document

On Green’s functions, propagator matrices, focusing functions and their mutual relations

Wapenaar, C.P.A. (author), Brackenhoff, J. (author), De Ridder, S. (author), Slob, E.C. (author), Snieder, R. (author)

Green’s functions and propagator matrices are both solutions of the wave equation, but whereas Green’s functions obey a causality condition in time (G = 0 for t < 0), propagator matrices obey a boundary condition in space. Marchenko-type focusing functions focus a wave field in space at zero time. We discuss the mutual relations between Green...

conference paper 2023

document

Wavefield focusing using a generalised, potentially asymmetric homogeneous Green's function

Diekmann, Leon (author), Vasconcelos, Ivan (author), Wapenaar, C.P.A. (author), Slob, E.C. (author), Snieder, Roel (author)

Marchenko-type integrals typically relate so-called focusing functions and Green's functions via the reflection response measured on the open surface of a volume of interest. Originating from one dimensional inverse scattering theory, the extension to two and three dimensions set in motion various new developments regarding imaging in complex...

journal article 2023

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Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

Wapenaar, C.P.A. (author), Dukalski, Marcin (author), Reinicke, Christian (author), Snieder, Roel (author)

Many seismic imaging methods use wavefield extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wavefield extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a...

journal article 2023

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Do we need up/down decomposition for Marchenko imaging?

Wapenaar, C.P.A. (author), Snieder, Roel (author), Ridder, Sjoerd de (author), Slob, E.C. (author)

Marchenko redatuming, imaging, monitoring and multiple elimination methods are based on Green’s function representations, with the underlying assumption that the wave field in the subsurface can be decomposed into downgoing and upgoing waves and that evanescent waves can be neglected. In this paper we show that up/down decomposition in the...

book chapter 2021

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Marchenko without up/down decomposition on the Marmousi model and retrieval of the refracted waves: Are they caused by the Marchenko algorithm?

Kiraz, Mert S. R. (author), Snieder, Roel (author), Wapenaar, C.P.A. (author)

Marchenko algorithms retrieve the Green’s function for arbitrary subsurface locations, and the retrieved Green’s function includes the primary and multiple reflected waves. The Marchenko algorithms require the estimate of the direct arrivals and the reflected waves; however, most previous Marchenko algorithms also require the up/down components...

book chapter 2021

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Focusing waves in an unknown medium without wavefield decomposition

Kiraz, Mert S. R. (author), Snieder, Roel (author), Wapenaar, C.P.A. (author)

The Gel'fand-Levitan equation, the Gopinath-Sondhi equation, and the Marchenko equation are developed for one-dimensional inverse scattering problems. Recently, a version of the Marchenko equation based on wavefield decomposition has been introduced for focusing waves in multi dimensions. However, wavefield decomposition is a limitation when...

journal article 2021

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Green’s function representations for Marchenko imaging without up/down decomposition

Wapenaar, C.P.A. (author), Snieder, Roel (author), de Ridder, Sjoerd (author), Slob, E.C. (author)

Marchenko methods are based on integral representations which express Green’s functions for virtual sources and/or receivers in the subsurface in terms of the reflection response at the surface. An underlying assumption is that inside the medium the wave field can be decomposed into downgoing and upgoing waves and that evanescent waves can be...

journal article 2021

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Accounting for free-surface multiples in Marchenko imaging

Singh, S. (author), Snieder, R (author), van der Neut, J.R. (author), Thorbecke, J.W. (author), Slob, E.C. (author), Wapenaar, C.P.A. (author)

Imagine placing a receiver at any location in the earth and recording the response at that location to sources on the surface. In such a world, we could place receivers around our reservoir to better image the reservoir and understand its properties. Realistically, this is not a feasible approach for understanding the subsurface. We have...

journal article 2017

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Imaging an unknown object in an unknown medium

Snieder, R (author), Wapenaar, C.P.A. (author)

Imaging an unknown object in a medium that is known, such as a medium with constant velocity, is not difficult because one knows exactly where the waves are when they interact with the object. It is much more challenging to image an object in an unknown medium, because in that case one may know the waves that one sends into the medium, but one...

abstract 2016

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Beyond Marchenko: Obtaining virtual receivers and virtual sources in the subsurface

Singh, S. (author), Wapenaar, C.P.A. (author), van der Neut, J.R. (author), Snieder, R (author)

By solving the Marchenko equations, the Green’s function can be retrieved between a virtual receiver in the subsurface to points at the surface (no physical receiver is required at the virtual location). We extend the idea of these equations to retrieve the Green’s function between any two points in the subsurface; i.e, between a virtual source...

conference paper 2016

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Imaging the earth's interior with virtual sources and receivers

Wapenaar, C.P.A. (author), van der Neut, J.R. (author), Thorbecke, J.W. (author), Slob, E.C. (author), Snieder, R (author)

abstract 2016

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Seismic reflection imaging, accounting for primary and multiple reflections

Wapenaar, C.P.A. (author), Van der Neut, J.R. (author), Thorbecke, J.W. (author), Broggini, F. (author), Slob, E.C. (author), Snieder, R. (author)

journal article 2015

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Marchenko imaging: Imaging with primaries, internal multiples, and free-surface multiples

Singh, S. (author), Snieder, R. (author), Behura, J. (author), van der Neut, J.R. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)

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 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...

journal article 2015

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Autofocusing imaging: Imaging with primaries, internal multiples and free-surface multiples

Singh, S. (author), Snieder, R. (author), Behura, J. (author), van der Neut, J.R. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)

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...

conference paper 2014

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Marchenko imaging

Wapenaar, C.P.A. (author), Thorbecke, J.W. (author), Van der Neut, J.R. (author), Broggini, F. (author), Slob, E.C. (author), Snieder, R. (author)

lecture notes 2014

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Autofocus imaging: Image reconstruction based on inverse scattering theory

Behura, J. (author), Wapenaar, C.P.A. (author), Snieder, R. (author)

Conventional imaging algorithms assume single scattering and therefore cannot image multiply scattered waves correctly. The multiply scattered events in the data are imaged at incorrect locations resulting in spurious subsurface structures and erroneous interpretation. This drawback of current migration/imaging algorithms is especially...

journal article 2014

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Marchenko imaging

Wapenaar, C.P.A. (author), Thorbecke, J.W. (author), Van der Neut, J.R. (author), Broggini, F. (author), Slob, E.C. (author), Snieder, R. (author)

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 in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic...

journal article 2014

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Data-driven wavefield focusing and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples

Broggini, F. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e., waves that have bounced multiple times between reflectors before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms...

journal article 2014

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Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

Wapenaar, C.P.A. (author), Thorbecke, J.W. (author), Van der Neut, J.R. (author), Broggini, F. (author), Slob, E.C. (author), Snieder, R. (author)

The methodology of Green’s function retrieval by cross-correlation has led to many interesting applications for passive and controlled-source acoustic measurements. In all applications, a virtual source is created at the position of a receiver. Here a method is discussed for Green’s function retrieval from controlled-source reflection data,...

journal article 2014

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Seismic reflector imaging using internal multiples with Marchenko-type equations

Slob, E.C. (author), Wapenaar, C.P.A. (author), Broggini, F. (author), Snieder, R. (author)

We present an imaging method that creates a map of reflection coefficients in correct one-way time with no contamination from internal multiples using purely a filtering approach. The filter is computed from the measured reflection response and does not require a background model. We demonstrate that the filter is a focusing wavefield that...

journal article 2014