1887

Abstract

Summary

Virtual sources can be created in several ways. In seismic interferometry, a virtual source is created by crosscorrelating responses at different receivers, which are illuminated from all directions. Seismic interferometry can be mathematically described by the homogeneous Green’s function representation, which is a closed boundary integral.

Virtual sources can also be created with the Marchenko method. For the Marchenko method it is sufficient that the position of the virtual source is illuminated from one side. We derive a single-sided homogeneous Green’s function representation, which is an open boundary integral along reflection measurements at the surface. Applying this representation, we obtain virtual sources and virtual receivers in the subsurface from real sources and receivers at the surface (note that in our earlier work on the Marchenko method the response to the virtual source was only obtained for receivers at the surface). The retrieved virtual data show the entire evolution of the response to a virtual source in the subsurface, including primary and multiple scattering at unknown interfaces.

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/content/papers/10.3997/2214-4609.201600623
2016-05-31
2020-05-25
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References

  1. Bojarski, N.N.
    [1983] Generalized reaction principles and reciprocity theorems for the wave equations, and the relationship between the time-advanced and time-retarded fields. Journal of the Acoustical Society of America, 74, 281–285.
    [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 wavefield focusing and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples. Geophysics, 79(3), WA107–WA115.
    [Google Scholar]
  4. Fokkema, J.T. and van den Berg, P.M.
    [1993] Seismic applications of acoustic reciprocity. Elsevier, Amsterdam.
    [Google Scholar]
  5. van der Neut, J., Wapenaar, K., Thorbecke, J., Slob, E. and Vasconcelos, I.
    [2015] An illustration of adaptive Marchenko imaging. The Leading Edge, 34, 818–822.
    [Google Scholar]
  6. Oristaglio, M.L.
    [1989] An inverse scattering formula that uses all the data. Inverse Problems, 5, 1097–1105.
    [Google Scholar]
  7. Porter, R.P.
    [1970] Diffraction-limited, scalar image formation with holograms of arbitrary shape. Journal of the Optical Society of America, 60, 1051–1059.
    [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. Wapenaar, C.P.A., Peels, G.L., Budejicky, V. and Berkhout, A.J.
    [1989] Inverse extrapolation of primary seismic waves. Geophysics, 54(7), 853–863.
    [Google Scholar]
  10. Wapenaar, K. and Fokkema, J.
    [2006] Green’s function representations for seismic interferometry. Geophysics, 71(4), SI33–SI46.
    [Google Scholar]
  11. Wapenaar, K., Thorbecke, J. and van der Neut, J.
    [2016] A single-sided homogeneous Green’s function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green’s function retrieval. Geophysical Journal International, 204, in press.
    [Google Scholar]
  12. Wapenaar, K., Thorbecke, J., van der Neut, J., Broggini, F., Slob, E. and Snieder, R.
    [2014] Marchenko imaging. Geophysics, 79(3), WA39–WA57.
    [Google Scholar]
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