Seismic wavefield redatuming with regularized multi-dimensional deconvolution

Luiken, Nick; Leeuwen, Tristan van

doi:10.1088/1361-6420/aba9d1

Cited by 10 publications

(16 citation statements)

References 38 publications

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“…Instead of inverting G −,− R,B , the target responseR tar can be resolved directly from equation 24 by recasting the problem in terms of linear operators, which avoids the stabilization of (G −,− R,B ) −1 needed in equation 25 (Luiken and van Leeuwen, 2020).…”

Section: Receiver Redatuming By Mddmentioning

confidence: 99%

Marchenko redatuming, imaging, and multiple elimination and their mutual relations

Wapenaar

Brackenhoff

Dukalski³

et al. 2021

GEOPHYSICS

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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. The retrieved Green's functions form the input for redatuming by multidimensional deconvolution (MDD). The redatumed reflection response is free of internal multiples related to the overburden. Alternatively, the redatumed response can be obtained by applying a second focusing function to the retrieved Green's functions. This process is called Marchenko redatuming by double focusing. It is more stable and better suited for an adaptive implementation than Marchenko redatuming by MDD, but it does not eliminate the multiples between the target and the overburden. An attractive efficient alternative is plane-wave Marchenko redatuming, which retrieves the responses to a limited number of plane-wave sources at the redatuming level. In all cases, an image of the subsurface can be obtained from the redatumed data, free of artefacts caused by internal multiples. Another class of Marchenko methods aims at eliminating the internal multiples from the reflection data, while keeping the sources and receivers at the surface. A specific characteristic of this form of multiple elimination is that it predicts and subtracts all orders of internal multiples with the correct amplitude, without needing a macro subsurface model. Like Marchenko redatuming, Marchenko multiple elimination can be implemented as an MDD process, a double dereverberation process, or an efficient plane-wave oriented process. We systematically discuss the different approaches to Marchenko redatuming, imaging and multiple elimination, using a common mathematical framework.

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Section: Receiver Redatuming By Mddmentioning

confidence: 99%

Marchenko redatuming, imaging, and multiple elimination and their mutual relations

Wapenaar

Brackenhoff

Dukalski³

et al. 2021

GEOPHYSICS

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“…Moreover, no theory exists to define how to choose different λ for each frequency inversion that are consistent with each other. Equally important is the source to receiver ratio and the band-limited character of the sources [29]. Finally, the absence of a clear causality constraint in ω-domain lead to solutions containing acausal events.…”

Section: Frequency Domain Mdd-regularized Least Squaresmentioning

confidence: 99%

“…In an effort to alleviate these issues, further physical priors can be included in the solution of the inverse problem primarily to impose desired physical constraints on the solution while also stabilizing the inverse problem. The inverse problem is therefore posed as a constrained least-squares problem which enforces the reconstruction of g to belong to a restricted subset of solutions G [29],…”

Section: Time Domain Mdd-constrained Least Squaresmentioning

confidence: 99%

“…Alternatively, MDD can also be solved in the time domain as a single coupled inverse problem: whilst this approach is less known and not widely adopted yet, it has recently been shown to be more robust as solving for the entire frequency spectrum at once acts as a natural regularizer and does not require the identification of damping parameters for each frequency independently. In this direction, pioneering work has been carried out by van der Neut and Herrmann [27], van der Neut et al [28], Luiken and van Leeuwen [29], Ravasi and Vasconcelos [30], who also proposed the use of different regularization and preconditioning strategies to further alleviate the ill-posedness of the inverse problem. More specifically, van der Neut and Herrmann [27] investigate the use of sparsifying transforms (i.e., Curvelets) in combination with sparsity-promoting inversion to improve the robustness of the solution to noise in the data and mitigates artefacts arising from limited-aperture source arrays.…”

Section: Introductionmentioning

confidence: 99%

“…More specifically, van der Neut and Herrmann [27] investigate the use of sparsifying transforms (i.e., Curvelets) in combination with sparsity-promoting inversion to improve the robustness of the solution to noise in the data and mitigates artefacts arising from limited-aperture source arrays. Van der Neut et al and Luiken and van Leeuwen [28,29] on the other hand, introduce physics-based preconditioners to guarantee the solution of the inverse problem to satisfy a priori information such as causality and reciprocity. Finally, in the context of acoustic laboratory experiments, time-domain MDD has also been recently shown great promise to remove domain boundary effects [7].…”

