Selectivity of spontaneous rupture propagation on a branched fault

Aochi, Hideo; Fukuyama, Eiichi; Matsu’ura, Mitsuhiro

doi:10.1029/2000gl011560

Cited by 58 publications

(64 citation statements)

References 10 publications

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“…[19] Boundary integral (BI) methods have been widely used to investigate spontaneous propagation of cracks in elastic media [e.g., Das, 1980;Andrews, 1985;Das and Kostrov, 1988;Cochard and Madariaga, 1994;Perrin et al, 1995;Geubelle and Rice, 1995;Ben-Zion and Rice, 1997;Kame and Yamashita, 1999;Aochi et al, 2000;Lapusta et al, 2000;Lapusta and Rice, 2003]. The main idea of BI methods is to confine the numerical consideration to the crack path, by expressing the elastodynamic response of the surrounding elastic media in terms of integral relationships between displacement discontinuities and tractions along the path.…”

Section: Boundary Integral Methodsmentioning

confidence: 99%

“…Mostly, crack propagation along planar interfaces has been studied. Recently, advances have been made in using BI methods to simulate crack propagation along a self-chosen path [e.g., Kame and Yamashita, 1999], along a network of planar paths [e.g., Aochi et al, 2000], and along a planar path embedded in a half-space [e.g., Chen and Zhang, 2004]. More complicated problems (such as a layered elastic medium, etc.)…”

Section: Boundary Integral Methodsmentioning

confidence: 99%

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Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

et al. 2005

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[1] The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergence and accuracy of the numerical methods is challenging, as we lack appropriate analytical solutions for comparison. As a complement to other methods of assessment, we compare solutions obtained by two independent numerical methods, a finite difference method and a boundary integral (BI) method. The finite difference implementation, called DFM, uses a traction-at-split-node formulation of the fault discontinuity. The BI implementation employs spectral representation of the stress transfer functional. The three-dimensional (3-D) test problem involves spontaneous rupture spreading on a planar interface governed by linear slip-weakening friction that essentially defines a cohesive law. To get a priori understanding of the spatial resolution that would be required in this and similar problems, we review and combine some simple estimates of the cohesive zone sizes which correspond quite well to the sizes observed in simulations. We have assessed agreement between the methods in terms of the RMS differences in rupture time, final slip, and peak slip rate and related these to median and minimum measures of the cohesive zone resolution observed in the numerical solutions. The BI and DFM methods give virtually indistinguishable solutions to the 3-D spontaneous rupture test problem when their grid spacing Dx is small enough so that the solutions adequately resolve the cohesive zone, with at least three points for BI and at least five node points for DFM. Furthermore, grid-dependent differences in the results, for each of the two methods taken separately, decay as a power law in Dx, with the same convergence rate for each method, the calculations apparently converging to a common, grid interval invariant solution. This result provides strong evidence for the accuracy of both methods. In addition, the specific solution presented here, by virtue of being demonstrably grid-independent and consistent between two very different numerical methods, may prove useful for testing new numerical methods for spontaneous rupture problems.Citation: Day, S. M., L. A. Dalguer, N. Lapusta, and Y. Liu (2005), Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture,

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Section: Boundary Integral Methodsmentioning

confidence: 99%

Section: Boundary Integral Methodsmentioning

confidence: 99%

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

et al. 2005

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“…The boundary integral equation method (BIEM) has been quite popular for crack and rupture propagation problems (Das, 1980;Andrews, 1985;Das and Kostrov, 1988;Perrin et al, 1995;Geubelle and Rice, 1995;Kame and Yamashita, 1999;Aochi et al, 2000;Lapusta et al, 2000;Day et al, 2005;Noda et al, 2009). BIEM reduces the problem to solving only for the solution along the fault, with the material response entering through convolutions over the past history of slip or tractions on the fault.…”

Section: Related Work On Seismic Wave Propagation and Dynamic Rupturementioning

confidence: 99%

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

2012

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We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics capable of handling complex geometries and multiple faults. The bulk material is an isotropic elastic solid cut by preexisting fault interfaces. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to ordinary differential equations involving local fields.The method is based on summation-by-parts finite difference operators with irregular geometries handled through coordinate transforms and multi-block meshes. Boundary conditions as well as block interface conditions (whether frictional or otherwise) are enforced weakly through the simultaneous approximation term method, resulting in a provably stable discretization.The theoretical accuracy and stability results are confirmed with the method of manufactured solutions. The practical benefits of the new methodology are illustrated in a simulation of a subduction zone megathrust earthquake, a challenging application problem involving complex free-surface topography, nonplanar faults, and varying material properties.

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“…Dynamic models of rupture through branched geometries have been used to understand the rupture path of strike-slip events with no material contrast [e.g., Aochi et al, 2000;Oglesby et al, 2003;Duan and Oglesby, 2007]. Here we show the results of an initial investigation into the role of material contrasts in determining the rupture path selection at the branching junction to assess the likelihood of multisegment strike-slip ruptures and activation of tsunamigenic splay faults during an earthquake.…”

Section: Introductionmentioning

confidence: 99%

Influence of material contrast on fault branching behavior

Dedontney

Rice

Dmowska

2011

Geophys. Res. Lett.

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Material contrasts across faults are a common occurrence, and it is important to understand if these material contrasts can influence the path of rupture propagation. Here we examine models, solved numerically, of rupture propagation through one type of geometric complexity, that of a fault branch stemming from a planar main fault on which rupture initiates. This geometry, with a material contrast across the main fault, could be representative of either a mature strike-slip fault or a subduction zone interface. We consider branches in both the compressional and extensional quadrants of the fault, and material configurations in which the branch fault is in either the stiffer or the more compliant material and configurations with no material contrast. We find that there are regimes in which this elastic contrast can influence the rupture behavior at a branching junction, but there are also stress states for which the branch activation will not depend on the orientation of the mismatch. For the scenarios presented here, both compressional and extensional side branches are more likely to rupture if the branch is on the side of the fault with the more compliant material versus the stiffer material. The stresses induced on the branch fault, by rupture traveling on the main fault, are different for the two orientations of material contrast. We show how the interactions between rupture on the two faults determine which faults are activated.

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Selectivity of spontaneous rupture propagation on a branched fault

Cited by 58 publications

References 10 publications

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

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

Influence of material contrast on fault branching behavior

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