Block-Krylov methods for multi-dimensional deconvolution

Luiken, Nick; Garg, Aayush

doi:10.1190/segam2019-3216690.1

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…Content may change prior to final publication. Citation information: DOI 10.1109/TGRS.2022.3179626, IEEE Transactions on Geoscience and Remote Sensing 3 [16] or iterative Block-Krylov solvers [26]. Alternatively, a time-domain formulation can be written as [20]:…”

Section: Theorymentioning

confidence: 99%

Stochastic Multi-Dimensional Deconvolution

Ravasi

Selvan

Luiken

2022

IEEE Trans. Geosci. Remote Sensing

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Geophysical measurements such as seismic datasets contain valuable information that originate from areas of interest in the subsurface; these seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden. Multi-Dimensional Deconvolution (MDD) is a powerful technique used at various stages of the seismic processing sequence to create ideal datasets deprived of such overburden effects. Whilst the underlying forward problem holds for a single source, a successful inversion of the MDD equations requires availability of a large number of sources alongside prior information, possibly introduced in the form of physical constraints (e.g., reciprocity and causality). In this work, we present a novel formulation of time-domain MDD based on a finite-sum functional. The associated inverse problem is then solved by means of stochastic gradient descent algorithms, where the gradients at each iteration are computed using a small subset of randomly selected sources. Through synthetic and field data examples, we show that the proposed method converges more stably than the conventional approach based on full gradients. Stochastic MDD represents a novel, efficient, and robust strategy to deconvolve seismic wavefields in a multi-dimensional fashion.

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Section: Theorymentioning

confidence: 99%

Stochastic Multi-Dimensional Deconvolution

Ravasi

Selvan

Luiken

2022

IEEE Trans. Geosci. Remote Sensing

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“…This expression can be physically interpreted as follows: the point spread function (PSF), Γ Γ Γ = ( P+ ) H P+ , acts as a blurring operator on the sought after solution, resulting in a band-limited cross-correlation function (CCF), C = ( P+ ) H P− . Inversion of the normal equations, C = Γ Γ Γ Ĝp , is performed for every frequency independently; this can be accomplished by means of either direct or block Krylov methods (Luiken et al, 2019).…”

Section: Frequency Domain Mddmentioning

confidence: 99%

Physics-based preconditioned multidimensional deconvolution in the time domain

Vargas

Vasconcelos

Ravasi

et al. 2022

Second International Meeting for Applied Geoscience &Amp; Energy

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Multi-Dimensional Deconvolution is a data-driven method that is at the center of key seismic processing applications -from suppressing multiples to inversion-based imaging. When posed in an interferometric context, it can grant access to overburdenfree seismic virtual surveys at a given datum in the subsurface. As such, it constitutes an essential processing operation that achieves multiple imaging objectives simultaneously in redatuming or target-oriented imaging: e.g., suppressing multiples, removing complex overburden effects, and retrieving amplitude consistent image gathers for impedance inversion. Despite its potential, the deconvolution process relies on the solution of an ill-conditioned linear inverse problem sensitive to noise artifacts due to incomplete acquisition, limited sources, and band-limited data. Typically, this inversion is performed in the Fourier domain where the estimation of optimal regularization parameters hinders accurate waveform reconstruction. We reformulate the problem in the time domain -long believed to be computationally intractable -and introduce several physical constraints that naturally drive the inversion towards a reduced set of reliable, stable solutions. This allows to successfully reconstruct the overburden-free reflection response beneath a complex salt body from noise-contaminated data.

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“…Inversion of the normal equations, C = ΓG, in the frequency domain is commonly done for each frequency slice individually. Since the stabilized point spread function is inverted per frequency component, the required memory is such that, operator and data matrices of size (n r × n s ) can be explicitly defined, therefore, this strategy is computationally feasible and in many cases direct or block Krylov methods can be used [48,49]. A major drawback in solving (8) lies in the difficulty of selecting an optimal regularization parameter, in fact, many of the parameter selection methods rely on solving the system multiples times and select λ based on an additional minimization problem [50].…”

Section: Frequency Domain Mdd-regularized Least Squaresmentioning

confidence: 99%

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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Block-Krylov methods for multi-dimensional deconvolution

Cited by 3 publications

References 3 publications

Stochastic Multi-Dimensional Deconvolution

Stochastic Multi-Dimensional Deconvolution

Physics-based preconditioned multidimensional deconvolution in the time domain

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

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