1887
Volume 72, Issue 7
  • E-ISSN: 1365-2478

Abstract

Abstract

The imaging condition is a crucial component of the reverse time migration. In its conventional form, it involves cross‐correlating the extrapolated source‐ and receiver‐side wavefields. Effective imaging conditions are usually developed to suppress imaging artefacts (e.g. low‐wavenumber artefacts) and enhance the image quality. For acoustic reverse time migration, not only the scalar pressure but also their spatial and/or time derivatives are used in the imaging condition, similar to the gradient terms of adjoint tomography. These operations implicitly introduce additional angle‐domain weighting factors to the image results. In this study, based on an analysis of angle‐dependent properties of the existing imaging conditions, we propose a new imaging condition tailored for acoustic reverse time migration. It can be implemented efficiently using the variables within the finite‐difference solver. Without explicitly measuring wave propagation directions, the proposed imaging condition can naturally suppress the low‐wavenumber artefacts while maintaining a relatively wider imaging aperture, thereby corresponding to a broader wavenumber sampling range. Additionally, the evolved imaging conditions for imaging elastic P–P and S–S scattering and reflections are also formulated. In the angle domain, we conduct a comparative analysis between existing imaging conditions and the newly proposed ones. Various numerical examples are provided to demonstrate the advantages of the new imaging conditions. A comprehensive understanding of their angle‐domain properties may be further beneficial to constructing reasonable inversion strategies for full waveform inversion.

© 2024 European Association of Geoscientists & Engineers. © 2024 European Association of Geoscientists & Engineers.
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2024-08-23
2026-02-11

