1887
Volume 45, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

A curvilinear-grid perfectly matched layer (PML) absorbing boundary condition for the second-order seismic acoustic wave equation is presented in this paper. The rectangular grids are transformed into curvilinear grids by using a mathematical mapping to fit the curvilinear boundary, and the original wave equation is reformulated under the curvilinear coordinate system. Based on the reformulated wave equation, theoretical expressions and analysis of the curvilinear-grid PML are given. Furthermore, PML model 1 with symmetric form and PML model 2 with asymmetric form are derived from the same acoustic wave equation. By combination with the finite difference (FD) method, these two models are applied to seismic wave modelling with surface topography. The results show that the absorption effect of these two models discretised by the same second-order time difference and second-order space difference are different, and the symmetric-form PML yields better modelling results than the asymmetric-form.

© 2014 ASEG
Loading

Article metrics loading...

/content/journals/10.1071/EG13066
2014-06-01
2026-01-18

  • From This Site

    /content/journals/10.1071/EG13066
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Appelö D. Kreiss G. 2006 A new absorbing layer for elastic waves: Journal of Computational Physics 215 642 660 10.1016/j.jcp.2005.11.006
    https://doi.org/10.1016/j.jcp.2005.11.006 [Google Scholar]
  2. Appelö D. Petersson N. A. 2009 A stable finite difference method for the elastic wave equation on complex geometries with free surfaces: Communications in Computational Physics 5 84 107
    [Google Scholar]
  3. Basu U. 2009 Explicit finite element perfectly matched layer for transient three-dimensional elastic waves: International Journal for Numerical Methods in Engineering 77 151 176 10.1002/nme.2397
    https://doi.org/10.1002/nme.2397 [Google Scholar]
  4. Bérenger J. P. 1994 A perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics 114 185 200 10.1006/jcph.1994.1159
    https://doi.org/10.1006/jcph.1994.1159 [Google Scholar]
  5. Bérenger J. P. 1996 Three-dimensional perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics 127 363 379 10.1006/jcph.1996.0181
    https://doi.org/10.1006/jcph.1996.0181 [Google Scholar]
  6. Chen J. Y. 2011 Application of the nearly perfectly matched layer for seismic wave propagation in 2D homogeneous isotropic media: Geophysical Prospecting 59 662 672 10.1111/j.1365‑2478.2011.00949.x
    https://doi.org/10.1111/j.1365-2478.2011.00949.x [Google Scholar]
  7. Chew W. Liu Q. 1996 Perfectly matched layers for elastodynamics: a new absorbing boundary condition: Journal of Computational Acoustics 4 341 359 10.1142/S0218396X96000118
    https://doi.org/10.1142/S0218396X96000118 [Google Scholar]
  8. Chew W. C. Weedon W. H. 1994 A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates: Microwave and Optical Technology Letters 7 599 604 10.1002/mop.4650071304
    https://doi.org/10.1002/mop.4650071304 [Google Scholar]
  9. Collino F. Tsogka C. 2001 Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media: Geophysics 66 294 307 10.1190/1.1444908
    https://doi.org/10.1190/1.1444908 [Google Scholar]
  10. Cummer S. A. 2003 A simple, nearly perfectly matched layer for general electromagnetic media: IEEE Microwave and Wireless Components Letters 13 128 130 10.1109/LMWC.2003.810124
    https://doi.org/10.1109/LMWC.2003.810124 [Google Scholar]
  11. Festa G. Vilotte J. P. 2005 The Newmark scheme as velocity–stress time-staggering: an effcient PML implementation for spectral element simulation of elastodynamics: Geophysical Journal International 161 789 812 10.1111/j.1365‑246X.2005.02601.x
    https://doi.org/10.1111/j.1365-246X.2005.02601.x [Google Scholar]
  12. Fornberg B. 1988 The pseudospectral method: accurate representation of interfaces in elastic wave calculations: Geophysics 53 625 637 10.1190/1.1442497
    https://doi.org/10.1190/1.1442497 [Google Scholar]
  13. Gao H. Zhang J. 2008 Implementation of perfectly matched layers in an arbitrary geometric boundary for elastic wave modeling: Geophysical Journal International 174 1029 1036 10.1111/j.1365‑246X.2008.03883.x
    https://doi.org/10.1111/j.1365-246X.2008.03883.x [Google Scholar]
  14. Hastings F. D. Schneider J. B. Broschat S. L. 1996 Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation: The Journal of the Acoustical Society of America 100 3061 3069 10.1121/1.417118
    https://doi.org/10.1121/1.417118 [Google Scholar]
  15. Hestholm S. O. Ruud B. O. 1998 3-D finite difference elastic wave modeling including surface topography: Geophysics 63 613 622 10.1190/1.1444360
    https://doi.org/10.1190/1.1444360 [Google Scholar]
  16. Komatitsch D. Martin R. 2007 An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation: Geophysics 72 SM155 SM167 10.1190/1.2757586
