple disconnected segments of slip). In this model, the slip-length scaling relation is intimately related to the spatial heterogeneity of the slip; linear scaling of average slip with rupture length only occurs when α is about 1.5, which is a relatively smooth spatial distribution of slip. We investigate suites of simulated ruptures with different smoothness, and we show that faults with large slip heterogeneity tend to have higher D/L ratios than those with spatially smooth slip. The model also predicts that rougher faults tend to generate larger numbers of small earthquakes, whereas smooth faults may have a uniform size distribution of earthquakes. This simple 1-D fault model suggests that some aspects of stress drop scaling are a consequence of whatever is responsible for the spatial heterogeneity of slip in earthquakes.

Pure and Applied Geophysics, 2004

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.

Journal of Geophysical Research: Solid Earth, 2018

Recent earthquakes have demonstrated that rupture may propagate through geometrically complex networks of faults. Ancient exhumed faults have the potential to reveal the details of complex rupture at seismogenic depths. We present a new set of field observational criteria for determining which of a population of pseudotachylyte fault veins formed in the same earthquake and apply it to map rupture networks representing single earthquakes. An exceptional exposure of an exhumed ancient strand of the Norumbega Shear Zone preserves evidence of multistranded earthquake rupture in the deep seismogenic zone of a continental transform fault. Individual fault strands slipped at least 2-18 cm, so significant slip is represented by each rupture network. Our data show that synchronously slipped faults intersect at angles of 0 to ∼55 ∘ , with the opening angles of fault intersections directed toward the dilational quadrants for dextral slip. Multistranded rupture on a fault network instead of rupture of a single fault may result in greater and/or more variable slip and cause slip rake to vary spatially and temporally. Slip on intersecting faults unequivocally means that there will be motion perpendicular to the average fault plane. Modern earthquakes displaying non-double-couple components to focal mechanism solutions and spatially varying rake, slip, and anomalous stress drop may be explained by rupture across fault networks that are too close (spatially and temporally) to be resolved seismically as separate events. Plain Language Summary Earthquake faults are often treated as simple planar features, but some recent earthquakes have shown that networks of faults can rupture together and produce very complicated patterns of deformation. We found an exposure of an ancient fault zone in Maine, USA, which preserves the pattern of ancient ruptures in the form of fossil earthquake slip surfaces. We mapped the networks of faults that slipped in individual earthquakes to show the geometry of complex earthquake ruptures at middle-crustal depths and predict what seismologists would observe if similar earthquakes are happening today.

Journal of Geophysical Research, 2000

We investigate the impact of variations in the friction and geometry on models of fault dynamics. We focus primarily on a three-dimensional continuum model with scalar displacements. Slip occurs on an embedded two-dimensional planar interface. Friction is characterized by a two-parameter rate and state law, incorporating a characteristic length for weakening, a characteristic time for healing, and a velocity-weakening steady state. As the friction parameters are varied, there is a crossover from narrow, self-healing slip pulses to crack-like solutions that heal in response to edge effects. For repeated ruptures the crack-like regime exhibits periodic or aperiodic systemwide events. The self-healing regime exhibits dynamical complexity and a broad distribution of rupture areas. The behavior can also change from periodicity or quasi-periodicity to dynamical complexity as the total fault size or the length-to-width ratio is increased. Our results for the continuum model agree qualitatively with analogous results obtained for a one-dimensional Burridõe-Knopoff model in which radiation effects are approximated by viscous dissipation. context of a three-dimensional continuum model and a one-dimensional Burridge-Knopoff model. In our studies, dynamical complexity refers to observations of a