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References

  1. Aki, K. & Richards, P.G. (1980) Quantitative seismology. New York: W. H. Freeman and Company.
     [Google Scholar]
  2. Alkhalifah, T. (2015a) Scattering‐angle based filtering of the waveform inversion gradients. Geophysical Journal International, 200(1), 363–373.
     [Google Scholar]
  3. Alkhalifah, T. (2015b) Conditioning the full‐waveform inversion gradient to welcome anisotropy. Geophysics, 80(3), R111–R122.
     [Google Scholar]
  4. Alkhalifah, T.A. (2016) Full waveform inversion in an anisotropic world: where are the parameters hiding?Bunnik: EAGE publications.
     [Google Scholar]
  5. Brandsberg‐Dahl, S., Chemingui, N., Whitmore, D., Crawley, S., Klochikhina, E. & Valenciano, A. (2013) 3D RTM angle gathers using an inverse scattering imaging condition [Expanded abstracts]. In: 83rd SEG annual international meeting, Houston, TX, USA. Houston, Society of Exploration Geophysicists. pp. 3958–3962.
  6. Chi, B., Gao, K. & Huang, L. (2021) Vector elastic deconvolution migration with dual wavefield decomposition. Geophysics, 86(4), S271–S282.
     [Google Scholar]
  7. Díaz, E. & Sava, P. (2016) Understanding the reverse time migration backscattering: noise or signal?Geophysical Prospecting, 64(3), 581–594.
     [Google Scholar]
  8. Douma, H., Yingst, D., Vasconcelos, I. & Tromp, J. (2010) On the connection between artifact filtering in reverse‐time migration and adjoint tomography. Geophysics, 75(6), S219–S223.
     [Google Scholar]
  9. Du, Q., Zhang, F., Liang, Z., Li, Q. & Fu, L.Y. (2024) Stress tensor double dot product imaging condition for elastic reverse time migration. Geophysical Prospecting, 72(4), 1277–1289.
     [Google Scholar]
  10. Duan, Y. & Sava, P. (2015) Scalar imaging condition for elastic reverse time migration. Geophysics, 80(4), S127–S136.
     [Google Scholar]
  11. Fei, T.W., Luo, Y., Yang, J., Liu, H. & Qin, F. (2015) Removing false images in reverse time migration: the concept of de‐primaryDe‐primary reverse time migration. Geophysics, 80(6), S237–S244.
     [Google Scholar]
  12. Fletcher, R.P., Fowler, P.J., Kitchenside, P. & Albertin, U. (2006) Suppressing unwanted internal reflections in prestack reverse‐time migration. Geophysics, 71(6), E79–E82.
     [Google Scholar]
  13. Guitton, A., Valenciano, A., Bevc, D. & Claerbout, J. (2007) Smoothing imaging condition for shot‐profile migration. Geophysics, 72(3), S149–S154.
     [Google Scholar]
  14. Guo, X., Shi, Y., Wang, W., Jing, H. & Zhang, Z. (2020) Wavefield decomposition in arbitrary direction and an imaging condition based on stratigraphic dip. Geophysics, 85(5), S299–S312.
     [Google Scholar]
  15. Han, B. (2022) An angle‐domain investigation on resolutions embedded in imaging conditions for reverse time migration [Extended abstracts]. In: 83rd EAGE annual conference & exhibition, Madrid, Spain. European Association of Geoscientists and Engineers. pp. 676.
  16. Han, B., Yan, Z., Tang, Y., Liu, S. & Gu, H. (2019) Analyses on diving‐wave imaging artifacts in RTM and an effective removal strategy based on wavelength‐dependent smoothing [Extended abstracts]. In: 89th SEG annual international meeting, San Antonio, TX, USA. Houston, Society of Exploration Geophysicists. pp. 4327–4331.
  17. Holicki, M., Drijkoningen, G. & Wapenaar, K. (2019) Acoustic directional snapshot wavefield decomposition. Geophysical Prospecting, 67(1), 32–51.
     [Google Scholar]
  18. Hu, J., Wang, H. & Wang, X. (2016) Angle gathers from reverse time migration using analytic wavefield propagation and decomposition in the time domain. Geophysics, 81(1), S1–S9.
     [Google Scholar]
  19. Jin, S., Madariaga, R., Virieux, J. & Lambaré, G. (1992) Two‐dimensional asymptotic iterative elastic inversion. Geophysical Journal International, 108(2), 575–588.
     [Google Scholar]
  20. Kim, D., Hwang, J., Min, D.‐J., Oh, J.‐W. & Alkhalifah, T. (2022) Two‐step full waveform inversion of diving and reflected waves with the diffraction‐angle‐filtering‐based scale‐separation technique. Geophysical Journal International, 229(2), 880–897.
     [Google Scholar]
  21. Liang, H., Zhang, H. & Liu, H. (2020) Waveform impedance sensitivity kernel for elastic reverse time migration [Expanded abstracts]. In: 90th SEG annual international meeting, Houston, TX, USA. Houston, Society of Exploration Geophysicists. pp. 2978–2982.
