AccScience Publishing / JSE / Article
Submit to JSE
Cite this article
2
Download
74
Views
Journal Browser
Volume | Year
Issue
Search
Forthcoming Issue
Current Issue
View All
News and Announcements
View All
ARTICLE

A multi-axial perfectly matched layer for finite-element time-domain simulation of anisotropic elastic wave propagation

HAIPENG LI1 ,  JINGYI CHEN2* ,  ZHENCONG ZHAO2 ,  JUNLUN LI1
Show Less
1 School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China.,
2 Seismic Anisotropy Group, Department of Geosciences, The University of Tulsa, Tulsa, OK 74104, U.S.A.,
JSE 2021, 30(2), 173–200;
Submitted: 7 January 2020 | Accepted: 27 December 2020 | Published: 1 April 2021
© 2021 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/ )
Download PDF
Cite
XML
Abstract

Li, H.P., Chen, J., Zhao, Z.C. and Li, J-L., 2021. A multi-axial perfectly matched layer for finite-element time-domain simulation of anisotropic elastic wave propagation. Journal of Seismic Exploration, 30: 173-200. In order to effectively suppress the spurious reflections from the truncated boundaries in seismic numerical modeling, various perfectly matched layer (PML) absorbing boundary conditions have been developed in the past decades. The multi-axial perfectly matched layer (M-PML) attenuates seismic waves in the PML domain depending on the wave propagation directions, which remains efficient even under the situation of grazing incidences. To take advantage of the finite-element method (FEM) in dealing with the complex subsurface structure and irregular topography, we develop a nonconvolutional split-field M-PML based on the second-order elastic wave formulation to simulate the finite-element time-domain seismic wave propagation in this paper. The proposed M-PML algorithm requires fewer splitting terms and less storage space compared to the second-order M-PML in the literature. Three numerical experiments are carried out to illustrate the stability and efficiency of the newly proposed M-PML when used in the finite-element anisotropic elastic wavefield simulation with an irregular topography.

Keywords
multi-axial perfectly matched layer
finite element
anisotropic elastic media
irregular free surface
References
  1. Aki, K. and Richards, P.G., 2002. Quantitative Seismology. W.H. Freeman & Co., SanFrancisco.
  2. Afanasiev, M., Boehm, C., van Driel, M., Krischer, L., Rietmann, M., May, D.A. and
  3. Fichtner, A., 2019. Modular and flexible spectral-element waveform modelling intwo and three dimensions. Geophys. J. Internat., 216: 1675-1692.
  4. Archer, G.C. and Whalen, T.M., 2005. Development of rotationally consistent diagonalmass matrices for plate and beam elements. Comput. Meth. Appl. Mechan.Engineer., 194: 675-689.
  5. Bao, H., Bielak, J., Ghattas, O., Kallivokas, L.F., O'Hallaron, D.R., Shewchuk, J.R. and
  6. Xu, J., 1998. Large-scale simulation of elastic wave propagation in heterogeneousmedia on parallel computers. Comput. Meth. App]. Mechan. Engineer., 152: 85-102.
  7. Bérenger, J.P., 1994. A perfectly matched layer for the absorption of electromagneticwaves. J. Computat. Phys., 114: 185-200.
  8. Bohlen, T. and Saenger, E.H., 2006. Accuracy of heterogeneous staggered-gridfinite-difference modeling of Rayleigh waves. Geophysics, 71(4), T109-T115.
  9. Cerjan, C., Kosloff, D., Kosloff, R. and Reshef, M., 1985. A nonreflecting boundarycondition for discrete acoustic and elastic wave equations. Geophysics, 50: 705-708.
  10. Chew, W.C. and Liu, Q.H., 1996. Perfectly matched layers for elastodynamics: a newabsorbing boundary condition. J. Computat. Acoust., 4: 341-359.
  11. Chew, W.C. and Weedon, W.H., 1994. A 3D perfectly matched medium from modified
  12. Maxwell's equations with stretched coordinates. Microw. Optic. Technol. Lett., 7:599-604.
  13. Collino, F. and Tsogka, C., 2001. Application of the perfectly matched absorbing layermodel to the linear elastodynamic problem in anisotropic heterogeneousmedia. Geophysics, 66: 294-307.
