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

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

document

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

document

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

document

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

document

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

document

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

document

On the estimation of attenuation from the ambient seismic field: Inferences from distributions of isotropic point scatterers

Weemstra, C. (author), Snieder, R (author), Boschi, Lapo (author)

journal article 2015

document

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

document

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

document

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

document

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

document

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

document

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

document

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

document

Data-driven Green's function retrieval and application to imaging with multidimensional deconvolution

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

An iterative method is presented that allows one to retrieve the Green's function originating from a virtual source located inside a medium using reflection data measured only at the acquisition surface. In addition to the reflection response, an estimate of the travel times corresponding to the direct arrivals is required. However, no detailed...

journal article 2014

document

On estimating attenuation from the amplitude of the spectrally whitened ambient seismic field

Weemstra, C. (author), Westra, W. (author), Snieder, R. (author), Boschi, L. (author)

Measuring attenuation on the basis of interferometric, receiver-receiver surface waves is a non-trivial task: the amplitude, more than the phase, of ensemble-averaged cross-correlations is strongly affected by non-uniformities in the ambient wavefield. In addition, ambient noise data are typically pre-processed in ways that affect the amplitude...

journal article 2014

document

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

document

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

document

Data-driven Green's function retrieval 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 bouncing multiple times between layers before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image...

journal article 2013