Prestack rank‐reducing noise suppression: Theory

Trickett, Stewart; Burroughs, Lynn

doi:10.1190/1.3255552

Cited by 37 publications

(19 citation statements)

References 9 publications

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“…For instance, eigenimage filtering (Ulrych et al, 1988), similar to filtering via the Karhunen-Loève transform (Jones and Levy, 1987), can operate directly on the seismic data in the t-x or f-x-y domain (Trickett, 2003). Recently, the singular spectrum analysis (SSA) method (Sacchi, 2009;Oropeza and Sacchi, 2011), also known as Cadzow filtering (Trickett, 2008;Trickett and Burroughs, 2009), was introduced to attenuate incoherent noise and for seismic data reconstruction (Oropeza and Sacchi, 2011;Gao et al, 2013). It is also important to note that reduced-rank filtering based on SSA has been also used to suppress coherent noise (Nagarajappa, 2012;Chiu, 2013).…”

Section: Introductionmentioning

confidence: 99%

Robust reduced-rank filtering for erratic seismic noise attenuation

2015

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Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two lower dimensional factor matrices. The iteratively reweighed least-squares method was used to approximately solve for the optimal robust factorization. Our algorithm was tested with synthetic and real data. In our synthetic examples, the data were contaminated with band-limited Gaussian noise and erratic noise. Then, denoising was carried out by means of f-x deconvolution, the classical SSA method, and the proposed robust SSA method. The f-x deconvolution and the classical SSA method failed to properly eliminate the noise and to preserve the desired signal. On the other hand, the robust SSA method was found to be immune to erratic noise and was able to preserve the desired signal. We also tested the robust SSA method with a data set from the Western Canadian Sedimentary Basin. The results with this data set revealed improved denoising performance in portions of data contaminated with erratic noise.

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Section: Introductionmentioning

confidence: 99%

Robust reduced-rank filtering for erratic seismic noise attenuation

2015

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“…In the absence of noise, the Hankel marix formed by seismic data is rank deficient [21,22]. However, due to noise in the observed data, the rank of the data Hankel matrix is higher than it should be.…”

Section: Introductionmentioning

confidence: 99%

“…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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“…It can handle irregular sampling and aliased noise with minimal spatial smearing of amplitudes. The eigenimage filter also relates to a class of denoising techniques that use rank reduction of a Hankel matrix to approximate the signals (Trickett and Burroughs 2009).…”

Section: Introductionmentioning

confidence: 99%

Coherent and random noise attenuation via multichannel singular spectrum analysis in the randomized domain

Chiu

2012

Geophysical Prospecting

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The attenuation of coherent and random noise still poses technical challenges in seismic data processing, especially in onshore environments. Multichannel Singular Spectrum Analysis (MSSA) is an existing and effective technique for random‐noise reduction. By incorporating a randomizing operator into MSSA, this modification creates a new and powerful filtering method that can attenuate both coherent and random noise simultaneously. The key of the randomizing operator exploits the fact that primary events after NMO are relatively horizontal. The randomizing operator randomly rearranges the order of input data and reorganizes coherent noise into incoherent noise but has a minimal effect on nearly horizontal primary reflections. The randomizing process enables MSSA to suppress both coherent and random noise simultaneously. This new filter, MSSARD (MSSA in the randomized domain) also resembles a combination of eigenimage and Cadzow filters. I start with a synthetic data set to illustrate the basic concept and apply MSSARD filtering on a 3D cross‐spread data set that was severely contaminated with ground roll and scattered noise. MSSARD filtering gives superior results when compared with a conventional 3D f‐k filter. For a random‐noise example, the application of MSSARD filtering on time‐migrated offset‐vector‐tile (OVT) gathers also produces images with higher signal‐to‐noise ratios than a conventional f‐xy deconvolution filter.

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Prestack rank‐reducing noise suppression: Theory

Cited by 37 publications

References 9 publications

Robust reduced-rank filtering for erratic seismic noise attenuation

Robust reduced-rank filtering for erratic seismic noise attenuation

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

Coherent and random noise attenuation via multichannel singular spectrum analysis in the randomized domain

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