1887

Abstract

Summary

Recent work on autofocusing with the Marchenko equation has shown how the Green’s function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green’s function from the location of the virtual source to the surface. The Green’s function is retrieved using only the reflection response of the medium and an estimate of the first arrival at the surface from the virtual source. Current techniques, however, only include primaries and internal multiples. Therefore, all surface-related multiples must be removed from the reflection response prior to the Green’s function retrieval. Here, we present a new scheme that includes primaries, internal multiples, and free-surface multiples. In other words, we retrieve the Green’s function in the presence of the free surface. The information needed for the retrieval are the reflection response at the acquisition surface and an estimate of the first arrival at the surface from the virtual source. The reflection response, in this case, includes the free-surface multiples; this makes it possible to include these multiples in the imaging operator and it obviates the need for surface-related multiple elimination.

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/content/papers/10.3997/2214-4609.20141367
2014-06-16
2024-04-29
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References

  1. Bakulin, A. and Calvert, R.
    [2006] The virtual source method: Theory and case study. Geophysics, 71(4), SI139–SI150.
    [Google Scholar]
  2. Broggini, F. and Snieder, R.
    [2012] Connection of scattering principles: a visual and mathematical tour. European Journal of Physics, 33(3), 593.
    [Google Scholar]
  3. Broggini, F., Snieder, R. and Wapenaar, K.
    [2012] Focusing the wavefield inside an unknown 1D medium: Beyond seismic interferometry. Geophysics, 77(5).
    [Google Scholar]
  4. Rose, J.
    [2002a] Time reversal, focusing and exact inverse scattering. Imaging of complex media with acoustic and seismic waves, 97–106.
    [Google Scholar]
  5. [2002b] ‘Single-sided’ autofocusing of sound in layered materials. Inverse problems, 18(6), 1923.
    [Google Scholar]
  6. Verschuur, D., Berkhout, A. and Wapenaar, C.
    [1992] Adaptive surface-related multiple elimination. Geophysics, 57(9), 1166–1177, ISSN 0016-8033, doi:10.1190/1.1443330.
    https://doi.org/10.1190/1.1443330 [Google Scholar]
  7. Wapenaar, C. and Grimbergen, J.
    [1996] Reciprocity theorems for one-way wavefields. Geophysical Journal International, 127(1), 169–177.
    [Google Scholar]
  8. Wapenaar, K., Broggini, F., Slob, E. and Snieder, R.
    [2013] Three-dimensional single-sided marchenko inverse scattering, data-driven focusing, green’s function retrieval, and their mutual relations. Phys. Rev. Lett., 110, 084301, doi:10.1103/PhysRevLett.110.084301.
    https://doi.org/10.1103/PhysRevLett.110.084301 [Google Scholar]
  9. Wapenaar, K., Thorbecke, J. and Draganov, D.
    [2004] Relations between reflection and transmission responses sponses of three-dimensional inhomogeneous media. Geophysical Journal International, 156(2), 179–194, doi:10.1111/j.1365‑246X.2003.02152.x.
    https://doi.org/10.1111/j.1365-246X.2003.02152.x [Google Scholar]
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