Curvelet-based POCS interpolation of nonuniformly sampled seismic records

Yang, Pengliang; Gao, Jinghuai; Chen, Wenchao

doi:10.1016/j.jappgeo.2011.12.004

Cited by 56 publications

(21 citation statements)

References 45 publications

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“…2 The convergence rate of these algorithms proves to be remarkably improved by the exponential and the data-driven decreasing thresholding schemes in Eqs. (24) and (25) (Gao et al, 2010Yang et al, 2011). The linear and exponential decreasing thresholding strategies are graphically plotted in Fig.…”

Section: Thresholding Strategiesmentioning

confidence: 99%

“…There are many such nice transforms available, such as the Fourier transform, various of orthogonal wavelet transforms, as well as the redundant transforms. Curvelet transform has been successfully applied by Hennenfent et al (2010), and also tested with the IST algorithm and POCS algorithm by us in Yang et al (2011). Even so, we mainly consider the fast Fourier transform (FFT) to analyze the seismic data.…”

Section: Tight Frame-based Transform Invoked: Fftmentioning

confidence: 99%

“…(2) Reconstruction with the aid of certain type of transforms such as the Fourier transform (Sacchi et al, 1998;Liu and Sacchi, 2004;Xu et al, 2005;Abma and Kabir, 2006;Naghizadeh, 2007), the Radon transform (Trad and Ulrych, 2002;Trad et al, 2003), the curvelet transform (Hennenfent, 2008;Hennenfent et al, 2010;Naghizadeh and Sacchi, 2010;Yang et al, 2011), etc., The latter is intended to exploit the transform domain sparsity and works well for irregularly sampled seismic records.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the basis pursuit denoising (BPDN) model (Chen et al, 2001), Herrmann and Hennenfent (2008) and Hennenfent et al (2010) applied the iterative shrinkage-thresholding (IST) algorithm to interpolation of nonuniformly recorded seismic traces. Another existing thresholding algorithm, namely the projection onto convex sets (POCS) method introduced by Abma and Kabir (2006), has been proved to solve this seismic interpolation problem equivalently (Yang et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Due to the slow convergence rate of these existing algorithms, researchers have studied the techniques to improve the convergence performance: Beck and Teboulle (2009) proposed a fast iterative shrinkage-thresholding algorithm (FISTA) from a more general mathematical background; Gao et al (2010) and Yang et al (2011) utilized the exponential decreasing thresholding strategy as the substitute of the linear one employed by Abma and Kabir;Gao et al (2011) even proposed a data-driven schedule.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Yang

Gao

Chen

2013

Computers & Geosciences

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Section: Thresholding Strategiesmentioning

confidence: 99%

Section: Tight Frame-based Transform Invoked: Fftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Yang

Gao

Chen

2013

Computers & Geosciences

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Curvelet‐based 3d Reconstruction of Digital Cores Using the Pocs Method

Wang

Chen

et al. 2015

Chinese J of Geophysics

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With the development of shale‐gas exploration and exploitation, exploitation is necessary to study the 3D spatial distribution of shale fractures for research on shale rock physics. Because of the limitation of instruments, accurate shale slice is discontinuous in depth, and the minimum interval between adjacent slices is inconsistent with horizontal resolution of digital cores. Those are the main factors which can prevent accuracy improvement of fracture characterization and physical modeling for digital cores. In order to study the 3D spatial distribution of fractures, this paper achieves reconstruction of 3D digital cores using the curvelet transform and Project Onto Convex Sets (POCS) method. Firstly, sample one per two slices in depth regularly for 3D dataset of sandstone obtained by X ray scanner, then reconstruct the 3D dataset using the proposed method. The reconstructed result is consistent with the original one and superior over the current method (spgl1), which approves the validity and superiority of the proposed method. Secondly, double the accurate 2D shale slices in depth that are obtained using focused ion beam scanning electron microscopy (FIB‐SEM). It generates the 3D digital cores in which the minimum interval between adjacent slices in depth is basically consistent with the horizontal resolution, weakens the discontinuity of shale slices in depth caused by the instrument limitations and makes the fracture distribution more clear. Tests on sandstone and accurate shale rocks demonstrate the validity and superiority of the proposed method.

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An Improved Projection Onto Convex Sets Method for Simultaneous Interpolation and Denoising

Cao

Wang

2015

Chinese J of Geophysics

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Sparsity‐promoted seismic interpolation is an important interpolation strategy; however, most existing interpolation methods merely focused on high signal‐to‐noise ratio data. Actually, noise is always contained in sampled data; the existence of noise will deteriorate interpolation results and makes interpolation challenging. Projection onto convex sets (POCS) method is an efficient method; however, it cannot get acceptable results for noisy data interpolation. A strategy for simultaneous interpolation and denoising is the weighted POCS method which uses an additional weighting factor to achieve denoising. In this paper, we demonstrate that the weighted projection onto convex sets (POCS) method is a method for unconstrained optimization model, and it can be deduced from the iterative thresholding method. In addition, an improved POCS method is proposed for interpolation and denoising without extra computation effort. Numerical examples on synthetic and field data demonstrate that the improved POCS method can get reliable results for noiseless and noisy data interpolation. First interpolation and then denoising examples proved that simultaneous interpolation and denoising is robust when the least thresholds are properly chosen.

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Curvelet-based POCS interpolation of nonuniformly sampled seismic records

Cited by 56 publications

References 45 publications

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

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

Curvelet‐based 3d Reconstruction of Digital Cores Using the Pocs Method

An Improved Projection Onto Convex Sets Method for Simultaneous Interpolation and Denoising

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