Boundary conditions for the numerical solution of wave propagation problems

Reynolds, Albert C.

doi:10.1190/1.1440881

Cited by 248 publications

(134 citation statements)

References 0 publications

Supporting

Mentioning

120

Contrasting

Unclassified

Order By: Relevance

“…Notice that after 3 seconds, seismic traces show small reflections because of the low effectiveness of Reynolds' absorbing boundary conditions, and they must not be interpreted as a deficiency of the numerical scheme. Comparison of traces in figure 4 with the original ones reported in [17] are qualitatively identical. A further assessment of mimetic waveforms in panel (b) can be performed by means of ray tracing, that can be done analytically.…”

Section: Test No 3: a Heterogeneity Testsupporting

confidence: 71%

“…Application of volumen-discretization numerical methods to wave propagation problems on such idealized infinite domains require absorbing boundary conditions to limit the actual computational domain. In the technical literature, there are several numerical techniques for implementing absorbing boundaries, but in this paper we adopt an approach based on the one-way wave equation proposed in [17] to simulate P wave propagation using a standard finite difference method. We already used this type of conditions in previous test No.…”

Section: Test No 3: a Heterogeneity Testmentioning

confidence: 99%

“…On the other hand, absorbing boundary conditions have multiple implementations in the technical literature, and their review will not be pursued here. In this article, we implement absorbing boundary conditions using techniques based on the one-way wave equation as in [17],…”

Section: Mimetic Schemementioning

confidence: 99%

See 2 more Smart Citations

A new mimetic scheme for the acoustic wave equation

Solano-Feo

Guevara-Jordan

Rojas

et al. 2016

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

A new mimetic finite difference scheme for solving the acoustic wave equation is presented. It combines a novel second order tensor mimetic discretizations in space and a leapfrog approximation in time to produce an explicit multidimensional scheme. Convergence analysis of the new scheme on a staggered grid shows that it can take larger time steps than standard finite difference schemes based on ghost points formulation. A set of numerical test problems gives evidence of the versatility of the new mimetic scheme for handling general boundary conditions.

show abstract

Section: Test No 3: a Heterogeneity Testsupporting

confidence: 71%

Section: Test No 3: a Heterogeneity Testmentioning

confidence: 99%

See 1 more Smart Citation

A new mimetic scheme for the acoustic wave equation

Solano-Feo

Guevara-Jordan

Rojas

et al. 2016

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…Considering the stability condition of the finite-difference method, we can replace the coefficient of q 2 p/qz 2 in Equation 23 by s/(1+s), where s = vDt/Dx, Dt is the temporal interval, and Dx is the spatial interval in x-direction; thus, Equation 23 becomes (Reynolds, 1978) …”

Section: Reynolds Boundarymentioning

confidence: 99%

“…Two main kinds of solutions have been proposed for this purpose: absorbing boundary conditions (ABCs) (e.g. Clayton and Engquist, 1977;Reynolds, 1978;Liao et al, 1984;Higdon, 1986;Higdon, 1991) and absorbing boundary layers (e.g. Cerjan et al, 1985;Kosloff and Kosloff, 1986;Compani-Tabrizi, 1986, Sochacki et al, 1987Bérenger, 1994;Komatitsch and Martin, 2007;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

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