  22. Liu, F., Zhang, G., Morton, S.A. & Leveille, J.P. (2011) An effective imaging condition for reverse‐time migration using wavefield decomposition. Geophysics, 76(1), S29–S39.
     [Google Scholar]
  23. Liu, S., Yan, Z., Gu, H., Tang, Y. & Liu, C. (2019) Imaging artefacts of artificial diving waves in reverse time migration: cause analysis in the angle domain and an effective removal strategy. Geophysical Prospecting, 67(3), 496–507.
     [Google Scholar]
  24. Luo, J. & Wu, R.‐S. (2018) Velocity and density reconstruction based on scattering angle separation. Pure and Applied Geophysics, 175(12), 4371–4387.
     [Google Scholar]
  25. Mulder, W.A. & Plessix, R.‐E. (2004) A comparison between one‐way and two‐way wave‐equation migration. Geophysics, 69(6), 1491–1504.
     [Google Scholar]
  26. Oh, J.‐W., Cheng, J. & Min, D.‐J. (2021) Diffraction‐angle filtering of gradient for acoustic full‐waveform inversion. Geophysics, 86(2), R173–R185.
     [Google Scholar]
  27. Op ʼt Root, T.J.P.M., Stolk, C.C. & De Hoop, M.V. (2012) Linearized inverse scattering based on seismic reverse time migration. Journal des Mathematiques Pures et Appliquees, 98, 211–238.
     [Google Scholar]
  28. Pan, W., Innanen, K.A. & Geng, Y. (2018) Elastic full‐waveform inversion and parametrization analysis applied to walk‐away vertical seismic profile data for unconventional (heavy oil) reservoir characterization. Geophysical Journal International, 213(3), 1934–1968.
     [Google Scholar]
  29. Ramos‐Martinez, J., Crawley, S., Zou, Z., Valenciano, A.A., Qiu, L. & Chemingui, N. (2016) A robust gradient for long wavelength FWI updates [Extended abstract]. In: 78th EAGE annual conference and exhibition, Vienna, Austria. Netherlands, European Association of Geoscientists and Engineers. pp. Th SRS2 03.
  30. Revelo, D.E. & Pestana, R.C. (2019) Up/down acoustic wavefield decomposition using a single propagation and its application in reverse time migration. Geophysics, 84(4), S341–S353.
     [Google Scholar]
  31. Rocha, D., Tanushev, N. & Sava, P. (2016a) Acoustic wavefield imaging using the energy norm. Geophysics, 81(4), S151–S163.
     [Google Scholar]
  32. Rocha, D., Tanushev, N. & Sava, P. (2016b) Isotropic elastic wavefield imaging using the energy norm. Geophysics, 81(4), S207–S219.
     [Google Scholar]
  33. Stolk, C., de Hoop, M. & Op't Root, T. (2009) Inverse scattering of seismic data in the reverse time migration (RTM) approach: proceedings of the project review. Geo‐Mathematical Imaging Group, Purdue University, 1, 91–108.
     [Google Scholar]
  34. Stolt, R.H. & Weglein, A.B. (2012) Seismic imaging and inversion. Application of linear inverse theory, vol. 1, Cambridge: Cambridge University Press.
     [Google Scholar]
  35. Suh, S. & Wang, B. (2013) Improving salt boundary imaging using an RTM inverse scattering imaging condition [Expanded abstracts]. In: 83rd SEG annual international meeting, Houston, TX, USA. Houston, Society of Exploration Geophysicists. pp. 3953–3957.
  36. Sun, Y. & Fei, T.W. (2021) Flank‐preserving deprimary reverse time migration. Geophysics, 86(1), S1–S15.
     [Google Scholar]
  37. Tarantola, A. (1984) Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49(8), 1259–1266.
     [Google Scholar]
  38. Tarantola, A. (1986) A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics, 51(10), 1893–1903.
     [Google Scholar]
  39. Virieux, J. & Operto, S. (2009) An overview of full‐waveform inversion in exploration geophysics. Geophysics, 74(6), WCC1–WCC26.
     [Google Scholar]
  40. Wang, G., Alkhalifah, T. & Wang, S. (2020) Enhancing low‐wavenumber information in reflection waveform inversion by the energy norm born scattering. IEEE Geoscience and Remote Sensing Letters, 19, 1–5.
     [Google Scholar]
  41. Wang, P., Yang, J., Huang, J., Sun, J. & Zhao, C. (2024) Consistency of the inverse scattering imaging condition, the energy norm imaging condition and the impedance kernel in acoustic and elastic reverse‐time migration. Journal of Geophysics and Engineering, 21, 614–633.
     [Google Scholar]
  42. Whitmore, N.D. & Crawley, S. (2012) Applications of RTM inverse scattering imaging conditions [Expanded abstract]. In: 82nd SEG annual international meeting, Las Vegas, NV, USA. Houston, Society of Exploration Geophysicists. pp. 1–6.
