1887

Abstract

Summary

Focusing functions are defined as wavefields that focus at a specified location in a heterogeneous subsurface. These functions can be directly related to Green’s functions and hence they can be used for seismic imaging of complete wavefields, including not only primary reflections but all orders of internal multiples. Recently, it has been shown that focusing functions can be retrieved from single-sided reflection data and an initial operator (which can be computed in a smooth background velocity model of the subsurface) by iterative substitution of the multidimensional Marchenko equation. In this work, we show that the Marchenko equation can also be inverted directly for the focusing functions. Although this approach is computationally more expensive than iterative substitution, additional constraints can easily be imposed. Such a flexibility might be beneficial in specific cases, for instance when the recorded data are incomplete or when additional measurements (e.g. from downhole receivers) are available.

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/content/papers/10.3997/2214-4609.201412939
2015-06-01
2024-03-28
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References

  1. Aravkin, A., Kumar, R., Mansour, H., Recht, B. and Herrmann, F.
    [2014] Fast methods for denoising matrix completion formulations, with applications to robust seismic data interpolation. SIAM Journal of Scientific Computing, 36, S237–S266.
    [Google Scholar]
  2. Broggini, F. and Snieder, R.
    [2012] Connection of scattering principles: A visual and mathematical tour. European Journal of Physics, 33, 593–613.
    [Google Scholar]
  3. Broggini, F., Snieder, R. and Wapenaar, K.
    [2014] Data-driven wave field focusing and imaging with multidimensional deconvolution: Numerical examples from reflection data with internal multiples. Geophysics, 79(3), WA107–WA115.
    [Google Scholar]
  4. da Costa Filho, C., Ravasi, M., Curtis, A. and Meles, G.
    [2014] Elastodynamic Green’s function retrieval through single-sided Marchenko inverse scattering. Physical Review E., 90, 063201.
    [Google Scholar]
  5. Lin, T.T.Y. and Herrmann, F.J.
    [2013] Robust estimation of primaries by sparse inversion via one-norm minimization. Geophysics, 78(3), R133–R150.
    [Google Scholar]
  6. Pauge, C.C. and Saunders, M.A.
    [1982] LSQR: An algorithm for sparse linear equations and sparse least squares. Transactions on Mathematical Software, 8(1), 43–71.
    [Google Scholar]
  7. Singh, S., Snieder, R., Behura, J., van der Neut, J., Wapenaar, K. and Slob, E.
    [2014] Autofocusing for retrieving the Green’s function in the presence of a free surface. 74th EAGE Conference and Exhibition, Extended Abstracts.
    [Google Scholar]
  8. Slob, E., Wapenaar, K., Broggini, F. and Snieder, R.
    [2014] Seismic reflector imaging using internal multiples with Marchenko-type equations. Geophysics, 79(2), S63–S76.
    [Google Scholar]
  9. Van der Neut, J., Vasconcelos, I. and Wapenaar, K.
    [2015] On Green’s function retrieval by iterative substitution of the coupled Marchenko equations. Geophysical Journal International, submitted.
    [Google Scholar]
  10. Wapenaar, K. and Slob, E.
    [2014] On the Marchenko equation for multicomponent single-sided reflection data. Geophysical Journal International, 199, 1367–1371.
    [Google Scholar]
  11. Wapenaar, K., Thorbecke, J., van der Neut, J., Broggini, F., Slob, E. and Snieder, R.
    [2014] Green’s function retrieval from reflection data, in absence of a receiver at the virtual source position. Journal of the Acoustical Society of America, 135(5), 2847–2861.
    [Google Scholar]
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