Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media

Collino, Francis; Tsogka, Chrysoula

doi:10.1190/1.1444908

Cited by 710 publications

(451 citation statements)

References 22 publications

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“…The method has been extended to various propagation models (the paraxial wave equations [15], the linearized Euler equations [22,24,32], etc. ), including in particular elastic wave propagation in isotropic [21] and anisotropic media [17]. Trying to use these PMLs for computing the propagation of seismic waves, we observed exponential blow up phenomena in some numerical experiments involving anisotropic media.…”

Section: Introductionmentioning

confidence: 99%

“…The very astonishing property of this layer model is that it is perfectly matched, which means that it generates no reflection at the interface between the physical domain and the absorbing medium (see [17]). This property can be shown through a plane wave analysis.…”

Section: Remarkmentioning

confidence: 99%

“…In [17], the authors have shown that it is possible to write a systematic way of designing a PML model for a general first-order hyperbolic system. In this section we briefly describe this general construction.…”

Section: Remarkmentioning

confidence: 99%

“…By definition, the slowness diagram is the set of points, in the plane of slowness vectorsS S ¼ k=x, that satisfy (17). It is also the union of two curves whose equations in polar coordinates are…”

Section: Harmonic Plane Waves and Slowness Diagramsmentioning

confidence: 99%

“…(21), written in the frequency domain, the x 1 derivatives o 1 into dðx; fðx 1 ÞÞo 1 , (see [16,17]), where…”

Section: Remarkmentioning

confidence: 99%

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Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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Perfectly matched layers (PML) are a recent technique for simulating the absorption of waves in open domains. They have been introduced for electromagnetic waves and extended, since then, to other models of wave propagation, including waves in elastic anisotropic media. In this last case, some numerical experiments have shown that the PMLs are not always stable. In this paper, we investigate this question from a theoretical point of view. In the first part, we derive a necessary condition for the stability of the PML model for a general hyperbolic system. This condition can be interpreted in terms of geometrical properties of the slowness diagrams and used for explaining instabilities observed with elastic waves but also with other propagation models (anisotropic MaxwellÕs equations, linearized Euler equations). In the second part, we specialize our analysis to orthotropic elastic waves and obtain separately a necessary stability condition and a sufficient stability condition that can be expressed in terms of inequalities on the elasticity coefficients of the model.

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Section: Introductionmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Harmonic Plane Waves and Slowness Diagramsmentioning

confidence: 99%

“…(21), written in the frequency domain, the x 1 derivatives o 1 into dðx; fðx 1 ÞÞo 1 , (see [16,17]), where…”

Section: Remarkmentioning

confidence: 99%

See 3 more Smart Citations

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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Sensitivity of seismic measurements to frequency‐dependent attenuation and upper mantle structure: An initial approach

Bellis

Holtzman

2014

JGR Solid Earth

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International audienceThis study addresses the sensitivity of seismic attenuation measurements to dissipative mechanisms and structure in the Earth’s upper mantle. The Andrade anelastic model fits experimental attenuation data with a mild power law frequency dependence and can be scaled from laboratory to Earth conditions. We incorporate this anelastic model into 400 km 1-D thermal profiles of the upper mantle. These continuous-spectrum models are approximated by multiple relaxation mechanisms that are implemented within a finite-difference scheme to perform wave propagation simulations in 1-D domains. In two sets of numerical experiments, we evaluate the measurable signature of the intrinsic attenuation structure. The two sets are defined by thermal profiles with added step functions of temperature, varying in (i) amplitude and depth or (ii) amplitude and sharpness. The corresponding synthetic data are processed using both the conventional t∗ approach, i.e., a linear regression of the displacement frequency spectrum, and an alternative nonlinear fit to identify the integrated value of attenuation and its frequency dependence. The measured sensitivity patterns are analyzed to assess the effects of the anelastic model and its spatial distribution on seismic data (in the absence of scattering effects). We have two straightforward results: (1) the frequency dependence power law is recoverable from the measurements; (2) t∗ is sensitive to both the depth and the amplitude of the step, and it is insensitive to the sharpness of the step, in the 0.25 to 2 Hz band. There is much potential for gaining information about the upper mantle thermodynamic state from careful interpretation of attenuation

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Seismic shaking in the North China Basin expected from ruptures of a possible seismic gap

Duan

Liu

Yin

2017

Geophysical Research Letters

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A 160 km long seismic gap, which has not been ruptured over ~8000 years, was identified recently in North China. In this study, we use a dynamic source model and a newly available high‐resolution 3‐D velocity structure to simulate long‐period ground motion (up to 0.5 Hz) from possibly worst case rupture scenarios of the seismic gap. We find that the characteristics of the earthquake source and the local geologic structure play a critical role in controlling the amplitude and distribution of the simulated strong ground shaking. Rupture directivity and slip asperities can result in large‐amplitude (i.e., >1 m/s) ground shaking near the fault, whereas long‐duration shaking may occur within sedimentary basins. In particular, a deep and closed Quaternary basin between Beijing and Tianjin can lead to ground shaking of several tens of cm/s for more than 1 min. These results may provide a sound basis for seismic mitigation in one of the most populated regions in the world.

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Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media

Cited by 710 publications

References 22 publications

Stability of perfectly matched layers, group velocities and anisotropic waves

Stability of perfectly matched layers, group velocities and anisotropic waves

Sensitivity of seismic measurements to frequency‐dependent attenuation and upper mantle structure: An initial approach

Seismic shaking in the North China Basin expected from ruptures of a possible seismic gap

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