ARTICLE

Least-squares reverse time migration of pure qP-wave in anisotropic media using low-rank finite-difference

GUOCHAO GAO1 JINQIANG HUANG2* ZHENCHUN LI3
Show Less
1 Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille 13397, France.,
2 Resource and Environmental Engineering College,Guizhou University, Guiyang 550025, China.,
3 School of Geosciences, China University of Petroleum (East China), Qingdao 266580, P.R. China.,
JSE 2021, 30(2), 121–146;
Submitted: 11 December 2019 | Accepted: 20 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/ )
Abstract

The pseudo-acoustic least-squares reverse time migration (PA-LSRTM) is often used for imaging of anisotropic media. Due to acoustic approximation, it, however, shows severe instability in the forward simulation, strong quasi-SV (qSV) wave residual in the demigration record, and terrible numerical dispersion in tilted transversely isotropic (TTI) media. The low-rank finite-difference (LFD) approach can effectively overcome these problems, but existing research only focuses on forward modeling, and no examples are found in LSRTM. For the first time in this paper, we derive the pure qP- wave linearized forward modeling and migration operators in TTI media with the help of LFD. Then, we implement pure qP-wave least-squares reverse time migration (LFD- LSRTM) in the inversion scheme. To improve the inversion efficiency, the plane-wave encoding technique is used, and to increase its robustness, the prestack parameterization is adopted. Finally, we obtain the prestack plane-wave least-squares reverse time migration (LFD-Pre-PLSRTM). Examples demonstrate that our method provides significant advantages in imaging TTI media, yielding satisfactory results with less expensive computation and more stable convergence compared to PA-LSRTM. More importantly, the proposed method can successfully avoid troubles caused by the acoustic approximation, and reasonably allow errors in the parameter model and noise in the data, making it possible to deal with real data.

