1887

Abstract

Summary

Full-waveform inversion is an ill-posed inverse problem, with non-unique solutions. We examine its non-uniqueness by exploring the null-space shuttle, which can generate an ensemble of data-fitting solutions efficiently. We construct this shuttle based on a quasi-Newton method, the square-root variable-metric (SRVM) method. This method enables a retrieval of the inverse data-misfit Hessian after the SRVM-based elastic FWI converges. Combining SRVM with randomised singular value decomposition (SVD), we obtain the eigenvector subspaces of the inverse data-misfit Hessian. The first one among them is considered to determine the null space of the elastic FWI result. Using the SRVM-based null-space shuttle we can modify the inverted result a posteriori in a highly efficient manner without corrupting data misfit. Also, because the SRVM method is embedded through elastic FWI, our method can be extended to multi-parameter problems. We confirm and highlight our methods with the elastic Marmousi example.

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/content/papers/10.3997/2214-4609.201901222
2019-06-03
2024-03-29
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References

  1. Deal, M.M. and Nolet, G.
    [1996] Nullspace shuttles. Geophysical Journal International, 124(2), 372–380.
    [Google Scholar]
  2. Fletcher, R. and Powell, M.J.
    [1963] A rapidly convergent descent method for minimization. The computer journal, 6(2), 163–168.
    [Google Scholar]
  3. Halko, N., Martinsson, P.G. and Tropp, J.A.
    [2011] Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM review, 53(2), 217–288.
    [Google Scholar]
  4. Hull, D.G. and Tapley, B.D.
    [1977] Square-root variable-metric methods for minimization. Journal of optimization theory and applications, 21(3), 251–259.
    [Google Scholar]
  5. Liberty, E., Woolfe, F., Martinsson, P.G., Rokhlin, V. and Tygert, M.
    [2007] Randomized algorithms for the low-rank approximation of matrices. Proceedings of the National Academy of Sciences, 104(51), 20167–20172.
    [Google Scholar]
  6. Liu, Q. and Peter, D.
    [2018] Square-Root Variable Metric based elastic full-waveform inversion – Part 2: Uncertainty estimation. Geophys. J. Int., submitted.
    [Google Scholar]
  7. Liu, Q., Peter, D. and Tape, C.
    [2018] Square-Root Variable Metric based elastic full-waveform inversion – Part 1: Theory and validation. Geophys. J. Int., submitted.
    [Google Scholar]
  8. Luo, Y.
    [2012] Seismic imaging and inversion based on spectral-element and adjoint methodss. Ph.D. thesis.
    [Google Scholar]
  9. Meju, M.A.
    [2009] Regularized extremal bounds analysis (REBA): An approach to quantifying uncertainty in nonlinear geophysical inverse problems. Geophysical Research Letters, 36(3).
    [Google Scholar]
  10. Morf, M. and Kailath, T.
    [1975] Square-root algorithms for least-squares estimation. IEEE Transactions on Automatic Control, 20(4), 487–497.
    [Google Scholar]
  11. Tarantola, A.
    [2005] Inverse problem theory and methods for model parameter estimation. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, USA.
    [Google Scholar]
  12. Virieux, A. and Operto, S.
    [2009] An overview of full-waveform inversion in exploration geophysics. Geophysics, 74(6), WCC1–WCC26.
    [Google Scholar]
  13. Williamson, W.E.
    [1975] Square-root algorithms for function minimization. AIAA Journal, 13(1), 107–109.
    [Google Scholar]
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