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Marchenko equations

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Journal Article
Journal: Geophysics
Published: 07 December 2016
Geophysics (2016) 82 (1): R19-R30.
...-scale details of the model are necessary). We can interpret the retrieved Green’s function as the response to sources at the surface for a virtual receiver in the subsurface. We obtain this Green’s function by solving the Marchenko equation, an integral equation pertinent to inverse scattering problems...
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Journal Article
Journal: Geophysics
Published: 22 May 2014
Geophysics (2014) 79 (3): WA39-WA57.
...Kees Wapenaar; Jan Thorbecke; Joost van der Neut; Filippo Broggini; Evert Slob; Roel Snieder ABSTRACT Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source...
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Journal Article
Journal: Geophysics
Published: 25 August 2016
Geophysics (2016) 81 (5): T265-T284.
...Joost van der Neut; Kees Wapenaar ABSTRACT Iterative substitution of the multidimensional Marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process. In so-called Marchenko imaging, a macro velocity model of the subsurface is required...
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Journal Article
Journal: The Leading Edge
Published: 01 January 2018
The Leading Edge (2018) 37 (1): 67a1-67a6.
... of Marchenko redatuming on a simple 1D acoustic lossless medium in which the coupled Marchenko equations are exact. Defined in a truncated version of the actual medium, the Marchenko focusing functions focus the wavefields at the virtual source location and are responsible for the subsequent retrieval...
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Journal Article
Journal: Geophysics
Published: 06 September 2017
Geophysics (2017) 82 (6): WB29-WB45.
... papers, but its implementation aspects have not yet been discussed in detail. Solving the Marchenko equation is an inverse problem. The Marchenko method computes a solution of the Marchenko equation by an (adaptive) iterative scheme or by a direct inversion. We have evaluated the iterative implementation...
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Journal Article
Journal: Geophysics
Published: 31 May 2017
Geophysics (2017) 82 (4): Q23-Q37.
...Satyan Singh; Roel Snieder ABSTRACT Recent papers show that imaging with the retrieved Green’s function constructed by the Marchenko equations, called Marchenko imaging, reduces artifacts from internal and free-surface multiples compared with standard imaging techniques. Even though artifacts...
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Journal Article
Journal: Geophysics
Published: 17 July 2015
Geophysics (2015) 80 (5): S165-S174.
...Satyan Singh; Roel Snieder; Jyoti Behura; Joost van der Neut; Kees Wapenaar; Evert Slob ABSTRACT Recent work on retrieving the Green’s function with the Marchenko equation shows how these functions for a virtual source in the subsurface can be obtained from reflection data. The response...
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Journal Article
Journal: Geophysics
Published: 08 August 2019
Geophysics (2019)
...Lele Zhang; Jan Thorbecke; Kees Wapenaar; Evert Slob ABSTRACT We have compared three data-driven internal multiple reflection elimination schemes derived from the Marchenko equations and inverse scattering series (ISS). The two schemes derived from Marchenko equations are similar but use different...
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Journal Article
Journal: Geophysics
Published: 23 March 2017
Geophysics (2017) 82 (3): Q13-Q21.
...Satyan Singh; Roel Snieder ABSTRACT By solving the Marchenko equations, one can retrieve the Green’s function (Marchenko Green’s function) between a virtual receiver in the subsurface and points at the surface (no physical receiver is required at the virtual location). We extend the idea behind...
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Journal Article
Journal: Geophysics
Published: 03 October 2017
Geophysics (2017) 82 (6): S439-S452.
... of sources and receivers have so far challenged the application of Marchenko redatuming to real-world scenarios. I combine the coupled Marchenko equations with a one-way version of the Rayleigh integral representation to obtain a new redatuming scheme that handles internal as well as free-surface multiples...
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Journal Article
Journal: The Leading Edge
Published: 01 July 2015
The Leading Edge (2015) 34 (7): 818-822.
