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Comparison between the nearly perfectly matched layer and unsplit convolutional perfectly matched layer methods using acoustic wave modeling
JINGYI CHEN1,2 ,
CHAOYING ZHANG3 ,
RALPH PHILLIP BORDING4
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1
Department of Geosciences, College of Engineering and Natural Sciences, University of Tulsa. Tulsa, OK 74104, U.S.A. jingyi-chen@utulsa.edu,
3
Department of Geological Sciences, University of Saskatchewan, Saskatoon, SK, Canada S7N 5E2. chaoying.zhang@usask.ca,
4
Computer Science Chair, Alabama A&M University, Normal, Alabama 35762, U.S.A. phil.bording@aamu.edu,
JSE 2010, 19(2), 173–185;
Submitted: 5 July 2009 | Accepted: 7 December 2009 | Published: 1 April 2010
© 2010 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Chen, J., Zhang, C. and Bording, R.P., 2010. Comparison between the nearly perfectly matched layer and unsplit convolutional perfectly matched layer methods using acoustic wave modeling. Journal of Seismic Exploration, 19: 173-185. The unsplit convolutional perfectly matched layer (CPML) and nearly perfectly matched layer (NPML) methods both have been proven to be very efficient algorithms for eliminating artificial reflections from the edges of the synthetic seismic wave models. Their absorbing performance and efficiency have been studied in separate works in several papers. Obviously, if we provide numerical comparisons between CPML and NPML in seismic modeling, it is very helpful to understand their performances and differences. In this paper, we will carry out these comparisons using 2D acoustic wave modeling codes with staggered-grid finite-difference schemes. For the implementation of the finite-difference operator, we employ fourth-order accuracy methods in space and second-order accuracy methods in time. In the model tests, we demonstrate that NPML has the same absorbing performance as CPML, with some very minor differences. We suggest that more analysis will be needed to study how these methods perform in the wide varieties of complex media that are typically used in seismic modeling.
Keywords
nearly perfectly matched layer
unsplit convolutional perfectly matched layer
acoustic modeling
staggered-grid finite-difference
References
- Bérenger, J., 1994. A perfectly matched layer for the absorption of electromagnetic waves. J.Computat. Phys., 114: 185-200.
- Bérenger, J., 2004. On the reflection from Cummer’s nearly perfectly matched layer. A perfectlymatched layer for the absorption of electromagnetic waves. IEEE Microw. Wirel. Compon.Lett., 14: 334-336.
- Bording, R.P., 2004. Finite difference modeling-nearly optimal sponge boundary conditions.
- Expanded Abstr., 74th Ann. Internat. SEG Mtg., Denver: 1921-1924.
- Carcione, J.M., 1996. Wave propagation in anisotropic, saturated porous media: plane wave theoryand numerical simulation. J. Acoust. Soc. Am., 99: 2655-2666.
- Carcione, J.M., 1998. Viscoelastic effective rheologies for modeling wave propagation in porousmedia. Geophys. Prosp., 46: 249-270.
- Cerjan, C., Kosloff, D., Kosloff, R. and Reshef, M., 1985. A nonreflecting boundary condition fordiscrete acoustic and elastic wave equations. Geophysics, 50: 705-708.
- Chen, J., Bording, R., Liu, E., Zhang, Z. and Badal, J., 2010. The application of the nearlyoptimal sponge boundary conditions for seismic wave propagation in poroelastic media. J.Seismic Explor., 19: 1-19.
- Clayton, R. and Engquist, B., 1977. Absorbing boundary conditions for acoustic and elastic waveequations. Bull. Seismol. Soc. Am., 67: 1529-1540.
- Collino, F. and Tsogka, C., 2001. Application of the PML absorbing layer model to the linearelastodynamic problem in anisotropic heterogeneous media. Geophysics, 66: 294-307.
- Cummer, S.A., 2003. A simple, nearly perfectly matched layer for general electromagnetic media.IEEE Microw. Wirel. Compon. Lett., 13: 137-140.
- Dai, N., Vafidis, A. and Kanasewich, E.R., 1995. Wave propagation in heterogeneous, porousmedia: A velocity-stress, finite-difference method. Geophysics, 60: 327-340.
