A robust absorbing layer method for anisotropic seismic wave modeling

Journal of Computational Physics

Volumn 279, Issue , 2014, Pages 218-240

  Metivier L ^a,b   Brossier, R ^b   Labbe S ^a   Operto, S ^c   Virieux, J ^b  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITÉ GRENOBLE ALPES   (France)

^c UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Absorbing layers; Anisotropy; Hyperbolic problems; Perfectly matched layers; Seismic wave modeling

Indexed keywords

ACOUSTIC WAVE PROPAGATION; ACOUSTICS; ANISOTROPIC MEDIA; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; SEISMIC WAVES; SEISMOLOGY; SHEAR WAVES;

ABSORBING LAYERS; ANISOTROPIC MEDIUM; HYPERBOLIC PROBLEMS; LAYER METHOD; PERFECTLY MATCHED LAYER; S-WAVES; SEISMIC IMAGING; SEISMIC WAVE MODELING; WAVE PROPAGATION MODELING; WAVEFIELDS;

ANISOTROPY;

EID: 84907484558     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2014.09.007     Document Type: Article

References (48)

1. Abarbanel S., Gottlieb D., Hesthaven J.S. Long-time behavior of the perfectly matched layer equations in computational electromagnetics. J. Sci. Comput. 2002, 17:405-422.
2. Abarbanel S., Gottlieb D., Hesthaven J.S. Well-posed perfectly matched layers for advective acoustics. J. Comput. Phys. 1999, 154(2):266-283.
3. Alkhalifah T. Acoustic approximations for processing in transversely isotropic media. Geophysics 1998, 63:623-631.
4. Alkhalifah T. An acoustic wave equation for anisotropic media. Geophysics 2000, 65:1239-1250.
5. Appelö D., Kreiss G. A new absorbing layer for elastic waves. J. Comput. Phys. 2006, 215(2):642-660.
6. Basu U., Chopra A.K. Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation. Comput. Methods Appl. Mech. Eng. 2003, 192:1337-1375.
7. Becache E., Fauqueux S., Joly P. Stability of perfectly matched layers, group velocities and anisotropic waves. J. Comput. Phys. 2003, 188:399-433.
8. Becache E., Givoli D., Hagstrom T. High-order absorbing boundary conditions for anisotropic and convective wave equations. J. Comput. Phys. 2010, 229:1099-1129.
9. Bérenger J.-P. A perfectly matched layer for absorption of electromagnetic waves. J. Comput. Phys. 1994, 114:185-200.
10. Bérenger J.P. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 1996, 127(2):363-379.
11. Bermúdez A., Hervella-Nieto L., Prieto A., Rodríguez R. An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. J. Comput. Phys. 2007, 223(2):469-488.
12. Burridge R. Elastic waves in anisotropic media 1996, Schlumberger-Doll Research.
13. Cerjan C., KosloffD., KosloffR., Reshef M. A nonreflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics 1985, 50(4):2117-2131.
14. Clayton R., Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Seismol. Soc. Am. 1977, 67:1529-1540.
15. Collino F. High order absorbing boundary conditions for wave propagation models: straight line boundary and corner cases. Proceedings of the Second International Conference on Mathematical and Numerical Aspects of Wave Propagation 1993, 161-171. SIAM, Delaware.
16. Collino F., Tsogka C. Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 2001, 66:294-307.
17. Diaz J., Joly P. A time domain analysis of PML models in acoustics. Comput. Methods Appl. Mech. Eng. 2006, 195(29-32):3820-3853.
18. Dmitriev M.M., Lisitsa V.V. Application of M-PML reflectionless boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part I: reflectivity. Numer. Anal. Appl. 2011, 4(4):271-280.
19. Duveneck E., Bakker P.M. Stable P-wave modeling for reverse-time migration in tilted TI media. Geophysics 2011, 76(2):S65-S75.
20. Duveneck E., Milcik P., Bakker P.M., Perkins C. Acoustic VTI wave equations and their application for anisotropic reverse-time migration. SEG Technical Program Expanded Abstracts 2008, vol. 27 (1):2186-2190.