  43. Wu, C., Wang, H., Zhou, Y. & Hu, J. (2019) Angle‐domain common‐image gathers in reverse‐time migration by combining the poynting vector with local‐wavefield decomposition. Geophysical Prospecting, 67(8), 2035–2060.
     [Google Scholar]
  44. Wu, Z. & Alkhalifah, T. (2017) Efficient scattering‐angle enrichment for a nonlinear inversion of the background and perturbations components of a velocity model. Geophysical Journal International, 210(3), 1981–1992.
     [Google Scholar]
  45. Wu, Z., Liu, Y. & Yang, J. (2023) Steeply dip structure imaging with prismatic waves incorporating wavefield decomposition. Geophysical Prospecting, 71(4), 518–538.
     [Google Scholar]
  46. Xie, X.B. (2015) An angle‐domain wavenumber filter for multi‐scale full‐waveform inversion [Expanded abstracts]. In: 85th SEG annual international meeting, New Orleans, LA, USA. Houston, Society of Exploration Geophysicists. pp. 1132–1137.
  47. Xie, X.B. & Wu, R.S. (2002) Extracting angle domain information from migrated wavefield [Expanded Abstracts]. In: 72nd SEG annual international meeting, Salt Lake City, UT, USA. Houston, Society of Exploration Geophysicists. pp. 1360–1363.
  48. Xie, X.B. & Wu, R.S. (2006) A depth migration method based on the full‐wave reverse‐time calculation and local one‐way propagation [Expanded abstracts]. In: 76th SEG annual international meeting, New Orleans, LA, USA. Houston, Society of Exploration Geophysicists. pp. 2333–2337.
  49. Yan, R. & Xie, X.‐B. (2012) An angle‐domain imaging condition for elastic reverse time migration and its application to angle gather extraction. Geophysics, 77(5), S105–S115.
     [Google Scholar]
  50. Yang, J. & Zhu, H. (2019) Isotropic elastic reverse‐time migration using impedance sensitivity kernel [Expanded abstracts]. In: 89th SEG annual international meeting, San Antonio, TX, USA. Houston, Society of Exploration Geophysicists. pp. 4440–4444.
  51. Yang, J., Zhu, H., Wang, W., Zhao, Y. & Zhang, H. (2018) Isotropic elastic reverse time migration using the phase‐and amplitude‐corrected vector P‐and S‐wavefields. Geophysics, 83(6), S489–S503.
     [Google Scholar]
  52. Yang, K. & Zhang, J. (2022) The inverse scattering imaging condition for anisotropic reverse time migration. Geophysics, 87(6), S303–S313.
     [Google Scholar]
  53. Yang, K., Dong, X. & Zhang, J. (2021) Polarity‐reversal correction for vector‐based elastic reverse time migration. Geophysics, 86(1), S45–S58.
     [Google Scholar]
  54. Yoon, K. & Marfurt, K.J. (2006) Reverse‐time migration using the Poynting vector. Exploration Geophysics, 37(1), 102–107.
     [Google Scholar]
  55. Zhang, Y. & Sun, J. (2009) Practical issues in reverse time migration: true amplitude gathers, noise removal and harmonic source encoding. First Break, 27(1), 29–35.
     [Google Scholar]
  56. Zheng, Y., Wang, Y. & Chang, X. (2018) 3D forward modeling of upgoing and downgoing wavefields using Hilbert transform. Geophysics, 83(1), F1–F8.
     [Google Scholar]
  57. Zhou, W., Brossier, R., Operto, S. & Virieux, J. (2015) Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation. Geophysical Journal International, 202(3), 1535–1554.
     [Google Scholar]
  58. Zhou, Y. & Wang, H. (2017) Ray + Kirchhoff inversion based RTM imaging condition with implicit directional wavefield decomposition [Expanded abstracts]. In: 87th SEG annual international meeting, Houston, TX, USA. Houston, Society of Exploration Geophysicists. pp. 4443–4447.
  59. Zhu, H., Luo, Y., Nissen‐Meyer, T., Morency, C. & Tromp, J. (2009) Elastic imaging and time‐lapse migration based on adjoint methods. Geophysics, 74(6), WCA167–WCA177.
     [Google Scholar]
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An imaging condition for acoustic reverse time migration with implicit angle‐dependent weighting factors and its extended applications for imaging elastic P–P and S–S data
Geophysical Prospecting 72, 2520 (2024); https://doi.org/10.1111/1365-2478.13566
/content/journals/10.1111/1365-2478.13566
/content/journals/10.1111/1365-2478.13566
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  • Article Type: Research Article
Keyword(s): full waveform; imaging; numerical study; seismics

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