  14. Festa, G. and Vilotte, J.P., 2005. The Newmark scheme as velocity-stresstime-staggering: an efficient PML implementation for spectral element simulationsof elastodynamics. Geophys. J. Internat., 161: 789-812.
  15. Giraldo, F.X. and Taylor, M.A., 2006. A diagonal-mass-matrix triangular-spectral-element method based on cubature points. J. Engineer. Mathemat., 56: 307-322.
  16. Hesthaven, J.S., 1998. On the analysis and construction of perfectly matched layers forthe linearized Euler equations. J. Computat. Phys., 142: 129-147.
  17. Hesthaven, J.S. and Teng, C.H., 2000. Stable spectral methods on tetrahedralelements. SIAM J. Sci. Comput., 21: 2352-2380.
  18. Higdon, R.L., 1992. Absorbing boundary conditions for acoustic and elastic waves instratified media. J. Computat. Phys., 101: 386-418.
  19. Kane, C., Marsden, J.E., Ortiz, M. and West, M., 2000. Variational integrators and the
  20. Newmark algorithm for conservative and dissipative mechanical systems. Internat. J.Numer. Meth. Engineer., 49: 1295-1325.
  21. Komatitsch, D., Erlebacher, G., Gdddeke, D. and Michéa, D., 2010. High-orderfinite-element seismic wave propagation modeling with MPI on a large GPUcluster. J. Computat. Phys., 229: 7692-7714.
  22. Komatitsch, D. and Martin, R., 2007. An unsplit convolutional perfectly matched layerimproved at grazing incidence for the seismic wave equation. Geophysics, 72(5):SM155-SM167.
  23. Komatitsch, D. and Tromp, J., 1999. Introduction to the spectral element method forthree-dimensional seismic wave propagation. Geophys. J. Internat., 139: 806-822.
  24. Komatitsch, D., Barnes, C. and Tromp, J., 2000. Wave propagation near a fluid-solidinterface: A spectral-element approach. Geophysics, 65: 623-631.
  25. Komatitsch, D. and Tromp, J., 2003. A perfectly matched layer absorbing boundarycondition for the second-order seismic wave equation. Geophys. J. Internat., 154:146-153.
  26. Krysl, P. and Endres, L., 2005. Explicit Newmark/Verlet algorithm for time integrationof the rotational dynamics of rigid bodies. Internat. J. Numer. Meth. Engineer., 62:2154-2177.
  27. Kuzuoglu, M. and Mittra, R., 1996. Frequency dependence of the constitutive parametersof causal perfectly matched anisotropic absorbers. IEEE Microw. Guided WaveLett., 6: 447-449.
  28. Lan, H., Chen, J., Zhang, Z., Liu, Y., Zhao, J. and Shi, R., 2016.. Application of aperfectly matched layer in seismic wavefield simulation with an irregular freesurface. Geophys. Prosp., 64: 112-128.
  29. Lan, H. and Zhang, Z., 2011. Three-dimensional wave-field simulation in heterogeneoustransversely isotropic medium with irregular free surface. Bull. Seismol. Soc.Am., 101: 1354-1370.
  30. Li, Y. and Bou Matar, O., 2010. Convolutional perfectly matched layer for elasticsecond-order wave equation. J. Acoust. Soc. Am., 127: 1318-1327.
  31. Liu, S., Li, X., Wang, W. and Liu, Y., 2014a. A mixed-grid finite element method with
  32. PML absorbing boundary conditions for seismic wave modelling. J. Geophys.Engineer., 11: 055009.
  33. Liu, Y., Teng, J., Lan, H., Si, X., and Ma, X., 2014b. A comparative study of finiteelement and spectral element methods in seismic — wavefieldmodeling. Geophysics, 79(2): T91-T104.
  34. Lysmer, J. and Drake, L.A., 1972. A finite element method for seismology. Methods incomputational physics, 11, 181-216.
  35. Marfurt, K.J., 1984. Accuracy of finite-difference and finite-element modeling of thescalar and elastic wave equations. Geophysics, 49: 533-549.
  36. Meng, W. and Fu, L.Y., 2017. Seismic wavefield simulation by a modified finite elementmethod with a perfectly matched layer absorbing boundary. J. Geophys.Engineer., 14: 852-864.
