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

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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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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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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 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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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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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

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Interferometric redatuming of autofocused primaries and internal multiples

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

Recently, an iterative scheme has been introduced to retrieve the down- and upgoing Green's functions at an arbitrary level ?F inside an acoustic medium as if there were a source at the surface. This scheme requires as input the reflection response acquired at the surface and the direct arrival of the transmission response from the surface to...

journal article 2013

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Three-dimensional Marchenko equation for Green's function retrieval “beyond seismic interferometry”

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

In recent work we showed with heuristic arguments that the Green's response to a virtual source in the subsurface can be obtained from reflection data at the surface. This method is called “Green's function retrieval beyond seismic interferometry”, because, unlike in seismic interferometry, no receiver is needed at the position of the virtual...

journal article 2013

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3D Marine CSEM Interferometry by Multidimensional Deconvolution in the Wavenumber Domain for a Sparse Receiver Grid

Hunziker, J.W. (author), Slob, E.C. (author), Fan, Y. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

We use interferometry by multidimensional deconvolution in combination with synthetic aperture sources in 3D to suppress the airwave and the direct field, and to decrease source uncertainty in marine Controlled-Source electromagnetics. We show with this numerical study that the method works for very large receiver spacing distances, even though...

conference paper 2013

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Data-driven green's function retrieval from reflection data: Theory and example

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

Recently we introduced a new approach for retrieving the Green's response to a virtual source in the subsurface from reflection data at the surface. Unlike in seismic interferometry, no receiver is needed at the position of the virtual source. Here we present the theory behind this new method. First we introduce the Green's function G and a so...

conference paper 2013

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Electromagnetic interferometry in wavenumber and space domains in a layered earth

Hunziker, J.W. (author), Slob, E.C. (author), Fan, Y. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

With interferometry applied to controlled-source electromagnetic data, the direct field and the airwave and all other effects related to the air-water interface can be suppressed in a data-driven way. Interferometry allows for retreival of the scattered field Green’s function of the subsurface or, in other words, the subsurface reflection...

journal article 2013

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Three-Dimensional Single-Sided Marchenko Inverse Scattering, Data-Driven Focusing, Green’s Function Retrieval, and their Mutual Relations

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

The one-dimensional Marchenko equation forms the basis for inverse scattering problems in which the scattering object is accessible from one side only. Here we derive a three-dimensional (3D) Marchenko equation which relates the single-sided reflection response of a 3D inhomogeneous medium to a field inside the medium. We show that this equation...

journal article 2013

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Synthesized 2D CSEM-interferometry Using Automatic Source Line Determination

Hunziker, J.W. (author), Slob, E.C. (author), Fan, Y. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

Interferometry by multidimensional deconvolution applied to Controlled-Source Electromagnetic data replaces the medium above the receivers by a homogeneous halfspace, suppresses the direct field and redatums the source positions to the receiver locations. In that sense, the airwave and any other interactions of the signal with the air-water...

conference paper 2012