1887

Abstract

Summary

The key to image domain least-squares migration is the explicit calculation of the Hessian matrix. However, the full Hessian matrix is too big and expensive to compute and save. Guitton (2004) directly approximates the non-diagonal inverse of the Hessian with a bank of non-stationary matching filters, which can be seen as a low-rank approximation of the true inverse Hessian. The filters have the amplitude-balancing effect, but the ability to increase the resolution is missing. In this paper, to capture as much effect of least-squares migration as possible, we use non-stationary matching filters to approximate the non-diagonal Hessian first, and then solve a constrained optimization problem with the sparse and TV regularization for the result of the image domain least-squares migration. Numerical examples illustrate that the inverted images of the proposed method have both more balanced amplitudes and higher resolution than conventional migration images.

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/content/papers/10.3997/2214-4609.201800650
2018-06-11
2024-03-29
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References

  1. Beylkin, G.
    (1985). Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform. Journal of Mathematical Physics, 26(1), 99–108.
    [Google Scholar]
  2. Fletcher, R. P., Nichols, D., Bloor, R., & Coates, R. T.
    (2016). Least-squares migration—Data domain versus image domain using point spread functions. The Leading Edge.
    [Google Scholar]
  3. Goldstein, T., & Osher, S.
    (2009). The split Bregman method for L1-regularized problems. SIAM journal on imaging sciences, 2(2), 323–343.
    [Google Scholar]
  4. Guitton, A.
    (2004). Amplitude and kinematic corrections of migrated images for nonunitary imaging operators. Geophysics, 69(4), 1017–1024.
    [Google Scholar]
  5. (2017). Fast 3D least-squares RTM by preconditioning with nonstationary matching filters. In SEG Technical Program Expanded Abstracts 2017 (pp. 4395–4399). Society of Exploration Geophysicists.
    [Google Scholar]
  6. Rickett, J. E., Guitton, A., & Gratwick, D.
    (2001, June). Adaptive multiple subtraction with non-stationary helical shaping filters. In 63rd EAGE Conference & Exhibition.
    [Google Scholar]
  7. Tang, Y.
    (2009). Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian. Geophysics, 74(6), WCA95–WCA107.
    [Google Scholar]
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