  37. Meza-Fajardo, K.C. and Papageorgiou, A.S., 2008. A nonconvolutional, split-field,perfectly matched layer for wave propagation in isotropic and anisotropic elasticmedia: Stability analysis. Bull. Seismol. Soc. Am., 98: 1811-1836.
  38. Meza-Fajardo, K.C. and Papageorgiou, A.S., 2010. On the stability of anon-convolutional perfectly matched layer for isotropic elastic media. Soil Dynam.Earthq. Engineer., 30(3): 68-81.
  39. Meza-Fajardo, K.C. and Papageorgiou, A.S., 2012. Study of the accuracy of themultiaxial perfectly matched layer for the elastic-wave equation. Bull. Seismol. Soc.Am., 102: 2458-2467.
  40. Nataf, F., 2005. New constructions of perfectly matched layers for the linearized Eulerequations. Compt. Rend. Mathemat., 340: 775-778.
  41. Newmark, N.M., 1959. A Method of Computation for Structural Dynamics. AmericanSociety of Civil Engineers, Reston, VA.
  42. Nissen-Meyer, T., Fournier, A. and Dahlen, F.A., 2007. A two - dimensional spectral -element method for computing spherical-earth seismograms - I. Moment - tensorsource. Geophys. J. Internat., 168: 1067-1092.
  43. Padovani, E., Priolo, E. and Seriani, G., 1994. Low and high order finite element method:experience in seismic modeling. J. Computat. Acoust., 2: 371-422.
  44. Peng, C. and Tokséz, M.N., 1995. An optimal absorbing boundary condition for elasticwave modeling. Geophysics, 60: 296-301.
  45. Ping, P., Zhang, Y. and Xu, Y., 2014. A multiaxial perfectly matched layer (M-PML) forthe long-time simulation of elastic wave propagation in the second-order equations. J.Appl. Geophys., 101: 124-135.
  46. Matzen, R., 2011. An efficient finite element time-domain formulation for the elasticsecond-order wave equation: A non-split complex frequency shifted convolutional
  47. PML. Internat. J. Numer. Meth. Engineer., 88: 951-973.
  48. Richter, G.R., 1994. An explicit finite element method for the wave equation. Appl.Numer. Mathemat., 16: 65-80.
  49. Sochacki, J., Kubichek, R., George, J., Fletcher, W.R. and Smithson, S., 1987.
  50. Absorbing boundary conditions and surface waves. Geophysics, 52: 60-71.
  51. Stacey, R., 1988. Improved transparent boundary formulations for the elastic-waveequation. Bull. Seismol. Soc. Am., 78: 2089-2097.
  52. Teixeira, F.L. and Chew, W.C., 2000. Complex space approach to perfectly matchedlayers: a review and some new developments. Internat. J. Numer. Modell.: Electron.Netw., Devic. Fields, 13: 441-455.
  53. Thomsen, L. , 1986. Weak elastic anisotropy. Geophysics, 51: 1954-1966.
  54. West, M., Kane, C., Marsden, J.E. and Ortiz, M., 2000. Variational integrators, thenewmark scheme, and dissipative systems. In Equadiff 99 (In 2 Volumes):1009-1011.
  55. Wu, S.R., 2006. Lumped mass matrix in explicit finite element method for transientdynamics of elasticity. Comput. Meth. Appl. Mechan. Engineer., 195(44-47):5983-5994.
  56. Zeng, C., Xia, J., Miller, R.D. and Tsoflias, G.P., 2011. Application of the multiaxialperfectly matched layer (M-PML) to near-surface seismic modeling with Rayleighwaves. Geophysics, 76(3): T43-T52.
  57. Zhao, J.G. and Shi, R.Q., 2013. Perfectly matched layer-absorbing boundary conditionfor finite-element time-domain modeling of elastic wave equations. Appl.Geophys., 10: 323-336.
  58. Zhou, B., Greenhalgh, S., Liu, X., Bouzidi, Y., Riahi, M.K. and Al-Khaleel, M., 2019.
  59. Failures of the perfectly-matched layer method in frequency-domain seismic wavemodelling in elastic anisotropic media. Expanded Abstr., 89th Ann. Internat. SEGMtg., San Antonio: 3750-3754.
Share
Back to top
Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here
Accept