High-resolution wave-equation amplitude-variation-with-ray-parameter (AVP) imaging with sparseness constraints

Wang, Juefu; Sacchi, Mauricio D.

doi:10.1190/1.2387139

Cited by 60 publications

(18 citation statements)

References 14 publications

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“…This may result in both inaccurate amplitudes and/or artefacts in the recovered structures which may also be treated in LSM by some form of regularization or preconditioning, respecting prior information to promote a more accurate representation of the subsurface model and introduce desired qualities. For example, Wang and Sacchi (2007) use a cost function for one-way wave-equation based LSM with regularization constraints for smoothness along offset-domain common image gathers (CIGs) and reflectivity sparseness in depth. Cabrales-Vargas and Marfurt (2013) also formulated a regularized least-squares Kirchhoff migration problem using a penalty function that controls the amount of roughness in common reflection point gathers (CRPGs).…”

Section: Introductionmentioning

confidence: 99%

Least-squares reverse time migration with radon preconditioning

Dutta

Agut

Giboli

et al. 2016

SEG Technical Program Expanded Abstracts 2016

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SummaryWe present a least-squares reverse time migration (LSRTM) method using Radon preconditioning to regularize noisy or severely undersampled data. A high resolution local radon transform is used as a change of basis for the reflectivity and sparseness constraints are applied to the inverted reflectivity in the transform domain. This reflects the prior that for each location of the subsurface the number of geological dips is limited. The forward and the adjoint mapping of the reflectivity to the local Radon domain and back are done through 3D Fourierbased discrete Radon transform operators. The sparseness is enforced by applying weights to the Radon domain components which either vary with the amplitudes of the local dips or are thresholded at given quantiles. Numerical tests on synthetic and field data validate the effectiveness of the proposed approach in producing images with improved SNR and reduced aliasing artifacts when compared with standard RTM or LSRTM.

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Section: Introductionmentioning

confidence: 99%

Least-squares reverse time migration with radon preconditioning

Dutta

Agut

Giboli

et al. 2016

SEG Technical Program Expanded Abstracts 2016

View full text Add to dashboard Cite

show abstract

“…The advantage of this formulation is that it uses curvelet-domain sparsity, which has proven to be a particularly powerful prior (Wang and Sacchi, 2007;Herrmann et al, 2008b,a;Hennenfent et al, 2008). We will report on the solution of Equation 11 elsewhere.…”

Section: Extensionsmentioning

confidence: 99%

Curvelet-based migration preconditioning and scaling

et al. 2009

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The extremely large size of typical seismic imaging problems has been one of the major stumbling blocks for iterative techniques to attain accurate migration amplitudes. These iterative methods are important because they complement theoretical approaches that are hampered by difficulties to control problems such as finite-acquisition aperture, sourcereceiver frequency response, and directivity. To solve these problems, we apply preconditioning, which significantly improves convergence of least-squares migration. We discuss different levels of preconditioning that range from corrections for the order of the migration operator to corrections for spherical spreading, and position and reflector-dip dependent amplitude errors. While the first two corrections correspond to simple scalings in the Fourier and physical domain, the third correction requires phase-space (space spanned by location and dip) scaling, which we carry out with curvelets. We show that our combined preconditioner leads to a significant improvement of the convergence of least-squares 'wave-equation' migration on a line from the SEG AA' salt model.

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“…Lustig et al, 2007, in magnetic resonance imaging). For example, when A is defined as A def = RMS H with M a modeling/demigration-like operator Wang and Sacchi, 2007). In this case, x 0 is the sparse representation of the Earth model in the S domain and y incomplete seismic data.…”

Section: Generalization Of the Concept Of Undersampling Artifactsmentioning

confidence: 99%

Simply denoise: Wavefield reconstruction via jittered undersampling

2008

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In this paper, we present a new discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements that are localized in the Fourier domain. Our work is motivated by empirical observations in the seismic community, corroborated by recent results from compressive sampling, which indicate favorable (wavefield) reconstructions from random as opposed to regular undersampling. As predicted by theory, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control and the main purpose of this paper is to introduce a sampling scheme, coined jittered undersampling, that shares the benefits of random sampling, while offering control on the maximum gap size. Our contribution of jittered sub-Nyquist sampling proves to be key in the formulation of a versatile wavefield sparsity-promoting recovery scheme that follows the principles of compressive sampling. After studying the behavior of the jittered undersampling scheme in the Fourier domain, its performance is studied for curvelet recovery by sparsity-promoting inversion (CRSI). Our findings on synthetic and real seismic data indicate an improvement of several decibels over recovery from regularly-undersampled data for the same amount of data collected.

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High-resolution wave-equation amplitude-variation-with-ray-parameter (AVP) imaging with sparseness constraints

Cited by 60 publications

References 14 publications

Least-squares reverse time migration with radon preconditioning

Least-squares reverse time migration with radon preconditioning

Curvelet-based migration preconditioning and scaling

Simply denoise: Wavefield reconstruction via jittered undersampling

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