Section: Introductionmentioning

confidence: 99%

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Time-Domain Multidimensional Deconvolution: A Physically Reliable and Stable Preconditioned Implementation

et al. 2021

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Multidimensional deconvolution constitutes an essential operation in a variety of geophysical scenarios at different scales ranging from reservoir to crustal, as it appears in applications such as surface multiple elimination, target-oriented redatuming, and interferometric body-wave retrieval just to name a few. Depending on the use case, active, microseismic, or teleseismic signals are used to reconstruct the broadband response that would have been recorded between two observation points as if one were a virtual source. Reconstructing such a response relies on the the solution of an ill-conditioned linear inverse problem sensitive to noise and artifacts due to incomplete acquisition, limited sources, and band-limited data. Typically, this inversion is performed in the Fourier domain where the inverse problem is solved per frequency via direct or iterative solvers. While this inversion is in theory meant to remove spurious events from cross-correlation gathers and to correct amplitudes, difficulties arise in the estimation of optimal regularization parameters, which are worsened by the fact they must be estimated at each frequency independently. Here we show the benefits of formulating the problem in the time domain and introduce a number of physical constraints that naturally drive the inversion towards a reduced set of stable, meaningful solutions. By exploiting reciprocity, time causality, and frequency-wavenumber locality a set of preconditioners are included at minimal additional cost as a way to alleviate the dependency on an optimal damping parameter to stabilize the inversion. With an interferometric redatuming example, we demonstrate how our time domain implementation successfully reconstructs the overburden-free reflection response beneath a complex salt body from noise-contaminated up- and down-going transmission responses at the target level.

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Target-oriented least-squares reverse-time migration using Marchenko double-focusing: reducing the artefacts caused by overburden multiples

Aydin

Neut

Wapenaar

2022

Geophysical Journal International

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Summary Geophysicists have widely used Least-squares reverse-time migration (LSRTM) to obtain high-resolution images of the subsurface. However, LSRTM is computationally expensive and it can suffer from multiple reflections. Recently, a target-oriented approach to LSRTM has been proposed, which focuses the wavefield above the target of interest. Remarkably, this approach can be helpful for imaging below complex overburdens and subsalt domains. Moreover, this approach can significantly reduce the computational burden of the problem by limiting the computational domain to a smaller area. Nevertheless, target-oriented LSRTM still needs an accurate velocity model of the overburden to focus the wavefield accurately and predict internal multiple reflections correctly. A viable alternative to an accurate velocity model for internal multiple prediction is Marchenko redatuming. This method is a novel data-driven method that can predict Green’s functions at any arbitrary depth, including all orders of multiples. The only requirement for this method is a smooth background velocity model of the overburden. Moreover, with Marchenko double-focusing, one can make virtual sources and receivers at a boundary above the target and bypass the overburden. This paper proposes a new algorithm for target-oriented LSRTM, which fits the Marchenko double-focused data with predicted data. The predicted data of the proposed method is modeled by a virtual source term created by Marchenko double-focusing on a boundary above the target of interest. This virtual source term includes all the interactions between the target and the overburden. Moreover, the Marchenko double-focused data and the virtual source term are free of multiples generated in the overburden. Consequently, our target-oriented LSRTM algorithm suppresses the multiples purely generated inside the overburden. It correctly accounts for all orders of multiples caused by the interactions between the target and the overburden, resulting in a significant reduction of the artifacts caused by the overburden internal multiple reflections and improves amplitude recovery in the target image compared to conventional LSRTM.

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Seismic wavefield redatuming with regularized multi-dimensional deconvolution

Cited by 10 publications

References 38 publications

Marchenko redatuming, imaging, and multiple elimination and their mutual relations

Marchenko redatuming, imaging, and multiple elimination and their mutual relations

Time-Domain Multidimensional Deconvolution: A Physically Reliable and Stable Preconditioned Implementation

Target-oriented least-squares reverse-time migration using Marchenko double-focusing: reducing the artefacts caused by overburden multiples

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