- Dong, L., She, D., Guan, L. and Ma, Z., 2005. An eigenvalue decomposition method to constructabsorbing boundary conditions for acoustic and elastic wave equations. J. Geophys. Engin.,2: 192-198.
- Faria, E.L. and Stoffa, P.L., 1994. Finite-difference modeling in transversely isotropic media.Geophysics, 59: 282-289.
- Fokkema, J.T. and van den Berg P.M., 1993. Seismic applications of acoustic reciprocity. ElsevierScience Publishers, Amsterdam.
- Guddati, M.N. and Lim, K.W., 2006. Continued fraction absorbing boundary conditions for convexpolygonal domains. Internat. J. Numer. Meth. Engin., 66: 949-977.
- Hassanzadeh, S., 1991. Acoustic modeling in fluid saturated porous media. Geophysics, 56:424-435,
- Higdon, R.L., 1991. Absorbing boundary conditions for elastic waves. Geophysics, 56: 231-241.
- Hu, W. and Cummer, S.A., 2004. The nearly perfectly matched layer is a perfectly matched layer.IEEE Antenn. Wirel. Propag. Lett., 3: 137-140.
- Hu, W. and Cummer, S.A., 2006. An FDTD model for low and high altitude lightning-generated
- EM fields. IEEE Transact. Antenn. Propag., 54: 1513-1522.
- Hu, W., Abubakar, A. and Habashy, T.M., 2007. Application of the nearly perfectly matched layerin acoustic wave modeling. Geophysics, 72: 169-175.
- Komatitsch, D. and Martin, R., 2007. An unsplit convolutional perfectly matched layer improvedat grazing incidence for the seismic wave equation. Geophysics, 72: SM155-SM167.
- Kuzuoglu, M. and Mittra, R., 1996. Frequency dependence of the constitutive parameters of causalperfectly matched anisotropic absorbers. IEEE Microw. Guided Wave Lett., 6: 447-449.
- Luebbers, R.J. and Hunsberger, F., 1992. FDTD for Nth-order dispersive media. IEEE Transact.Antenn. Propag., 40: 1297-1301.
- Madariaga, R., 1976. Dynamics of an expanding circular fault. Bull. Seismmol. Soc. Am., 65:163-182.COMPARISON BETWEEN NPML AND CPML 185
- Martin, R., Komatitsch, D. and Ezziani, A., 2008. An unsplit convolutional perfectly matched layerimproved at grazing incidence for seismic wave propagation in poroelastic media.Geophysics, 73: T51-T61.
- Mittet, R., 2002. Free-surface boundary conditions for elastic staggered-grid modeling schemes.Geophysics, 67: 1616-1623.
- Moczo, P., Kristek, J. and Halada, L., 2000. 3D fourth-order staggered-grid finite-differenceschemes: Stability and Grid dispersion. Bull. Seismol. Soc. Am., 90: 587-603.
- Quarteroni, A., Tagliani, A. and Zampieri, E., 1998. Generalized Galerkin approximations of elasticwaves with absorbing boundary conditions. Comput. Meth. Appl. Mechan. Engin., 163:323-341.
- Roden, J.A. and Gedney, S.D., 2000. Convolutional PML (CPML): an efficient FDTDimplementation of the CFS-PML for arbitrary media. Microw. Optic. Technol. Lett., 27:334-339.
- Sheen, D.H., Tuncay, K., Baag, C.E. and Ortoleva, P.J., 2006. Parallel implementation of avelocity-stress staggered-grid finite-difference method for 2-D poroelastic wave propagation.Comput. Geoscienc., 32: 1182-1191.
- Virieux, J., 1986. P-SV wave propagation in heterogeneous media: velocity-stress finite-differencemethod. Geophysics, 51: 889-901.
- Yao, Z. and Margrave, G.F., 2000. Elastic wavefield modeling in 3D by fourth-order staggered gridfinite difference technique. CREWES Research Report 12.
- Zeng, Y.Q. and Liu, Q.H., 2001. A staggered-grid finite-difference method with perfectly matchedlayers for poroelastic wave equations. J. Acoust. Soc. Am., 109: 2571-2580.
