Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation

Hastings, Frank D.; Schneider, John B.; Broschat, Shira L.

doi:10.1121/1.417118

Cited by 277 publications

(136 citation statements)

References 29 publications

(28 reference statements)

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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%

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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%

“…to the solution of the frequency domain version of (21). 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]).…”

Section: Remarkmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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“…Abarbanel and Gottlieb, 1997;Liu and Tao, 1997;Qi and Geers, 1998;Liu, 1999;Katsibas and Antonopoulos, 2002;Diaz and Joly, 2006;Bermúdez et al, 2007) and elastic wave simulations (e.g. Chew and Liu, 1996;Hastings et al, 1996;Collino and Tsogka, 2001;Festa and Nielsen, 2003;Komatitsch and Tromp, 2003;Basu and Chopra, 2004;Appelö and Kreiss, 2006;Komatitsch and Martin, 2007;Yang et al, 2007;Lan et al, 2013). The PML has been further extended to other methods, such as the pseudo-spectral method (Liu, 1998), the finite element method (Collino and Tsogka, 2001), the spectral element method , and the grid method (Xu and Zhang, 2008).…”

Section: Perfectly Matched Layermentioning

confidence: 99%

“…Cerjan et al, 1985;Compani-Tabrizi, 1986;Kosloff and Kosloff, 1986;Sochacki et al, 1987), the perfectly matched layer (PML) (e.g. Bérenger, 1994;Chew and Liu, 1996;Hastings et al, 1996;Collino and Tsogka, 2001;Marcinkovich and Olsen, 2003;Wang and Tang, 2003), and the hybrid absorbing boundary condition Sen, 2010, 2012).…”

Section: Introductionmentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

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Abstract. Absorbing boundary conditions are necessary in numerical simulation for reducing the artificial reflections from model boundaries. In this paper, we overview the most important and typical absorbing boundary conditions developed throughout history. We first derive the wave equations of similar methods in unified forms; then, we compare their absorbing performance via theoretical analyses and numerical experiments. The Higdon boundary condition is shown to be the best one among the three main absorbing boundary conditions that are based on a one-way wave equation. The Clayton and Engquist boundary is a special case of the Higdon boundary but has difficulty in dealing with the corner points in implementaion. The Reynolds boundary does not have this problem but its absorbing performance is the poorest among these three methods. The sponge boundary has difficulties in determining the optimal parameters in advance and too many layers are required to achieve a good enough absorbing performance. The hybrid absorbing boundary condition (hybrid ABC) has a better absorbing performance than the Higdon boundary does; however, it is still less efficient for absorbing nearly grazing waves since it is based on the one-way wave equation. In contrast, the perfectly matched layer (PML) can perform much better using a few layers. For example, the 10-layer PML would perform well for absorbing most reflected waves except the nearly grazing incident waves. The 20-layer PML is suggested for most practical applications. For nearly grazing incident waves, convolutional PML shows superiority over the PML when the source is close to the boundary for large-scale models. The Higdon boundary and hybrid ABC are preferred when the computational cost is high and high-level absorbing performance is not required, such as migration and migration velocity analyses, since they are not as sensitive to the amplitude errors as the full waveform inversion.

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“…This technique was originally developed for two dimensional electromagnetic wave problems [9] and later on expanded to three dimensional problems [10], [11]. Others have applied the method to elastodynamic wave fields [12], [13], [14] and acoustic wave fields [15], [16].…”

Section: Introductionmentioning

confidence: 99%