Dynamic faulting studied by a finite difference method

Virieux, J.; Madariaga, R.

doi:10.1016/0148-9062(83)91702-3

Cited by 46 publications

(91 citation statements)

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“…The elastodynamic equations of motion can be written as the following system of nine first-order equations (Madariaga 1976; Virieux and Madariaga 1982;Chouet 1986)…”

Section: The Fluid-driven Crack Modelmentioning

confidence: 99%

“…The equations of motion [Eqs. (61) to (63)] constitute a set of first-order hyperbolic equations for stresses, pressure, and velocities which can be solved numerically by centered finite differences (Madariaga 1976;Aki et al 1977;Fehler and Aki 1978;Virieux and Madariaga 1982;Virieux 1984Virieux , 1986Chouet 1986). The numerical solution is accurate to within 10 % error in the phase velocity for wavelengths A > 5Lln, where n is the number of grid points over the length L of the crack.…”

Section: The Fluid-driven Crack Modelmentioning

confidence: 99%

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New Methods and Future Trends in Seismological Volcano Monitoring

Chouet

1996

Monitoring and Mitigation of Volcano Hazards

186

168

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Volcanic processes operate over a wide range of time scales that require a variety of instruments and techniques for their study. Short-period seismology typically covers the band 0.1-1 s, while broadband seismology can extend that band to 0.1-100 s. Borehole strainmeters may be used to cover the very wide band from 0.1 s to 100 days and Global Positioning System (GPS) surveys are useful to track deformation over time scales ranging from days to decades. Arrays of threecomponent broadband seismographs coupled with arrays of borehole strainmeters are required to monitor the dynamics of magmatic and hydrothermal fluids prior to and during eruptions. Inversions of broadband data may be performed to image the forces operating at a source and infer the fluid pathway geometry and mass transport balance in a volcano. The accuracy of such inversions depends on the degree of resolution achieved for the volcanic structure. High-resolution tomography based on iterative inversions of seismic travel-time data can image three-dimensional structures at a scale of a few hundred meters provided adequate local short-period earthquake data are available. Hence, forces in a volcano are potentially resolvable for periods longer than a few seconds. Studies of long-period events and tremor at periods ~ I s offer constraints on pressure fluctuations resulting from unsteady mass transport, and observations of volcano-tectonic activity tell us about hydraulic fracturing processes, as well as brittle response of the rock matrix to stress changes induced by rapid injection and/or withdrawal of fluids. Short-period networks are routinely used to monitor, locate, and assess the source properties of volcano-tectonic earthquakes and long-period events, while small-aperture seismic antennas are required to track tremor and separate source, path, and site effects in tremor wavefields. This chapter reviews quantitative methods used in the interpretation of source processes and structures in volcanoes and discusses some of the major challenges faced by volcano seismologists in their quest to understand eruptive behavior.

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“…The elastodynamic equations of motion can be written as the following system of nine first-order equations (Madariaga 1976; Virieux and Madariaga 1982;Chouet 1986)…”

Section: The Fluid-driven Crack Modelmentioning

confidence: 99%

Section: The Fluid-driven Crack Modelmentioning

confidence: 99%

New Methods and Future Trends in Seismological Volcano Monitoring

Chouet

1996

Monitoring and Mitigation of Volcano Hazards

186

168

View full text Add to dashboard Cite

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“…Finite difference methods have been widely used, but mostly for planar faults (e.g., [2,16,38,40,64]). Nonplanar fault geometries have also been incorporated in finite difference methods using coordinate transform techniques (e.g., [14,15,31] ).…”

Section: Introductionmentioning

confidence: 99%

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

OReilly

Nordström

Kozdon

et al. 2015

Commun. Comput. Phys.

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Abstract.A numerical method suitable for wave propagation problems in complex geometries is developed for simulating dynamic earthquake ruptures with realistic friction laws. The numerical method couples an unstructured, node-centered finite volume method to a structured, high order finite difference method. In this work we our focus attention on 2-D antiplane shear problems. The finite volume method is used on unstructured triangular meshes to resolve earthquake ruptures propagating along a nonplanar fault. Outside the small region containing the geometrically complex fault, a high order finite difference method, having superior numerical accuracy, is used on a structured grid. The finite difference method is coupled weakly to the finite volume method along interfaces of collocated grid points. Both methods are on summation-by-parts form. The simultaneous approximation term method is used to weakly enforce the interface conditions. At fault interfaces, fault strength is expressed as a nonlinear function of sliding velocity (the jump in particle velocity across the fault) and a state variable capturing the history dependence of frictional resistance. Energy estimates are used to prove that both types of interface conditions are imposed in a stable manner. Stability and accuracy of the numerical implementation are verified through numerical experiments, and efficiency of the hybrid approach is confirmed through grid coarsening tests. Finally, the method is used to study earthquake rupture propagation along the margins of a volcanic plug. AMS subject classifications: 35L05,35L65,35Q35,65M06,65M08,65M12,65Z05

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“…Due to its relative simplicity, the finite difference method (FDM) on a uniform grid was used in the first three-dimensional simulations of planar cracks under shear loading conditions (Archuleta and Frazier, 1978 ;Virieux and Madariaga, 1982;Day, 1982), and it has been adapted to non-uniform grids in inhomogeneous media (Mikumo et al, 1987;Mikumo and Miyatake, 1993). The technique was however shown (Andrews, 1985) to produce an excessive "smear out" of elastodynamic waves, which hinders resolution of stress peaks radiated ahead of the crack and may affect the overall propagation behavior of faults.…”

Section: Introductionmentioning

confidence: 99%

A spectral method for three-dimensional elastodynamic fracture problems

Geubelle¹

1995

Journal of the Mechanics and Physics of Solids

200

209

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We present a numerical formulation for three-dimensional elastodynamic problems of fracture on planar cracks and faults. Stress and displacement components are given a spectral representation as finite Fourier series in space coordinates parallel to the fracture plane. The formulation is based on an exact representation, involving a convolution integral for each Fourier mode, of the elastodynamic relation existing between the time-dependent Fourier coefficients for the tractions acting on the fracture plane and for the resulting displacement discontinuities. A wide range of constitutive models can be used to relate the local value of the strength on the fracture plane with the displacement and velocity history. Efficiency of the code is achieved by using an explicit time integration scheme and by computing the conversion between the spatial and spectral distributions through a FFT algorithm. The method is particularly suited to implementation on massively parallel computers ; a CM-5 was used in this work. The stability and precision of the formulation are discussed for tensile (mode I) situations in a detailed modal analysis, and numerical results are compared with existing three-dimensional elastodynamic solutions. The adequacy of the method to investigate various three-dimensional dynamic fracture problems involving non-propagating and propagating tensile cracks is illustrated, including crack growth along a plane of heterogeneous fracture toughness.

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Dynamic faulting studied by a finite difference method

Cited by 46 publications

References 0 publications

New Methods and Future Trends in Seismological Volcano Monitoring

New Methods and Future Trends in Seismological Volcano Monitoring

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

A spectral method for three-dimensional elastodynamic fracture problems

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