...Joost van der Neut; Kees Wapenaar; Jan Thorbecke; Evert Slob; Ivan Vasconcelos Abstract In Marchenko imaging, wavefields are retrieved at specified focal points in the subsurface through an iterative scheme derived from the multidimensional Marchenko equation. The method requires seismic-reflection...
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Journal Article
Journal: Geophysics
Published: 21 August 2017
Geophysics (2017) 82 (6): Q53-Q66.
... to impulsive sources at the earth’s surface. These wavefields can be obtained from actual measurements in the subsurface, they can be numerically modeled, or they can be retrieved by solving a multidimensional Marchenko equation. As output, we retrieved virtual reflection and transmission responses...
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Journal Article
Journal: Geophysics
Published: 01 February 1983
Geophysics (1983) 48 (2): 163-170.
... Marchenko equation. The differentiability constraints on the acoustic impedance are somewhat relaxed compared to the more standard approach of beginning with the wave equation. The solution for plane waves at normal incidence is given along with a good approximate solution which is easily obtainable...
Journal Article
Journal: Geophysics
Published: 12 March 2014
Geophysics (2014) 79 (2): S63-S76.
... ′ = − t d ( z i , z 0 ) t f 1 − ( z 0 , z i , − t ′ ) R ( z 0 , t − t ′ ) d t ′ , (17) which are coupled Marchenko-type equations ( Lamb, 1980 ) valid on the interval − t d ( z i...
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Journal Article
Journal: Geophysics
Published: 07 August 2018
Geophysics (2018) 83 (5): S409-S419.
... be predicted in equation  9 . In general, as the internal multiples generators in this example are relatively deep, our approach is not heavily affected by these seven near-offset traces in each shot record. The initial step of the iterative scheme in Marchenko redatuming is to convolve the surface...
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Journal Article
Journal: Geophysics
Published: 01 March 2019
Geophysics (2019) 84 (2): F35-F45.
... that will disrupt the focus. Marchenko methods design energy to inject to destructively interfere with these scattered waves, reducing them to zero amplitude. To estimate M k + using equation  6 , we start with the estimate f k − 1 − produced by the previous iteration (or the initial...
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Journal Article
Journal: Geophysics
Published: 29 November 2018
Geophysics (2018) 83 (6): S579-S590.
... Marchenko equations, which results in focusing functions. These focusing functions, in turn, relate the wavefield measured at the acquisition surface to directionally decomposed Green’s functions at specified virtual receiver positions (coinciding with the focal points of the focusing functions) inside...
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Journal Article
Journal: Geophysics
Published: 18 March 2016
Geophysics (2016) 81 (2): Q15-Q26.
.... However, inaccuracies in Marchenko Green’s functions or in the implementation of equation  3a–3c may affect the results. For example, equation  3a–3c requires knowledge of velocity c ( x ) and density ρ ( x ) along integration boundaries S i . These quantities are rarely...
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Journal Article
Journal: Geophysics
Published: 11 January 2017
Geophysics (2017) 82 (2): Q1-Q12.
....2006.03296.x . GJINEA 0956-540X Slob E. Wapenaar K. Broggini F. Snieder R. , 2014 , Seismic reflector imaging using internal multiples with Marchenko-type equations : Geophysics , 79 , no.  2 , S63 – S76 , doi: http://dx.doi.org/10.1190/geo2013-0095.1 . GPYSA7 0016-8033...
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Journal Article
Journal: Geophysics
Published: 09 November 2016
Geophysics (2016) 82 (1): A1-A5.
... in Marchenko imaging : Geophysics , 81 , this issue, doi: 10.1190/geo2015-0646.1 . Slob , E. , K. Wapenaar , F. Broggini , and R. Snieder , 2014 , Seismic reflector imaging using internal multiples with Marchenko-type equations : Geophysics , 79 , no.  2 , S63 – S76 , doi...
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