1887
Volume 52, Issue 6
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Migration velocity analysis (MVA) has been widely used for large scale model construction. To make full use of the wavefield information and obtain stable inversion results, wave-equation-based methods, such as differential semblance optimisation (DSO) or travel-time tomography, become popular in recent years. Compared with traditional ray-based methods, wave-equation-based methods are intrinsically more robust, which can accurately describe subsurface wave phenomenon and thus solve multipathing problem occurred in ray-based methods especially in dramatically lateral variation areas. Although robust for wave-equation-based methods, the inversion results can be severely affected by spurious oscillations, such as migration smile, due to uneven illumination and limited geometry observations. To eliminate those artefacts and improve imaging and inversion results, we introduce a new asymptotic inversion method in subsurface offset domain based on two-way wave equation. The new method, derived from the generalised Radon transform, introduces a new weighting function which can be treated as an approximate inverse under the assumption of high-frequency approximation. By applying the new weighting function to the practical applications, the imaging artefacts can be significantly attenuated. Furthermore, we extend the new method to DSO with a new form of velocity inversion expressions. We also give three numerical examples to illustrate the effectiveness of the method. It appears smooth and is free of artefacts both in gradients and imaging results, which leads to stable imaging and reliable model update.

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2021-11-02
2026-01-12
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References

  1. Biondi, B., and P.Sava. 1999. Wave-equation migration velocity analysis. 69th Annual International Meeting, SEG, Expanded Abstracts, 1723–6.
  2. Biswas, R., and M.K.Sen. 2017. 2D full-waveform inversion and uncertainty estimation using the reversible jump Hamiltonian Monte Carlo. 87th Annual International Meeting, SEG, Expanded Abstracts, 1280–5.
  3. Beylkin, G.1987. Discrete Radon transform. IEEE Transactions on Acoustics, Speech, and Signal Processing35: 162–72.
    [Google Scholar]
  4. Bleistein, N.1987. On the imaging of reflectors in the earth. Geophysics52: 931–42.
    [Google Scholar]
  5. Bunks, C., F.M.Saleck, S.Zaleski, and G.Chavent. 1995. Multiscale seismic waveform inversion. Geophysics60: 1457–73.
    [Google Scholar]
  6. Chauris, H., and E.Cocher. 2017. From migration to inversion velocity analysis. Geophysics82: S207–23.
    [Google Scholar]
  7. Chauris, H., C.Lameloise, and E.Cocher. 2015. Inversion velocity analysis: The importance of regularization. 77th Annual International Conference and Exhibition, EAGE, Extended Abstracts, WS05–A02.
  8. Chen, P., and O.Ghattas. 2018. Hessian-based sampling for high-dimensional model reduction. International Journal for Uncertainty Quantification9: 103–21.
    [Google Scholar]
  9. Engquist, B., B.D.Froese, and Y.Yang. 2016. Optimal transport for seismic full waveform inversion. Communications in Mathematical Sciences14: 2309–30.
    [Google Scholar]
  10. Fang, Z., D.S.Curt, K.Rachel, and F.J.Herrmann. 2018. Uncertainty quantification for inverse problems with weak partial-differential-equation constraints. Geophysics83: R629–47.
    [Google Scholar]
  11. Hager, W.W., and H.Zhang. 2006. A survey of nonlinear conjugate gradient methods. Pacific Journal of Optimization2: 35–8.
    [Google Scholar]
  12. Hou, J., and W.W.Symes. 2015. An approximate inverse to the extended born modeling operator. Geophysics80: R331–49.
    [Google Scholar]
  13. Hou, J., and W.W.Symes. 2016. Inversion velocity analysis via approximate born inversion. 86th Annual International Meeting, SEG, Expanded Abstracts, 5274–9.
  14. Lameloise, C., H.Chauris, and M.Noble. 2015. Improving the gradient of the image-domain objective function using quantitative migration for a more robust migration velocity analysis. Geophysical Prospecting63: 391–404.
    [Google Scholar]
  15. Leeuwen, T.V., and F.J.Herrmann. 2013. Mitigating local minima in full-waveform inversion by expanding the search space. Geophysical Journal International195: 661–7.
    [Google Scholar]
  16. Li, Y., and H.Chauris. 2018. Coupling direct inversion to common-shot image-domain velocity analysis. Geophysics83: R497–514.
    [Google Scholar]
  17. Liu, Q., and D.Peter. 2019. Square-Root variable Metric based elastic full-waveform inversion – part 2: Uncertainty estimation. Geophysical Journal International218: 1100–20.
    [Google Scholar]
  18. Liu, Y., and M.K.Sen. 2010. A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation. Geophysics75: A1–6.
    [Google Scholar]
  19. Luo, Y., and G.T.Schuster. 1991. Wave-equation traveltime inversion. Geophysics56: 645–53.
    [Google Scholar]
  20. Martin, J., L.C.Wilcox, C.Burstedde, and O.Ghattas. 2012. A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM Journal on Scientific Computing34: A1460–87.
    [Google Scholar]
  21. Métivier, L., R.Brossier, Q.Merigot, E.Oudet, and J.Virieux. 2016. An optimal transport approach for seismic tomography: Application to 3D full waveform inversion. Inverse Problems32: 115008.
    [Google Scholar]
  22. Miller, D., M.Oristaglio, and G.Beylkin. 1987. A new slant on seismic imaging: migration and integral geometry. Geophysics52: 943–64.
    [Google Scholar]
  23. Plessix, R.2006. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International167: 495–503.
    [Google Scholar]
  24. Pratt, R.G.1999. Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model. Geophysics64: 888–901.
    [Google Scholar]
  25. Pratt, R.G., C.Shin, and G.J.Hick. 1998. Gauss-Newton and full Newton methods in frequency space seismic waveform inversion. Geophysical Journal International133: 341–62.
    [Google Scholar]
  26. Qin, B., T.Allemand, and G.Lambaré. 2015. Full waveform inversion using preserved amplitude reverse time migration. 85th Annual International Meeting, SEG, Expanded Abstracts, 1252–7.
  27. Shen, P.2012. An RTM based automatic migration velocity analysis in image domain. 82nd Annual International Meeting, SEG, Expanded Abstracts, 1–5.
  28. Shen, P., and W.W.Symes. 2013. Subsurface domain image warping by horizontal contraction and its application to wave-equation migration velocity analysis. 83rd Annual International Meeting, SEG, Expanded Abstracts, 4715–19.
  29. Shen, P., and W.W.Symes. 2015. Horizontal contraction in image domain for velocity inversion. Geophysics80: R95–110.
    [Google Scholar]
  30. Shen, P., W.W.Symes, and C.C.Stolk. 2003. Differential semblance velocity analysis by wave equation migration. 73rd Annual International Meeting, SEG, Expanded Abstracts, 2132–5.
  31. Symes, W.W.2008. Migration velocity analysis and waveform inversion. Geophysical Prospecting56: 756–90.
    [Google Scholar]
  32. Tarantola, A.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49: 1259–66.
    [Google Scholar]
  33. Virieux, J., and S.Operto. 2009. An overview of full-waveform inversion in exploration geophysics. Geophysics74: WCC1–26.
    [Google Scholar]
  34. Zhu, H., S.Li, S.Fomel, G.Stadler, and O.Ghattas. 2016. A Bayesian approach to estimate uncertainty for full-waveform inversion using a priori information from depth migration. Geophysics81: R307–23.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Acoustic; imaging; reconstruction; reverse-time; velocity; wave equation

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