Acta Geophysica

, Volume 64, Issue 5, pp 1605–1625 | Cite as

Implementation of Elastic Prestack Reverse-Time Migration Using an Efficient Finite-Difference Scheme

  • Hongyong Yan
  • Lei Yang
  • Hengchang Dai
  • Xiang-Yang Li
Open Access


Elastic reverse-time migration (RTM) can reflect the underground elastic information more comprehensively than single-component Pwave migration. One of the most important requirements of elastic RTM is to solve wave equations. The imaging accuracy and efficiency of RTM depends heavily on the algorithms used for solving wave equations. In this paper, we propose an efficient staggered-grid finite-difference (SFD) scheme based on a sampling approximation method with adaptive variable difference operator lengths to implement elastic prestack RTM. Numerical dispersion analysis and wavefield extrapolation results show that the sampling approximation SFD scheme has greater accuracy than the conventional Taylor-series expansion SFD scheme. We also test the elastic RTM algorithm on theoretical models and a field data set, respectively. Experiments presented demonstrate that elastic RTM using the proposed SFD scheme can generate better images than that using the Taylor-series expansion SFD scheme, particularly for PS images. FurH. thermore, the application of adaptive variable difference operator lengths can effectively improve the computational efficiency of elastic RTM.

Key words

seismic imaging elastic wave wavefield extrapolation finite-difference 


  1. Balch, A.H., and C. Erdemir (1994), Sign-change correction for prestack migration of P-S converted wave reflections, Geophys. Prospect. 42, 6, 637–663, DOI: 10.1111/j.1365-2478.1994.tb00233.x.CrossRefGoogle Scholar
  2. Baysal, E., D.D. Kosloff, and J.W.C. Sherwood (1983), Reverse time migration, Geophysics 48, 11, 1514–1524, DOI: 10.1190/1.1441434.CrossRefGoogle Scholar
  3. Bérenger, J.P. (1994), A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114, 2, 185–200, DOI: 10.1006/jcph.1994.1159.CrossRefGoogle Scholar
  4. Chang, W.F., and G.A. McMechan (1987), Elastic reverse-time migration, Geophysics 52, 10, 1365–1375, DOI: 10.1190/1.1442249.CrossRefGoogle Scholar
  5. Chang, W.F., and G.A. McMechan (1994), 3D elastic prestack reverse-time depth migration, Geophysics 59, 4, 597–609, DOI: 10.1190/1.1443620.CrossRefGoogle Scholar
  6. Chung, W., S. Pyun, H.S. Bae, C. Shin, and K.J. Marfurt (2012), Implementation of elastic reverse-time migration using wavefield separation in the frequency domain, Geophys. J. Int. 189, 3, 1611–1625, DOI: 10.1111/j.1365-246X.2012.05431.x.CrossRefGoogle Scholar
  7. Dablain, M.A. (1986), The application of high-order differencing to the scalar wave equation, Geophysics 51, 1, 54–66, DOI: 10.1190/1.1442040.CrossRefGoogle Scholar
  8. Dellinger, J., and J. Etgen (1990), Wave-field separation in two-dimensional anisotropic media, Geophysics 55, 7, 914–919, DOI: 10.1190/1.1442906.CrossRefGoogle Scholar
  9. Dong, L.G., Z.T. Ma, J.Z. Cao, H.Z. Wang, J.H. Gao, B. Lei, and S.Y. Xu (2000), A staggered-grid high-order difference method of one-order elastic wave equation, Chin. J. Geophys. 43, 411–419 (in Chinese).Google Scholar
  10. Du, Q., Y. Zhu, and J. Ba (2012), Polarity reversal correction for elastic reverse time migration, Geophysics 77, 2, S31–S41, DOI: 10.1190/geo2011–0348.1.CrossRefGoogle Scholar
  11. Du, Q., X. Gong, M. Zhang, Y. Zhu, and G. Fang (2014), 3D PS-wave imaging with elastic reverse-time migration, Geophysics 79, 5, S173–S184, DOI: 10.1190/geo2013-0253.1.CrossRefGoogle Scholar
  12. Gray, S.H., J. Etgen, J. Dellinger, and D. Whitmore (2001), Seismic migration problems and solutions, Geophysics 66, 5, 1622–1640, DOI: 10.1190/1.1487107.CrossRefGoogle Scholar
  13. Hokstad, K. (2000), Multicomponent Kirchhoff migration, Geophysics 65, 3, 861–873, DOI: 10.1190/1.1444783.CrossRefGoogle Scholar
  14. Kindelan, M., A. Kamel, and P. Sguazzero (1990), On the construction and efficiency of staggered numerical differentiators for the wave equation, Geophysics 55, 1, 107–110, DOI: 10.1190/1.1442763.CrossRefGoogle Scholar
  15. Kuo, J.T., and T.F. Dai (1984), Kirchhoff elastic wave migration for the case of noncoincident source and receiver, Geophysics 49, 8, 1223–1238, DOI: 10.1190/1.1441751.CrossRefGoogle Scholar
