Dynamic modelling of the flat 2-D crack by a semi-analytic BIEM scheme

Tada, Taku; Madariaga, Raúl

doi:10.1002/1097-0207(20010110)50:1<227::aid-nme166>3.0.co;2-5

Cited by 34 publications

(35 citation statements)

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“…(1). We first derive asymptotic expressions for the integration kernels obtained by Cochard and Madariaga (1994) for the anti-plane strain crack and by Tada and Yamashita (1997) and Tada and Madariaga (2001) for the in-plane crack. The employment of these asymptotic expressions is a key factor in our development of the efficient BIEM-ST.…”

Section: Boundary Integral Equation Methodsmentioning

confidence: 99%

“…We begin with the prevalent exact expressions of the discrete integration kernels derived by Tada and Madariaga (2001) for the in-plane shear crack, in which the BIE is discretized assuming a slip velocity D that is constant on each spatio-temporal discrete element. We approximate a non-planar fault by an array of line elements so that the deformation due to slip on a non-planar fault can be given by the sum of contributions from all the elements.…”

Section: Boundary Integral Equation Methodsmentioning

confidence: 99%

“…The exact expressions for the function I σ pq (·) (p, q = 1, 2) are written as (Tada and Madariaga, 2001). We find that the asymptotic expressions valid for βt/r 1 are given by…”

Section: Efficient Calculation Of Integration Kernelsmentioning

confidence: 99%

“…For numerical implementation, the Courant-Friedrichs-Lewy (CFL) parameter is taken to be 0.5, and the temporal collocation points are chosen at the top of each unit time-step interval (i.e. e t = 1 following the definition of Tada and Madariaga, 2001). We adopt the following procedure to investigate how the error is generated during all of the time steps.…”

Section: Error In Slip Velocitymentioning

confidence: 99%

“…Boundary integral equation methods based on the spatiotemporal formulation (BIEM-ST) are widely used as an ef-fective numerical tool in the simulation of dynamic earthquake ruptures because they are able to treat non-planar faults accurately (Kame and Yamashita, 1999a, b;Tada and Madariaga, 2001;Aochi and Fukuyama, 2002;Aochi et al, 2003;Kame and Yamashita, 2003;Ando et al, 2004). Generally, in the two-dimensional (2-D) BIEM-ST, the change in the stress tensor σ pq on a fault can be described in terms of the fault slip velocity in a discretized form:…”

Section: Introductionmentioning

confidence: 99%

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An efficient boundary integral equation method applicable to the analysis of non-planar fault dynamics

2007

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We develop a novel and efficient boundary integral equation method based on the spatio-temporal formulation for the two-dimensional dynamic and quasistatic analyses of an earthquake fault in a single scheme. A major advantage of this method is its applicability to the analysis of non-planar faults with the same degree of accuracy as to that of planar faults. Calculation time and memory requirement are reduced through the employment of asymptotic representations of the integration kernels appearing in the convolution integral. Asymptotic kernels are factorized into terms dependent on space or time alone, resulting in efficient numerical computations. In addition, the dependence on time is found to vanish in the asymptotic kernels far behind the S-wave front, which also contributes to the time-saving efficiency of the calculations. We show that, in a dynamic analysis, if a 3% error is allowed for the slip rate, computation time and memory requirement are reduced by 25% and 45%, respectively, in an in-plane fault case, and by 60% and 75%, respectively, in an anti-plane fault case. This method can be employed as a powerful numerical tool in simulating an entire earthquake cycle consisting of both quasi-static and dynamic processes with a more realistic non-planar geometry of faults.

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Section: Boundary Integral Equation Methodsmentioning

confidence: 99%

Section: Boundary Integral Equation Methodsmentioning

confidence: 99%

“…The exact expressions for the function I σ pq (·) (p, q = 1, 2) are written as (Tada and Madariaga, 2001). We find that the asymptotic expressions valid for βt/r 1 are given by…”

Section: Efficient Calculation Of Integration Kernelsmentioning

confidence: 99%

Section: Error In Slip Velocitymentioning

confidence: 99%