Keywords
anisotropy
least-squares migration
pure qP-wave
low-rank finite difference
inversion
References
  1. Alkhalifah, T., 1998. Acoustic approximations for processing in transversely isotropicmedia. Geophysics, 63: 623-631.
  2. Chen, K. and Sacchi, M.D., 2017. Elastic least-squares reverse time migration vialinearized elastic full-waveform inversion with pseudo-Hessian preconditioning.Geophysics, 82(5): 1-S358.
  3. Chu, C., Macy, B.K. and Anno, P.D., 2013. Pure acoustic wave propagation intransversely isotropic media by the pseudospectral method. Geophys. Prosp., 61:556-567.
  4. Dai, W. and Schuster, G.T., 2013. Plane-wave least-squares reverse-time migration.Geophysics, 78(4): S165-S177.
  5. Dai, W. and Schuster, J., 2009. Least-squares migration of simultaneous sources datawith a deblurring filter. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston:2990-2994.
  6. Dai, W., Fowler, P. and Schuster, G.T., 2012. Multi-source least-squares reverse timemigration. Geophys. Prosp., 60: 681-695.
  7. Dai, W., Wang, X. and Schuster, G.T., 2011. Least-squares migration of multisourcedata with a deblurring filter. Geophysics, 76(5): R135-R146.
  8. Dong, S., Cai, J., Guo, M., Suh, S., Zhang, Z., Wang, B. and Li, E.Z., 2012. Least-squares reverse time migration: Towards true amplitude imaging and improvingthe resolution. Expanded Abstr., 82nd Ann. Internat. SEG Mtg., Las Vegas: 1-5.
  9. Duan, Y., Guitton, A. and Sava, P., 2017. Elastic least-squares reverse time migration.Geophysics, 82(4): 5-S325.
  10. Dutta, G. and Schuster, G.T., 2014. Attenuation compensation for least-squares reversetime migration using the viscoacoustic-wave equation. Geophysics, 79(6): S251-
  11. Fang, G., Fomel, S., Du, Q. and Hu, J., 2014. Lowrank seismic-wave extrapolation on astaggered grid. Geophysics, 79(3): T157-T168.
  12. Feng, Z. and Schuster, G.T., 2017. Elastic least-squares reverse time migration.Geophysics, 82(2): 3-S157.
  13. Fomel, S., Ying, L. and Song, X., 2010. Seismic wave extrapolation using lowranksymbol approximation. Expanded Abstr., 80th Ann. Internat. SEG Mtg., Denver:3092-3096.
  14. Fomel, S., Ying, L. and Song, X., 2013. Seismic wave extrapolation using lowranksymbol approximation. Geophys. Prosp., 61: 526-536.
  15. Gu, B., Li, Z., Yang, P., Xu, W. and Han, J., 2017. Elastic least-squares reverse-timemigration with hybrid 11/12 misfit function. Geophysics, 82(3): S271-S291.
  16. Guo, P. and McMechan, G.A., 2018. Compensating Q effects in viscoelastic media byadjoint-based least-squares reverse time migration. Geophysics, 83(2): S151-2.
  17. Hou, J. and Symes, W.W., 2016. Accelerating extended least-squares migration withweighted conjugate gradient iteration. Geophysics, 81(4): 5-S179.
  18. Huang, J., Li, C. and Li, Z., 2017. Plane-wave least-squares reverse time migration inanisotropic media using low-rank finite difference. Extended Abstr., 79th EAGEConf., Paris..
  19. Huang, J., Si, D., Li, Z. and Huang, J., 2016. Plane-wave least-squares reverse timemigration in complex VTI media. Expanded Abstr., 86th Ann. Internat. SEGMtg., Dallas: 441-446.
  20. Liu, Y., Symes, W.W. and Li, Z., 2013. Multisource least-squares extended reverse timemigration with preconditioning guided gradient method. Expanded Abstr., 83rdAnn. Internat. SEG Mtg., Houston: 3709-3715.
  21. Nocedal, J., 1980. Updating quasi-Newton matrices with limited storage. Mathem.Computat., 35(151): 773-782.
  22. Plessix, R.E., 2006. A review of the adjoint-state method for computing the gradient of afunctional with geophysical applications. Geophys. J. Internat., 167: 495-503.
  23. Qu, Y., Huang, J., Li, Z., Guan, Z. and Li, J., 2017. Attenuation compensation inanisotropic least-squares reverse time migration. Geophysics, 82(6): 1-S423.
  24. Song G., Huang R., Tian J., Chen Y., Chen P., and Yang Y., 2016. A new QP-waveequation for 2D VTI media. Expanded Abstr., 86th Ann. Internat. SEG Mtg.,Dallas: 3977-3981.
  25. Song, X. and Alkhalifah, T., 2013. Modeling of pseudoacoustic P-waves in orthorhombicmedia with a low-rank approximation. Geophysics, 78(4): C33-C40.
  26. Song, X., Fomel, S. and Ying, L., 2013. Lowrank finite-differences and lowrank Fourierfinite-differences for seismic wave extrapolation in the acoustic approximation.Geophys. J. Internat., 193: 960-969.
  27. Sun, J., Fomel, S., Zhu, T. and Hu, J., 2016. Q-compensated least-squares reverse timemigration using low-rank one-step wave extrapolation. Geophysics, 81(4): 1-9.
  28. Tang, Y., 2009. Target-oriented wave-equation least-squares migration/inversion withphase-encoded Hessian. Geophysics, 74(6): WCA95-WCA107.
  29. Tarantola, A., 1984. Linearized inversion of seismic reflection data. Geophys. Prosp.,32: 998-1015.
  30. Thomsen, L., 1986. Weak elastic anisotropy. Geophysics, 51: 1954-1966.
  31. Wong, M., Biondi, B. and Ronen, S., 2010. Joint least-squares inversion of up-anddown-going signal for ocean bottom data sets. Expanded Abstr., 80th Ann.Internat. SEG Mtg., Denver: 2752-2756.
  32. Wong, M., Biondi, B.L. and Rone, S., 2015. Imaging with primaries and free-surfacemultiples by joint least-squares reverse time migration. Geophysics, 80(6): 3-
  33. Wong, M., Ronen, S. and Biondi, B., 2011. Least-squares reverse timemigration/inversion for ocean bottom data: A case study. Expanded Abstr., 81stAnn. Internat. SEG Mtg., San Antonio: 2369-2373.
  34. Xu, S. and Zhou, H., 2014. Accurate simulations of pure quasi-P-waves in complexanisotropic media. Geophysics, 79(6): T341-T348.
  35. Yang, J., Zhu, H., McMechan, G., Zhang, H. and Zhao, Y., 2019. Elastic least-squaresreverse-time migration in vertical transverse isotropic media. Geophysics, 84(6):9-S553.
  36. Zhan, G., Pestana, R.C. and Stoffa, P.L., 2012. Decoupled equations for reverse timemigration in tilted transversely isotropic media. Geophysics, 77(2): T37-T45.
  37. Zhan, G., Pestana, R.C. and Stoffa, P.L., 2013. An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation. J. Geophys.Engineer., 10(2): 025004.
  38. Zhang, Y., Duan, L. and Xie, Y., 2015. A stable and practical implementation of least-squares reverse-time migration. Geophysics, 80(1): V23-V31.
  39. Zhang, Y., Zhang, H. and Zhang, G., 2011. A stable TTI reverse time migration and itsimplementation. Geophysics, 76(3): WA3-WA11.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing