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 neglected. We present a new derivation of Green’s function representations which circumvents these assumptions, both for the acoustic and the elastodynamic situation. These representations form the basis for research into new Marchenko methods which have the potential to handle refracted and evanescent waves and to more accurately image steeply dipping reflectors.

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

PreviousNext No AccessSecond International Meeting for Applied Geoscience & EnergyTowards understanding the impact of the evanescent elastodynamic mode coupling in Marchenko equation-based demultiple methodsAuthors: Marcin DukalskiChristian ReinickeKees WapenaarMarcin DukalskiAramco Delft Global Research CenterSearch for more papers by this author, Christian ReinickeAramco Delft Global Research CenterSearch for more papers by this author, and Kees WapenaarDelft University of TechnologySearch for more papers by this authorhttps://doi.org/10.1190/image2022-3745607.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail AbstractMarchenko equation-based methods promise data-driven, true-amplitude internal multiple elimination. The method is exact in 1-D acoustic media, however it needs to be expanded to account for the presence of 2- and 3-D elastodynamic wave-field phenomena, such as compressional (P) to shear (S) mode conversions, total reflections or evanescent waves. Mastering high waveform-fidelity methods such as this, could further advance amplitude vs offset analysis and lead to improved reservoir characterization. This method-expansion may comprise of re-evaluating the underlying assumptions and/or appending the scheme with additional constraints (e.g. minimum phase). To do that, one may need to better understand the construction of the Marchenko equation solutions, the so-called focusing functions, in a mathematically simple and numerically stable fashion. The latter could be a challenge at large angles of incidence where the elastodynamic effects and evanescent waves start playing a dominant role. We demonstrate that the elastodynamic focusing functions are the bridge between the Marchenko equation theory and the transfer matrix formalism. Using the latter, we show how we can try to gain further insights into how time-reversal (correlations) behaves when either of the elastic modes becomes evanescent. We also show how this construction allows us to shed light on into the mathematical properties of elastodynamic inverse transmissions, which takes us a step closer towards understanding the elastodynamic minimum phase reconstruction.Keywords: Internal multiples, Marchenko method, modelingPermalink: https://doi.org/10.1190/image2022-3745607.1FiguresReferencesRelatedDetailsCited byThe propagator and transfer matrix for a 3D inhomogeneous dissipative acoustic medium, expressed in Marchenko focusing functionsKees Wapenaar, Sjoerd de Ridder, Marcin Dukalski, and Christian Reinicke15 August 2022 Second International Meeting for Applied Geoscience & EnergyISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2022 Pages: 3694 publication data© 2022 Published in electronic format with permission by the Society of Exploration Geophysicists and the American Association of Petroleum GeologistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 15 Aug 2022 CITATION INFORMATION Marcin Dukalski, Christian Reinicke, and Kees Wapenaar, (2022), "Towards understanding the impact of the evanescent elastodynamic mode coupling in Marchenko equation-based demultiple methods," SEG Technical Program Expanded Abstracts : 2827-2831. https://doi.org/10.1190/image2022-3745607.1 Plain-Language Summary KeywordsInternal multiplesMarchenko methodmodelingPDF DownloadLoading ... 

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Towards understanding the impact of the evanescent elastodynamic mode coupling in Marchenko equation-based demultiple methods

Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions, and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, source vectors, and wave-field vectors. The matrix-vector formalism also allows the formulation of representations in which propagator matrices replace the Green's matrices. These propagator matrices, in turn, can be expressed in terms of Marchenko-type focusing functions. An advantage of the representations with propagator matrices and focusing functions is that the boundary integrals in these representations are limited to a single open boundary. This makes these representations a suitable basis for developing advanced inverse scattering, imaging and monitoring methods for wave fields acquired on a single boundary. 

Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions

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

PreviousNext No AccessSecond International Meeting for Applied Geoscience & EnergyThe propagator and transfer matrix for a 3D inhomogeneous dissipative acoustic medium, expressed in Marchenko focusing functionsAuthors: Kees WapenaarSjoerd de RidderMarcin DukalskiChristian ReinickeKees WapenaarDelft University of TechnologySearch for more papers by this author, Sjoerd de RidderUniversity of LeedsSearch for more papers by this author, Marcin DukalskiAramco Delft Global Research CenterSearch for more papers by this author, and Christian ReinickeAramco Delft Global Research CenterSearch for more papers by this authorhttps://doi.org/10.1190/image2022-3735927.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail AbstractStandard Marchenko redatuming and imaging schemes neglect evanescent waves and are based on the assumption that decomposition into downgoing and upgoing waves is possible in the subsurface. Recently we have shown that propagator matrices, which circumvent these assumptions, can be expressed in terms of Marchenko focusing functions. In this paper we generalize the relation between the propagator matrix and the Marchenko focusing functions for a 3D inhomogeneous dissipative medium. Moreover, for the same type of medium we discuss a relation between the transfer matrix and the Marchenko focusing functions.Keywords: Marchenko, multiple, propagatorPermalink: https://doi.org/10.1190/image2022-3735927.1FiguresReferencesRelatedDetails Second International Meeting for Applied Geoscience & EnergyISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2022 Pages: 3694 publication data© 2022 Published in electronic format with permission by the Society of Exploration Geophysicists and the American Association of Petroleum GeologistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 15 Aug 2022 CITATION INFORMATION Kees Wapenaar, Sjoerd de Ridder, Marcin Dukalski, and Christian Reinicke, (2022), "The propagator and transfer matrix for a 3D inhomogeneous dissipative acoustic medium, expressed in Marchenko focusing functions," SEG Technical Program Expanded Abstracts : 3141-3145. https://doi.org/10.1190/image2022-3735927.1 Plain-Language Summary KeywordsMarchenkomultiplepropagatorPDF DownloadLoading ... 

https://repository.tudelft.nl/islandora/object/uuid%3Af679a158-5ec9-4af3-a168-123a57cc1e6a/datastream/OBJ/download

The propagator and transfer matrix for a 3D inhomogeneous dissipative acoustic medium, expressed in Marchenko focusing functions

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 waves propagate horizontally at the focusing level. Here, the Marchenko equation for focusing without wavefield decomposition is derived, and by iteratively solving the Marchenko equation, the Green's function for an arbitrary location in the medium is retrieved from the scattered waves recorded on a closed receiver array and an estimate of the direct-wave without wavefield decomposition.

Focusing waves in an unknown medium without wavefield decomposition

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 of the Marchenko equation for the Green’s function retrieval. We use the Marmousi model to retrieve the Green’s function without using the up/down components of the Marchenko equation and show that the retrieved Green’s function matches with the numerically modeled Green’s function. We also show that the refracted waves can be successfully produced independently from the acquisition geometry, i.e., singlesided or two-sided; however, the retrieval of refracted waves that arrive before the first primary waves is inconsistent with the requirement that the Green’s function vanishes before the direct wave. Even though we retrieve such refracted waves, they are caused by the injection of the direct wave into su ciently detailed background velocity and density models instead of operations of the Marchenko algorithm on the recorded wavefields.

Mert S. R. Kiraz

Papers

Focusing waves in an unknown medium without wavefield decomposition

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