ARTICLE

Nearly perfectly matched layer boundary condition for second-order anisotropic acoustic wave equations

CAN OZSOY* JINGYI CHEN1 QUNSHAN ZHANG2 JIANGUO ZHAO3 GULSAH METIN1,*
Show Less
1 Department of Geosciences, The University of Tulsa, Tulsa, OK 74104, U.S.A.,
2 Repsol Service Company, The Woodlands, Texas 77380, U.S.A.,
3 College of Geophysics and Information Engineering, China University of Petroleum, Beijing 102249, P.R. China.,
JSE 2013, 22(5), 489–500;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 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

Ozsoy, C., Chen, J., Zhang, Q., Zhao, J. and Metin, G., 2013. Nearly perfectly matched layer boundary condition for second-order anisotropic acoustic wave equations. Journal of Seismic Exploration, 22: 489-500. During the numerical simulation of seismic wave propagation, the artificial layers are used at the computational boundaries to truncate the unbounded media which cause the unwanted reflections. In this study, the validity of the nearly perfectly matched layer as an absorbing layer, which has proven to be very efficient for first-order acoustic and elastic wave equations in stress and velocity, is detailed investigated to suppress those spurious reflections for second-order anisotropic acoustic wave equations. The numerical test results show that the nearly perfectly matched layer has a significant performance to absorb the outgoing waves at the model edges.

Keywords
nearly perfectly matched layer
second-order
anisotropic
acoustic equations
numerical modeling
References
  1. Alkhalifah, T., 2000. An acoustic wave equation for anisotropic media. Geophysics, 65: 1239-1250.
  2. Bérenger, J., 1994. A perfectly matched layer for the absorption of electromagnetic waves. J.
  3. Computat. Phys., 114: 185-200.
  4. Chen, J. and Zhao, J., 2011. Application of the nearly perfectly matched layer to seismic-wave
  5. propagation modeling in elastic anisotropic media. Bull. Seismol. Soc. Am., 101: 2866-2871.
  6. Chen, J., 2012. Nearly perfectly matched layer method for seismic wave propagation in poroelastic
  7. media. Can. J. Explor. Geophys., 37: 24-29.
  8. Collino, F. and Tsogka, C., 2001. Application of the PML absorbing layer model to the linear
  9. elastodynamic problem in anisotropic heterogeneous media. Geophysics, 66: 294-307.
  10. Courant, R., Friedrichs, K.O. and Lewy, H., 1928. Ueber die partiellen differenzengleichungen der
  11. mathematischen physik. Mathemat. Annalen, 100: 32-74.
  12. Cummer, S.A., 2003. A simple, nearly perfectly matched layer for general electromagnetic media.
  13. IEEE Microwave Wirel. Compon. Lett., 13: 137-140.
  14. Du, X., Fletcher, R.P. and Fowler, P.J., 2008. A new pseudo-acoustic wave equation for VTI
  15. media. Extended Abstr., 70th EAGE Conf., Rome: H033.
  16. Helbig, K., 1983. Elliptical anisotropy - Its significance and meaning. Geophysics, 48: 825-832.
  17. Hastings, F.D., Schneider, J.B. and Broschat, S.L., 1996. Application of the perfectly matched
  18. layer (PML) absorbing boundary condition to elastic wave propagation. J. Acoust. Soc. Am.,
  19. 100: 3061-3069.
  20. Hu, W., Abubakar, A. and Habashy, T., 2007. Application of the nearly perfectly matched layer
  21. in acoustic wave modeling. Geophysics, 72: 169-175.
  22. Kelly, K.R., Ward, R.W., Treitel, S. and Alford, R.M., 1976. Synthetic seismograms: A
  23. finite-difference approach. Geophysics, 41: 2-27.
  24. Komatitsch, D. and Tromp, J., 2003. A Perfectly Matched Layer (PML) absorbing condition for
  25. the second-order elastic wave equation. Geophys. J. Internat., 154: 146-153.
  26. McGarry, R. and Moghaddom, P., 2009. NPML boundary conditions for second-order wave
  27. equations. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston: 3590-3594.
  28. Metin, G., Chen, J. and Ozsoy, C., 2013. Application of nearly perfectly matched layer with
  29. second-order acoustic equations in seismic numerical modeling. J. Geol. Geosci., 2: 120.
  30. doi: 10.4172/2329-6755. 1000120. :
  31. Thomsen, L., 1986. Weak elastic anisotropy. Geophysics, 51: 1954-1966.
  32. Tsvankin, I., Gaiser, J., Grechka, V., van der Baan, M. and Thomsen, L., 2010. Seismic
  33. anisotropy in exploration and reservoir characterization: An overview. Geophysics, 75: A15-
  34. A29.
  35. Zeng, Y., He, J. and Liu, Q., 2001. The application of the perfectly matched layer in numerical
  36. modeling of wave propagation in poroelastic media. Geophysics, 66: 1258-1266.
  37. Zhou, H., Zhang, G. and Bloor, R., 2006. An anisotropic acoustic wave equation for VTI media.
  38. Extended Abstr., 68th EAGE Conf., Vienna: H033.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing