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  • Seismic interferometry and beyond

    Kees Wapenaar, Evert Slob, Joost van der Neut,

    Jan Thorbecke, Filippo Broggini and Roel Snieder

    Workshop “Waves in complex media” Grenoble, December 13, 2013

  • •  Introduction • Green’s functions and focusing functions •  3-D Marchenko equations •  Iterative solution • Green’s function retrieval • Marchenko imaging • Conclusions

  • •  Introduction • Green’s functions and focusing functions •  3-D Marchenko equations •  Iterative solution • Green’s function retrieval • Marchenko imaging • Conclusions

  • The Seismic Reflection Technique

    Petroleum Handbook 1948 (Shell)

  • geophones dynamite

    Acquisition on land

    Seismic vibrator

  • hydrophones

    airgun

    Acquisition at sea

  • hydrophones

    airgun

    Simplifying assumption: Primaries only

  • Surface-related multiples:

  • Surface-related multiples: Relatively easy removable

  • Internal multiples: very difficult

  • False images of internal multiples

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    False images of internal multiples

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    Solution 1: receivers in a borehole

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    Solution 2: Marchenko imaging

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    Interferometric Green’s function representation: Sources at , enclosing the medium Receivers inside the medium, at VS position

    ∂D

    xB xA ∂D

    (Phys. Rev. Lett., 2004)

    G(xB ,xA, t) +G(xB ,xA,−t) ≈ �

    ∂D dx

    � G(xB ,x, t+ t

    �)G(xA,x, t �)dt�

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    x�i

    ∂D0

    x��0 x0 Single-sided Green’s function representation: Sources and receivers at , at one side of the medium No receiver at VS!

    ∂D0

    G(x��0 ,x � i, t) = f2(x

    � i,x

    �� 0 ,−t) +

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f2(x�i,x0, t�)dt�

    (Phys. Rev. Lett., 2013)

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    2500 Assumption: Lossless medium Approximation: Evanescent field not included

    x�i

    ∂D0

    x��0 x0

    G(x��0 ,x � i, t) = f2(x

    � i,x

    �� 0 ,−t) +

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f2(x�i,x0, t�)dt�

    (Phys. Rev. Lett., 2013)

  • •  Introduction • Green’s functions and focusing functions •  3-D Marchenko equations •  Iterative solution • Green’s function retrieval • Marchenko imaging • Conclusions

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    x�i

    ∂D0

    x��0 x0

    G(x��0 ,x � i, t)− f2(x�i,x��0 ,−t) =

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f2(x�i,x0, t�)dt�

    Single-sided Green’s function representation

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    G−,+(x��0 ,x � i, t) + f

    − 1 (x

    �� 0 ,x

    � i, t) =

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f+1 (x0,x�i, t�)dt�

    x�i

    ∂D0

    x��0 x0 Decomposed Single-sided Green’s function representations

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    ∂D0 0

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    1.0

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    2.0

    2.5

    3.0

    -2000 -1000 0 1000 2000 x��0 x

    �� 0x0

    G−,+(x��0 ,x � i, t) + f

    − 1 (x

    �� 0 ,x

    � i, t) =

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f+1 (x0,x�i, t�)dt�

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    x�i ∂Di

    x��0 · · · · · · · · · · · · · · · · · · · · · x��0 0

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    2.0

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    G−,+(x��0 ,x � i, t) + f

    − 1 (x

    �� 0 ,x

    � i, t) =

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f+1 (x0,x�i, t�)dt�

    ∂D0

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    ∂Di

    G−,+(x��0 ,x � i, t) + f

    − 1 (x

    �� 0 ,x

    � i, t) =

    ∂D0 dx0

    � t

    −∞ R(x��0 ,x0, t− t�)f+1 (x0,x�i, t�)dt�

    x�i

    x0 · · · · · · · · · ·x0 ∂D0

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    ∂Dix�i

    x0 · · · · · · · · · ·x0 ∂D0

    f+1 (x0,x � i, t)

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    ∂Dix�i

    x0 · · · · · · · · · ·x0 ∂D0

    f+1 (x0,x � i, t)

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    ∂Dix�i

    x0 · · · · · · · · · ·x0 ∂D0

    f+1 (x0,x � i, t)

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    ∂Dix�i

    x0 · · · · · · · · · ·x0 ∂D0

    f+1 (x0,x � i, t)

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    ∂Dix�i

    x0 · · · · · · · · · ·x0 ∂D0

    f+1 (x0,x � i, t)

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    ∂Dix�i

    x0 · · · · · · · · · ·x0 ∂D0

    f+1 (x0,x � i, t)

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