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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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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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van der Neut, J.R. (author), Brackenhoff, J.A. (author), Meles, G.A. (author), Zhang, L. (author), Slob, E.C. (author), Wapenaar, C.P.A. (author)A Green's function in an acoustic medium can be retrieved from reflection data by solving a multidimensional Marchenko equation. This procedure requires a priori knowledge of the initial focusing function, which can be interpreted as the inverse of a transmitted wavefield as it would propagate through the medium, excluding (multiply)...journal article 2022
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van der Neut, J.R. (author), Brackenhoff, J. (author), Meles, Giovanni Angelo (author), Slob, E.C. (author), Wapenaar, C.P.A. (author)Green’s functions in an unknown elastic layered medium can be retrieved from single-sided reflection data by solving a Marchenko equation. This methodology requires a priori knowledge of all forward-scattered (non-converted and converted) waveforms. Moreover, the medium should satisfy stringent monotonicity conditions, which are often not met in...conference paper 2022
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Wapenaar, C.P.A. (author), Slob, E.C. (author)Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum...journal article 2022
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van der Neut, J.R. (author), Brackenhoff, Joeri (author), Meles, Giovanni Angelo (author), Slob, E.C. (author), Wapenaar, C.P.A. (author)By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and...journal article 2022
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van der Neut, J.R. (author), Brackenhoff, J. (author), Meles, G. (author), Zhang, L. (author), Slob, E.C. (author), Wapenaar, C.P.A. (author)Green’s functions in an unknown medium can be retrieved from single-sided reflection data by solving a multidimensional Marchenko equation. This methodology requires knowledge of the direct wavefield throughout the medium, which should include forward-scattered waveforms. In practice, the direct field is often computed in a smooth background...conference paper 2021
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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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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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Thorbecke, J.W. (author), Zhang, L. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)The Marchenko multiple elimination (MME) and transmission compensation schemes retrieve primary reflections in the two-way traveltime domain without model information or using adaptive subtraction. Both schemes are derived from projected Marchenko equations and are similar to each other, but they use different time-domain truncation operators...journal article 2021
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Wapenaar, C.P.A. (author), Brackenhoff, J.A. (author), Dukalski, Marcin (author), Meles, G.A. (author), Slob, E.C. (author), Staring, M. (author), Thorbecke, J.W. (author), van der Neut, J.R. (author), Zhang, L. (author), Reinicke Urruticoechea, C. (author)With the Marchenko method it is possible to retrieve Green's functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusing functions. A macro model of the subsurface is needed to estimate the first arrival; the internal multiples are retrieved entirely from the reflection data....journal article 2021
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Meles, G.A. (author), Zhang, L. (author), Thorbecke, J.W. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)Seismic images provided by reverse time migration can be contaminated by artefacts associated with the migration of multiples. Multiples can corrupt seismic images, producing both false positives, that is by focusing energy at unphysical interfaces, and false negatives, that is by destructively interfering with primaries. Multiple prediction...journal article 2020
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Wapenaar, C.P.A. (author), Staring, M. (author), Brackenhoff, J.A. (author), Zhang, L. (author), Thorbecke, J.W. (author), Slob, E.C. (author)Since the introduction of the Marchenko method in geophysics, many variants have been developed. Using a compact unified notation, we review redatuming by multidimensional deconvolution and by double focusing, virtual seismology, double dereverberation and transmission-compensated Marchenko multiple elimination, and discuss the underlying...conference paper 2020
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Meles, G.A. (author), Zhang, L. (author), Thorbecke, J.W. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)<br/>abstract 2020
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Meles, G.A. (author), Zhang, L. (author), Thorbecke, J.W. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)Seismic images provided by reverse time migration can be contaminated by artefacts associated with the migration of multiples.<br/><br/>Multiples can corrupt seismic images, producing both false positives, i.e. by focusing energy at unphysical interfaces, and false negatives, i.e. by destructively interfering with primaries. Multiple-related...conference paper 2020
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Slob, E.C. (author), Wapenaar, C.P.A. (author), Treitel, Sven (author)Acoustic inversion in one-dimension gives impedance as a function of travel time.<br/>Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the...journal article 2020
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Zhang, L. (author), Thorbecke, J.W. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require...journal article 2019
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Zhang, L. (author), Thorbecke, J.W. (author), Wapenaar, C.P.A. (author), Slob, E.C. (author)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 truncation operators. The first scheme creates a new data set without internal multiple reflections. The...journal article 2019
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Wapenaar, C.P.A. (author), Brackenhoff, J.A. (author), Thorbecke, J.W. (author), van der Neut, J.R. (author), Slob, E.C. (author), Verschuur, D.J. (author)A virtual acoustic source inside a medium can be created by emitting a time-reversed point-source response from the enclosing boundary into the medium. However, in many practical situations the medium can be accessed from one side only. In those cases the time-reversal approach is not exact. Here, we demonstrate the experimental design and...journal article 2018
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- van der Neut, J.R. (author), Brackenhoff, Joeri (author), Staring, Myrna (author), Zhang, L. (author), de Ridder, S.A.L. (author), Slob, E.C. (author), Wapenaar, C.P.A. (author) journal article 2018