  16. Li, J., D. Yang, and F. Liu (2013), An efficient reverse time migration method using local nearly analytic discrete operator, Geophysics 78, 1, S15–S23, DOI: 10.1190/geo2012-0247.1.CrossRefGoogle Scholar
  17. Li, J., M. Fehler, D. Yang, and X. Huang (2015), 3D weak-dispersion reverse time migration using a stereo-modeling operator, Geophysics 80, 1, S19–S30, DOI: 10.1190/geo2013-0472.1.CrossRefGoogle Scholar
  18. Liu, F., G. Zhang, S.A. Morton, and J.P. Leveille (2009), An optimized wave equation for seismic modeling and reverse time migration, Geophysics 74, 6, WCA153–WCA158, DOI: 10.1190/1.3223678.CrossRefGoogle Scholar
  19. Liu, Y. (2014), Optimal staggered-grid finite-difference schemes based on leastsquares for wave equation modeling, Geophys. J. Int. 197, 2, 1033–1047, DOI: 10.1093/gji/ggu032.CrossRefGoogle Scholar
  20. Liu, Y., and M.K. Sen (2009), An implicit staggered-grid finite-difference method for seismic modeling, Geophys. J. Int. 179, 1, 459–474, DOI: 10.1111/j.1365-246X.2009.04305.x.CrossRefGoogle Scholar
  21. Liu, Y., and M.K. Sen (2011a), Finite-difference modeling with adaptive variablelength spatial operators, Geophysics 76, 4, T79–T89, DOI: 10.1190/1.3587223.CrossRefGoogle Scholar
  22. Liu, Y., and M.K. Sen (2011b), Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes, Bull. Seismol. Soc. Am. 101, 1, 141–159, DOI: 10.1785/0120100041.CrossRefGoogle Scholar
  23. Pei, Z. (2004), Numerical modeling using staggered-grid high order finite difference of elastic wave equation on arbitrary relief surface, Oil Geophys. Prospect. 39, 629–634 (in Chinese).Google Scholar
  24. Sun, R., and G.A. McMechan (2001), Scalar reverse-time depth migration of prestack elastic seismic data, Geophysics 66, 5, 1519–1527, DOI: 10.1190/1.1487098.CrossRefGoogle Scholar
  25. Sun, R., G.A. McMechan, and H.-H. Chuang (2011), Amplitude balancing in separating P- and S-waves in 2D and 3D elastic seismic data, Geophysics 76, 3, S103–S113, DOI: 10.1190/1.3555529.CrossRefGoogle Scholar
  26. Virieux, J. (1986), P-SV wave propagation in heterogeneous media: Velocity stress finite difference method, Geophysics 51, 4, 889–901, DOI: 10.1190/1.1442147.CrossRefGoogle Scholar
  27. Whitmore, D. (1983), Iterative depth migration by backward time propagation. In: 53rd Annual International Meeting, SEG, Expanded Abstracts, 382–385.Google Scholar
  28. Yan, H., Y. Liu, and H. Liu (2013), Elastic prestack reverse-time migration using the time-space domain high-order staggered-grid finite-difference method. In: 83rd Annual International Meeting, SEG, Expanded Abstracts, 4005–4009.Google Scholar
  29. Yan, H., L. Yang, and H. Liu (2015), Acoustic reverse-time migration using optimal staggered-grid finite-difference operator based on least squares, Acta Geophys. 63, 3, 715–734, DOI: 10.2478/s11600-014-0259-9.CrossRefGoogle Scholar
  30. Yan, J., and P. Sava (2008), Isotropic angle-domain elastic reverse-time migration, Geophysics 73, 6, S229–S239, DOI: 10.1190/1.2981241.CrossRefGoogle Scholar
  31. Yan, R., and X.B. Xie (2012), An angle-domain imaging condition for elastic reverse time migration and its application to angle gather extraction, Geophysics 77, 5, S105–S115, DOI: 10.1190/geo2011-0455.1.CrossRefGoogle Scholar
  32. Yang, L., H. Yan, and H. Liu (2014), Least squares staggered-grid finite-difference for elastic wave modeling, Explor. Geophys. 45, 4, 255–260, DOI: 10.1071/EG13087.CrossRefGoogle Scholar
  33. Yang, L., H. Yan, and H. Liu (2015), Optimal rotated staggered-grid finitedifference schemes for elastic wave modeling in TTI media, J. Appl. Geophys. 122, 40–52, DOI: 10.1016/j.jappgeo.2015.08.007.CrossRefGoogle Scholar
  34. Zhang, Y., and J. Sun (2009), Practical issues of reverse time migration: True amplitude gathers, noise removal and harmonic-source encoding, First Break 26, 19–25.Google Scholar
  35. Zhou, H., and G. Zhang (2011), Prefactored optimized compact finite difference schemes for second spatial derivatives, Geophysics 76, 5, WB87–WB95, DOI: 10.1190/geo2011-0048.1CrossRefGoogle Scholar

Copyright information

© Yan et al. 2016

Authors and Affiliations

  • Hongyong Yan
    • 1
    • 2
  • Lei Yang
    • 1
    • 3
  • Hengchang Dai
    • 2
  • Xiang-Yang Li
    • 2
  1. 1.Key Laboratory of Petroleum Resources Research, Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina
  2. 2.British Geological SurveyMurchison HouseEdinburghUK
  3. 3.University of Chinese Academy of SciencesBeijingChina

Personalised recommendations