Rank‐reduction‐based trace interpolation

Trickett, Stewart; Burroughs, Lynn; Milton, A. F.; Walton, Larry; Dack, Rob

doi:10.1190/1.3513645

Cited by 146 publications

(38 citation statements)

References 12 publications

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“…These methods use the predictability of linear events in the frequency-space domain to interpolate aliased data at high frequencies with fi lters derived from low frequencies. Finally, a third group of methods is based on rank reduction (Trickett et al, 2010;Kreimer and Sacchi, 2011). Properly sampled multichannel data are embedded into a low-rank Hankel matrix.…”

Section: Introductionmentioning

confidence: 99%

A fast-convergence POCS seismic denoising and reconstruction method

Pan

et al. 2015

Appl. Geophys.

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The effi ciency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets (POCS) algorithm, we propose an inversely proportional threshold model that defi nes the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coeffi cient section and slower than in the exponential threshold in the small-coeffi cient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak refl ections. To improve the fl exibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and fi eld data. The results suggest that the inversely proportional threshold model improves the computational effi ciency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.

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Section: Introductionmentioning

confidence: 99%

A fast-convergence POCS seismic denoising and reconstruction method

Pan

et al. 2015

Appl. Geophys.

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“…There exist many effective methods to reconstruct the complete seismic wavefield depending on different acquisition geometries (Trickett et al, 2010;Naghizadeh and Sacchi, 2010). These methods can be roughly classified into two categories:…”

Section: Introductionmentioning

confidence: 99%

“…However, fully recording the seismic data is unrealistic for many reasons: a finite number of active recording channels, surface obstacles, as well as some other physical and financial constraints (Curry, 2008). Therefore, the prestack trace interpolation of these uniformly or nonuniformly sampled seismic records prior to migration is seriously needed (Trickett et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

On analysis-based two-step interpolation methods for randomly sampled seismic data

Yang

Gao

Chen

2013

Computers & Geosciences

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“…Trickett furthered Cadzow filtering by applying eigenimage filtering to 3D data frequency slices and later extended F-x Cadzow filtering to F-xy Cadzow filtering by forming a larger Hankel matrix of Hankel matrices (Level-2 Block Hankel matrix) in multiple spatial dimensions [21][22][23]. In 2013, Gao et al [13] developed a rank reduction denoising and reconstruction scheme that is used to reconstruct prestack data that depend on four spatial dimensions by forming a Level-4 Block Toeplitz matrix.…”

Section: Introductionmentioning

confidence: 99%

A fast SVD for multilevel block Hankel matrices with minimal memory storage

Qiao

2014

Numer Algor

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Motivated by the Cadzow filtering in seismic data processing, this paper presents a fast SVD method for multilevel block Hankel matrices. A seismic data presented as a multidimensional array is first transformed into a two dimensional multilevel block Hankel (MBH) matrix. Then the Lanczos process is applied to reduce the MBH matrix into a bidiagonal or tridiagonal matrix. Finally, the SVD of the reduced matrix is computed using the twisted factorization method. To achieve high efficiency, we propose a novel fast MBH matrix-vector multiplication method for the Lanczos process. In comparison with existing fast Hankel matrix-vector multiplication methods, our method applies 1-D, instead of multidimensional, FFT and requires minimum storage. Moreover, a partial SVD is performed on the reduced matrix, since complete SVD is not required by the Caszow filtering. Our numerical experiments show that our fast MBH matrix-vector multiplication method significantly improves both the computational cost and storage requirement. Our fast MBH SVD algorithm is particularly efficient for large size multilevel block Hankel matrices.

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Rank‐reduction‐based trace interpolation

Cited by 146 publications

References 12 publications

A fast-convergence POCS seismic denoising and reconstruction method

A fast-convergence POCS seismic denoising and reconstruction method

On analysis-based two-step interpolation methods for randomly sampled seismic data

A fast SVD for multilevel block Hankel matrices with minimal memory storage

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