21. Engquist B., Majda A. Absorbing boundary conditions of the numerical simulation of waves. Math. Comput. 1977, 31:629-651.
22. Etgen J., Gray S.H., Zhang Y. An overview of depth imaging in exploration geophysics. Geophysics 2009, 74(6):WCA5-WCA17.
23. Givoli D. High-order non-reflecting boundary conditions without high-order derivatives. J. Comput. Phys. 2001, 170(2):8.
24. Grechka V., Zhang L., Rector J.W. Shear waves in acoustic anisotropic media. Geophysics 2004, 69:576-582.
25. Halpern L., Petit-Bergez S., Rauch J. The analysis of matched layers. Confluent. Math. 2011, 3(2):159-236.
26. Hastings F.D., Schneider J.B., Broschat S.L. Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation. J. Acoust. Soc. Am. 1996, 100:3061-3069.
27. Hesthaven J. On the analysis and construction of perfectly matched layers for the linearized Euler equations. J. Comput. Phys. 1998, 142:129-147.
28. Hu F.Q. On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer. J. Comput. Phys. 1996, 129(1):201-219.
29. Israeli M., Orszag S.A. Approximation of radiation boundary conditions. J. Comput. Phys. 1981, 41:115-135.
30. Komatitsch D., Martin R. An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics 2007, 72(5):SM155-SM167.
31. Komatitsch D., Tromp J. A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation. Geophys. J. Int. 2003, 154(1):146-153.
32. Kreiss H.O., Lorenz J. Initial-Boundary Value Problems and the Navier-Stokes Equations. Classics in Applied Mathematics 2004, vol. 47. SIAM.
33. Martin R., Komatitsch D. An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation. Geophys. J. Int. 2009, 179:333-344.
34. Martin R., Komatitsch D., Ezziani A. An unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave propagation in poroelastic media. Geophysics 2008, 73(4):51-61.
35. Métivier L., Brossier R., Operto S., Virieux J. A robust absorbing layer method for seismic wave simulation in anisotropic media. Expanded Abstracts 2014.
36. Métivier L., Brossier R., Operto S., Virieux J. SMART: robust absorbing layer and S-waves filtering for acoustic anisotropic wave simulation. Expanded Abstracts 2014.
37. Meza-Fajardo K.C., Papageorgiou A.S. A nonconvolutional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis. Bull. Seismol. Soc. Am. 2008, 98(4):1811-1836.
38. Operto S., Virieux J., Ribodetti A., Anderson J.E. Finite-difference frequency-domain modeling of visco-acoustic wave propagation in two-dimensional TTI media. Geophysics 2009, 74(5):T75-T95.
39. Qi Q., Geers T.L. Evaluation of the perfectly matched layer for computational acoustics. J. Comput. Phys. 1998, 139(1):166-183.
40. Saenger E.H., Gold N., Shapiro S.A. Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion 2000, 31:77-92.
41. Tago J., Métivier L., Virieux J. Smart layers: a simple and robust alternative to PML approaches for elastodynamics. Geophys. J. Int. 2014, 199(2):700-706. 10.1093/gji/ggu298.
42. Thomsen L.A. Weak elastic anisotropy. Geophysics 1986, 51:1954-1966.
43. Virieux J. P-SV wave propagation in heterogeneous media, velocity-stress finite difference method. Geophysics 1986, 51:889-901.
44. Virieux J., Operto S. An overview of full waveform inversion in exploration geophysics. Geophysics 2009, 74(6):WCC1-WCC26.
45. Yang D., Wang S., Zhang Z., Teng J. n-times absorbing boundary conditions for compact finite-difference modeling of acoustic and elastic wave propagation in the 2D TI medium. Bull. Seismol. Soc. Am. 2003, 93(6):2389-2401.
46. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas Propag. 1966, 14:302-307.
47. Zhang Y., Zhang H., Zhang G. A stable TTI reverse time migration and its implementation. Geophysics 2011, 76(3):WA3-WA11.
48. Zhou H., Zhang G., Bloor R. An anisotropic acoustic wave equation for modeling and migration in 2D TTI media. Expanded Abstracts - New Orleans 2006, vol. 25:194-198. Society of Exploration Geophysics.