    https://doi.org/10.1190/1.2757586 [Google Scholar]
  17. Komatitsch D. Tromp J. 2003 A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation: Geophysical Journal International 154 146 153 10.1046/j.1365‑246X.2003.01950.x
    https://doi.org/10.1046/j.1365-246X.2003.01950.x [Google Scholar]
  18. Li Y. Bou Matar O. 2010 Convolutional perfectly matched layer for elastic second-order wave equation: The Journal of the Acoustical Society of America 127 1318 1327 10.1121/1.3290999
    https://doi.org/10.1121/1.3290999 [Google Scholar]
  19. Marcinkovich C. Olsen K. 2003 On the implementation of perfectly matched layers in a three-dimensional fourth-order velocity-stress finite difference scheme: Journal of Geophysical Research 108 2276 2292 10.1029/2002JB002235
    https://doi.org/10.1029/2002JB002235 [Google Scholar]
  20. Matzen R. 2011 An efficient finite element time-domain formulation for the elastic second-order wave equation: a non-split complex frequency shifted convolutional PML: International Journal for Numerical Methods in Engineering 88 951 973 10.1002/nme.3205
    https://doi.org/10.1002/nme.3205 [Google Scholar]
  21. Nakata N. Tsuji T. Matsuoka T. 2011 Acceleration of computation speed for elastic wave simulation using a Graphic Processing Unit: Exploration Geophysics 42 98 104 10.1071/EG10039
    https://doi.org/10.1071/EG10039 [Google Scholar]
  22. Oishi Y. Piggott M. D. Maeda T. Kramer S. C. Collins G. S. Tsushima H. Furumura T. 2013 Three-dimensional tsunami propagation simulations using an unstructured mesh finite element model: Journal of Geophysical Research: Solid Earth 118 2998 3018 10.1002/jgrb.50225
    https://doi.org/10.1002/jgrb.50225 [Google Scholar]
  23. Roden J. A. Gedney S. D. 2000 Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media: Microwave and Optical Technology Letters 27 334 339 10.1002/1098‑2760(20001205)27:5<334::AID‑MOP14>3.0.CO;2‑A
    https://doi.org/10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A [Google Scholar]
  24. Tarrass I. Giraud L. Thore P. 2011 New curvilinear scheme for elastic wave propagation in presence of curved topography: Geophysical Prospecting 59 889 906
    [Google Scholar]
  25. Tessmer E. Kosloff D. 1994 3-D elastic modeling with surface topography by a Chebyshev spectral method: Geophysics 59 464 473 10.1190/1.1443608
    https://doi.org/10.1190/1.1443608 [Google Scholar]
  26. Wang T. Tang X. 2003 Finite-difference modeling of elastic wave propagation: a nonsplitting perfectly matched layer approach: Geophysics 68 1749 1755 10.1190/1.1620648
    https://doi.org/10.1190/1.1620648 [Google Scholar]
  27. Xiao L. Z. Liu Y. 2013 Geophysical modeling: Journal of Geophysics and Engineering 10 1 2 10.1088/1742‑2132/10/5/050201
    https://doi.org/10.1088/1742-2132/10/5/050201 [Google Scholar]
  28. Yuan S. Y. Wang S. X. Tian N. 2009 Min Fresnel zone relative to large offsets: Oil Geophysical Prospecting 44 387 392
    [Google Scholar]
  29. Yuan, S. Y., Wang, S. X., He, Y. X., and Tian, N., 2011, Second-order wave equation modeling in time domain with surface topography using embedded boundary method and PML: 73rd Annual International Meeting, EAGE, Expanded Abstracts, 10151.
  30. Zeng Y. Q. He J. Q. Liu Q. H. 2001 The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Geophysics 66 1258 1266 10.1190/1.1487073
    https://doi.org/10.1190/1.1487073 [Google Scholar]
  31. Zeng C. Xia J. H. Miller R. D. Tsoflias G. P. 2011 Application of the multiaxial perfectly matched layer (M-PML) to near-surface seismic modeling with Rayleigh waves: Geophysics 76 T43 T52 10.1190/1.3560019
    https://doi.org/10.1190/1.3560019 [Google Scholar]
  32. Zhang J. Gao H. 2011 Irregular perfectly matched layers for 3D elastic wave modeling: Geophysics 76 T27 T36 10.1190/1.3533999
    https://doi.org/10.1190/1.3533999 [Google Scholar]
  33. Zhang J. Liu T. 1999 P-SV-wave propagation in heterogeneous media: grid method: Geophysical Journal International 136 431 438 10.1111/j.1365‑246X.1999.tb07129.x
    https://doi.org/10.1111/j.1365-246X.1999.tb07129.x [Google Scholar]
  34. Zhang W. Shen Y. 2010 Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling: Geophysics 75 T141 T154 10.1190/1.3463431
    https://doi.org/10.1190/1.3463431 [Google Scholar]
  35. Zhou H. Wang S. X. Li G. F. Shen J. S. 2010 Analysis of complicated structure seismic wave fields: Applied Geophysics 7 185 192 10.1007/s11770‑010‑0243‑3
    https://doi.org/10.1007/s11770-010-0243-3 [Google Scholar]
/content/journals/10.1071/EG13066
Loading
Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation
Exploration Geophysics 45, 94 (2014); https://doi.org/10.1071/EG13066
/content/journals/10.1071/EG13066
/content/journals/10.1071/EG13066
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): acoustic wave equation; finite difference; perfectly matched layer; seismic modeling; surface topography

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error