Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods

Kozdon, Jeremy E.; Dunham, Eric M.; Nordström, Jan

doi:10.1007/s10915-012-9624-5

Cited by 90 publications

(104 citation statements)

References 58 publications

(72 reference statements)

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“…We use a two-dimensional plane strain model that incorporates strongly rate-weakening friction on the fault and Drucker-Prager viscoplasticity to account for inelastic deformation of the off-fault material. Detailed descriptions of friction, plasticity, and material parameters can be found in Dunham et al [2011aDunham et al [ , 2011b; the numerical method (a high-order finite difference method) is described in Dunham et al [2011a] and Kozdon et al [2011Kozdon et al [ , 2012.…”

Section: Model Descriptionmentioning

confidence: 99%

Additional shear resistance from fault roughness and stress levels on geometrically complex faults

2013

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[1] The majority of crustal faults host earthquakes when the ratio of average background shear stress b to effective normal stress eff is b / eff 0.6. In contrast, mature plate-boundary faults like the San Andreas Fault (SAF) operate at b / eff 0.2. Dynamic weakening, the dramatic reduction in frictional resistance at coseismic slip velocities that is commonly observed in laboratory experiments, provides a leading explanation for low stress levels on mature faults. Strongly velocity-weakening friction laws permit rupture propagation on flat faults above a critical stress level pulse / eff 0.25. Provided that dynamic weakening is not restricted to mature faults, the higher stress levels on most faults are puzzling. In this work, we present a self-consistent explanation for the relatively high stress levels on immature faults that is compatible with low coseismic frictional resistance, from dynamic weakening, for all faults. We appeal to differences in structural complexity with the premise that geometric irregularities introduce resistance to slip in addition to frictional resistance. This general idea is quantified for the special case of self-similar fractal roughness of the fault surface. Natural faults have roughness characterized by amplitude-to-wavelength ratios˛between 10 -3 and 10 -2 . Through a second-order boundary perturbation analysis of quasi-static frictionless sliding across a band-limited self-similar interface in an ideally elastic solid, we demonstrate that roughness induces an additional shear resistance to slip, or roughness drag, given by drag = 8 3˛2 G * / min , for G * = G/(1 -) with shear modulus G and Poisson's ratio , slip , and minimum roughness wavelength min . The influence of roughness drag on fault mechanics is verified through an extensive set of dynamic rupture simulations of earthquakes on strongly rate-weakening fractal faults with elastic-plastic off-fault response. The simulations suggest that fault rupture, in the form of self-healing slip pulses, becomes probable above a background stress level b pulse + drag . For the smoothest faults (˛ 10 -3 ), drag is negligible compared to frictional resistance, so that b pulse 0.25 eff . However, on rougher faults (˛ 10 -2 ), roughness drag can exceed frictional resistance. We expect that drag ultimately departs from the predicted scaling when roughness-induced stress perturbations activate pervasive off-fault inelastic deformation, such that background stress saturates at a limit ( b 0.6 eff ) determined by the finite strength of the off-fault material. We speculate that this strength, and not the much smaller dynamically weakened frictional strength, determines the stress levels at which the majority of faults operate.Citation: Fang, Z., and E. M. Dunham (2013), Additional shear resistance from fault roughness and stress levels on geometrically complex faults,

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Section: Model Descriptionmentioning

confidence: 99%

Additional shear resistance from fault roughness and stress levels on geometrically complex faults

2013

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“…The results presented here are given in [8], [9], [7], [4]. The figures and tables in Sections 3.1-3.2 and Figure 1 are included with kind permission from Springer Science+Business Media B.V.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The elastic wave equations govern the wave propagation between the faults. For a read-up on these problems see [8], [9].…”

Section: Modeling Related To Earthquake Simulationsmentioning

confidence: 99%

“…Note that the full methodology is presented in [8], [9], [7], [4]. The problem is motivated by the recent magnitude 9.0 Tohoku-Oki, Japan, megathrust earthquake and the resulting tsunami.…”

Section: Application To a Subduction Zone Megathrust Earthquakementioning

confidence: 99%

“…For this problem, the method must be extended to handle multi-block interfaces, far-field boundaries, complex initial conditions, realistic friction laws and a multitude of other complex physical considerations. We do not intend to go through this in this paper, but refer the reader to [9], [7], [4].…”

Section: Application To a Subduction Zone Megathrust Earthquakementioning

confidence: 99%

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Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

Nordström

2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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We discuss linear and nonlinear boundary conditions for wave propagation problems. The concepts of well-posedness and stability are discussed by considering a specific example of a boundary condition occurring in the modeling of earthquakes. That boundary condition can be formulated in a linear and nonlinear way and implemented in a characteristic and non-characteristic way. These differences are discussed and the implications and difficulties are pointed out. Numerical simulations that illustrate the theoretical discussion are presented together with an application that show that the methodology can be used for practical problems.

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Predicting fault damage zones by modeling dynamic rupture propagation and comparison with field observations

Johri

Dunham²,

Zoback

et al. 2014

J. Geophys. Res. Solid Earth

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We use a two-dimensional plane strain dynamic rupture model with strongly rate-weakening friction and off-fault Drucker-Prager plasticity to model damage zones associated with buried second-order thrust faults observed in the SSC reservoir. The modeling of ruptures propagating as self-sustaining pulses is performed in the framework of continuum plasticity where the plasticity formulation includes both deviatoric and volumetric plastic strains. The material deforming inelastically due to stress perturbations generated by the propagating rupture is assumed to be the damage zone associated with the fault. Dilatant plastic strains are converted into a fracture population by assuming that the dilatant plastic strain is manifested in the form of fractures. The cumulative effect of multiple slip events is considered by superposition of the plastic strain field obtained from individual slip events. The relative number of various magnitude slip events is chosen so as to honor the Gutenberg-Richter law. Results show that the decay of fracture density (F) with distance (r) from the fault can be described by a power law F = F 0 r À n . The fault constant F 0 represents the fracture density at unit distance from the fault. The decay rate (n) in fracture density is approximately 0.85 close to the fault and increases to~1.4 at larger distances (>10 m). Modeled damage zones are approximately 60-100 m wide. These attributes are similar to those observed in the SSC reservoir using wellbore image logs and those reported in outcrop studies. Considering fault roughness affects local damage zone characteristics, these characteristics are similar to those modeled around planar faults at a scale (~10 m) that affects bulk fluid-flow properties.

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Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods

Cited by 90 publications

References 58 publications

Additional shear resistance from fault roughness and stress levels on geometrically complex faults

Additional shear resistance from fault roughness and stress levels on geometrically complex faults

Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

Predicting fault damage zones by modeling dynamic rupture propagation and comparison with field observations

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