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Marchenko equations

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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: Geophysics
Published: 12 March 2014
Geophysics (2014) 79 (2): S63–S76.
... ′ ) R ( z 0 , t − t ′ ) d t ′ , (17) which are coupled Marchenko-type equations ( Lamb, 1980 ) valid on the interval − t d ( z i , z 0 ) < t < t d ( z i , z 0 ) . These can be solved...
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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: 07 December 2016
Geophysics (2017) 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: 11 February 2021
Geophysics (2021) 86 (2): S143–S154.
... as well as dense and regular sampling, currently constrain their practical applicability. We have reformulated the Marchenko equations to handle the case in which there are gaps in the source geometry while the receiver sampling remains regular (or the opposite, by means of reciprocity). Using synthetic...
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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: 15 February 2023
Geophysics (2023) 88 (2): V59–V73.
... that includes solving the Marchenko equation with a trivial constraint, evaluating the energy conservation condition of its solutions to find the spatially dependent error syndrome, using the 1.5D minimum-phase reconstruction for each shot gather to find the spatially dependent constraint, and finally using...
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Journal Article
Journal: Geophysics
Published: 08 August 2019
Geophysics (2019) 84 (5): S365–S372.
...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: 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: 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: 05 February 2021
Geophysics (2021) 86 (2): Q15–Q25.
.... The resulting Green’s function is used as the input to a Marchenko equation-based approach to predict the complex interference pattern of all overburden-generated internal multiples at once. In this approach, no a priori information about the subsurface is needed. In theory, the interbed multiples can...
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Journal Article
Journal: Geophysics
Published: 02 October 2023
Geophysics (2023) 88 (6): S189–S201.
... using convolutional interferometry. The second method emphasizes primary reflection retrieval (PRR) by capturing primary reflections without adaptive subtraction. It is derived from a modified method based on the Gel’fand-Levitan-Marchenko equation. Testing with the Pluto salt model, we find...
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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: 19 February 2021
Geophysics (2021) 86 (2): F9–F23.
... Marchenko equations and are similar to each other, but they use different time-domain truncation operators. The MME scheme retrieves a new data set without internal multiple reflections. The transmission-compensated Marchenko multiple elimination scheme does the same and additionally compensates...
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Journal Article
Journal: Geophysics
Published: 07 May 2020
Geophysics (2020) 85 (4): A25–A29.
..., but their implementation comes at a considerable computational cost. We have derived a scheme to image the subsurface of the medium with significantly reduced computational cost and artifacts. This scheme is based on the projected Marchenko equations. The measured reflection response is required as input, and a data set...
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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: Geophysics
Published: 22 September 2023
Geophysics (2023) 88 (6): T289–T303.
... and Marchenko methods, for which the Green’s functions are retrieved from reflection data by solving a Marchenko equation. To estimate the uncertainty of velocities, I apply a Bayesian framework to the inverse problem. Our results indicate that the method does not depend on the earth’s scattering potential...
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Journal Article
Journal: Geophysics
Published: 09 January 2020
Geophysics (2020) 85 (2): S65–S70.
... information or adaptive subtraction. This scheme was originally derived from coupled Marchenko equations, but it was modified to make it model independent. It filters primary reflections with their two-way traveltimes and physical amplitudes from measured seismic data. The MME scheme is applied to a deepwater...
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