A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation

Komatitsch, Dimitri; Tromp, Jeroen

doi:10.1046/j.1365-246x.2003.01950.x

Cited by 349 publications

(170 citation statements)

References 41 publications

Supporting

Mentioning

167

Contrasting

Unclassified

Order By: Relevance

“…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%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

View full text Add to dashboard Cite

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.

show abstract

Section: Perfectly Matched Layermentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

View full text Add to dashboard Cite

show abstract

“…They combine the advantages of both previous methods since they are easy to implement, retain the sparsity of the system matrix, and can be applied close to the boundary of the scatterer. The methodology has since been extended to other wave equations and is now widely used for the numerical solution of problems in acoustic scattering [12,13], seismology [14,15], linear elasticity [16,17,18], and ultrasound [19], to name but a few.…”

Section: Introductionmentioning

confidence: 99%

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

Cimpeanu

Martinsson

Heil

2015

Journal of Computational Physics

View full text Add to dashboard Cite

This paper presents a parameter-free perfectly matched layer (PML) method for the finite-element-based solution of the Helmholtz equation. We employ one of Bermúdez et al.'s unbounded absorbing functions for the complex coordinate mapping underlying the PML. With this choice, the only free parameter that controls the accuracy of the numerical solution for a fixed numerical cost (characterised by the number of elements in the bulk and the PML regions) is the thickness of the perfectly matched layer, δ PML . We show that, for the case of planar waves, the absorbing function performs best for PMLs whose thickness is much smaller than the wavelength. We then perform extensive numerical experiments to explore its performance for non-planar waves, considering domain shapes with smooth and polygonal boundaries, different solution types (smooth and singular), and a wide range of wavenumbers, k, to identify an optimal range for the normalised PML thickness, kδ PML , such that, within this range, the error introduced by the presence of the PML is consistently small and insensitive to change. This implies that if the PML thickness is chosen from within this range * Corresponding author URL: http://www3.imperial.ac.uk/people/radu.cimpeanu11 (Radu Cimpeanu), http://www.maths.manchester.ac.uk/~mheil/ (Matthias Heil) Preprint submitted to Journal of Computational PhysicsMay 4, 2015 no further PML optimisation is required, i.e. the method is parameter-free. We characterise the dependence of the error on the discretisation parameters and establish the conditions under which the convergence of the solution under mesh refinement is controlled exclusively by the discretisation of the bulk mesh.

show abstract

“…These can be improved through different time stepping methods (see Noh et al 2013) or improved absorbing boundary techniques (e.g. Komatitsch & Tromp 2003). Also of note is that the 2-D full waveform simulation does not display a direct body S-wave.…”

Section: O M Pa R I S O N W I T H 2 -D F U L L Wav E F O R M S I M mentioning

confidence: 99%

A numerical approach for modelling fault-zone trapped waves

Gulley

Kaipio

Eccles

et al. 2017

Geophysical Journal International

View full text Add to dashboard Cite

A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation

Cited by 349 publications

References 41 publications

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

A numerical approach for modelling fault-zone trapped waves

Contact Info

Product

Resources

About