Deconvolution with curvelet‐domain sparsity

Kumar, Vishal; Herrmann, Felix J.

doi:10.1190/1.3059287

Cited by 6 publications

(4 citation statements)

References 10 publications

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“…), multiple attenuation (Herrmann, Böniger and Verschuur ; Donno, Chauris and Noble ); seismic data interpolation and recovery (Herrmann and Hennenfent ; Naghizadeh and Sacchi ; Shahidi et al . ); sparse deconvolution (Kumar and Herrmann ); amplitude versus offset inversion (Hennenfent and Herrmann ); migration imaging (Douma and de Hoop ; Chauris and Nguyen ). Their results show that the curvelet transform has a great advantage on the analysis and processing of seismic data.…”

Section: Introductionmentioning

confidence: 99%

“…It has a good ability to capture the local singularity of non-stationary signals (Mallat 1989). This ability can 2015; Dong et al 2017), surface wave suppression (Yarham, Boeniger and Herrmann 2006;Boustani et al 2013), multiple attenuation (Herrmann, Böniger and Verschuur 2007;Donno, Chauris and Noble 2010); seismic data interpolation and recovery (Herrmann and Hennenfent 2008;Naghizadeh and Sacchi 2010;Shahidi et al 2013); sparse deconvolution (Kumar and Herrmann 2008); amplitude versus offset inversion (Hennenfent and Herrmann 2004); migration imaging (Douma and de Hoop 2004;Chauris and Nguyen 2008). Their results show that the curvelet transform has a great advantage on the analysis and processing of seismic data.…”

Section: Introductionmentioning

confidence: 99%

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Time‐frequency analysis based on curvelet transforms with time skewing

Wang

Gross

et al. 2019

Geophysical Prospecting

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Oil and gas exploration gradually changes to the deep and complex areas. The quality of seismic data restricts the effective application of conventional time‐frequency analysis technology, especially in the case of low signal‐to‐noise ratio. To address this problem, we propose a curvelet‐based time‐frequency analysis method, which is suitable for seismic data, and takes into account the lateral variation of seismic data. We first construct a kind of curvelet adapted to seismic data. By adjusting the rotation mode of the curvelet in the form of time skewing, the scale parameter can be directly related to the frequency of the seismic data. Therefore, the curvelet coefficients at different scales can reflect the time‐frequency information of the seismic data. Then, the curvelet coefficients, which represent the dominant azimuthal pattern, are converted to the time‐frequency domain. Since the curvelet transform is a kind of sparse representation for the signal, the screening process of the dominant coefficient masks most of the random noise, which enables the method to adapt for the low signal‐to‐noise ratio data. Results of synthetic and field data experiments using the proposed method demonstrate that it is a good approach to identify weak signals from strong noise in the time‐frequency domain.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time‐frequency analysis based on curvelet transforms with time skewing

Wang

Gross

et al. 2019

Geophysical Prospecting

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show abstract

“…Curvelets (Candes and Donoho ) were the first representation systems to sparsely approximate multi‐dimensional data containing singularities. Curvelet transform was successfully applied for different aspects of seismic processing, such as seismic imaging (Chauris ; Kumar and Herrmann ; Sun et al . ; Sun, Chauris and Ma ; Wu and Hung ) and noise attenuation (Herrmann ; Donno, Chauris and Noble ; Yu and Yan ; de Franco and de Moraes ; Cao and Shao ; Ge et al .…”

Section: Introductionmentioning

confidence: 99%

“…Curvelets (Candes and Donoho 2003) were the first representation systems to sparsely approximate multi-dimensional data containing singularities. Curvelet transform was successfully applied for different aspects of seismic processing, such as seismic imaging (Chauris 2006;Kumar and Herrmann 2008;Sun et al 2009;Sun, Chauris and Ma 2010;Wu and Hung 2015) and noise attenuation (Herrmann 2008;Donno, Chauris and Noble 2010;Yu and Yan 2011;de Franco and de Moraes 2015;Cao and Shao 2017;Ge et al 2017). The digital implementation (Chauris and Nguyen 2008) of the curvelet transform is challenging since rotation, which is used to treat different orientations in data, does not preserve the integer lattice.…”

Section: Introductionmentioning

confidence: 99%

Seismic channel edge detection using 3D shearlets—a study on synthetic and real channelised 3D seismic data

Karbalaali

Javaherian

Dahlke

et al. 2018

Geophysical Prospecting

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Automatic feature detection from seismic data is a demanding task in today's interpretation workstations. Channels are among important stratigraphic features in seismic data both due to their reservoir capability or drilling hazard potential. Shearlet transform as a multi‐scale and multi‐directional transformation is capable of detecting anisotropic singularities in two and higher dimensional data. Channels occur as edges in seismic data, which can be detected based on maximizing the shearlet coefficients through all sub‐volumes at the finest scale of decomposition. The detected edges may require further refinement through the application of a thinning methodology. In this study, a three‐dimensional, pyramid‐adapted, compactly supported shearlet transform was applied to synthetic and real channelised, three‐dimensional post‐stack seismic data in order to decompose the data into different scales and directions for the purpose of channel boundary detection. In order to be able to compare the edge detection results based on three‐dimensional shearlet transform with some famous gradient‐based edge detectors, such as Sobel and Canny, a thresholding scheme is necessary. In both synthetic and real data examples, the three‐dimensional shearlet edge detection algorithm outperformed Sobel and Canny operators even in the presence of Gaussian random noise.

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Simultaneous seismic interpolation and denoising based on sparse inversion with a 3D low redundancy curvelet transform

Cao

Zhao

2017

Exploration Geophysics

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Deconvolution with curvelet‐domain sparsity

Cited by 6 publications

References 10 publications

Time‐frequency analysis based on curvelet transforms with time skewing

Time‐frequency analysis based on curvelet transforms with time skewing

Seismic channel edge detection using 3D shearlets—a study on synthetic and real channelised 3D seismic data

Simultaneous seismic interpolation and denoising based on sparse inversion with a 3D low redundancy curvelet transform

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