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

Cao, Jingjie; Zhao, Jingtao

doi:10.1071/eg15097

Cited by 13 publications

(2 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are a number of mathematical transforms studied in the seismological community such as Fourier transform (Zwartjes and Gisolf ), wavelet transform (Mousavi, Langston and Horton ; Anvari et al . ), curvelet transform (Herrmann and Hennenfent ; Cao, Wang and Wang ; Cao and Zhao ), Radon transform (Trad, Ulrych and Sacchi ; Latif and Mousa ; Gong, Wang and Du ), seislet transform (Fomel and Liu ; Gan et al . ) and dreamlet transform (Wu, Geng and Wu ; Huang, Wu and Wang ).…”

Section: Introductionmentioning

confidence: 99%

“…It first transforms the observed seismic data into certain sparsepromoting domain (in which the signal can be represented by a few basis) and then apply a thresholding or masking operator (Wang, Cao and Yang 2011;Chen et al 2018b). There are a number of mathematical transforms studied in the seismological community such as Fourier transform (Zwartjes and Gisolf 2007), wavelet transform (Mousavi, Langston and Horton 2016;Anvari et al 2017), curvelet transform (Herrmann and Hennenfent 2008;Cao, Wang and Wang 2014;Cao and Zhao 2017), Radon transform (Trad, Ulrych and Sacchi 2002;Latif and Mousa 2017;Gong, Wang and Du 2018), seislet transform (Fomel and Liu 2010;Gan et al 2016) and dreamlet transform (Wu, Geng and Wu 2011;Huang, Wu and Wang 2018).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

De‐aliased and de‐noise Cadzow filtering for seismic data reconstruction

Huang

Feng

Chen

2019

Geophysical Prospecting

View full text Add to dashboard Cite

Cadzow filtering is currently considered as one of the most effective approaches for seismic data reconstruction. The basic version of Cadzow filtering first reorders each frequency slice of the seismic data (to be reconstructed) to a block Hankel/Toeplitz matrix, and then implements a rank‐reduction operator, that is truncated singular value decomposition, to the Hankel/Toeplitz matrix. However, basic Cadzow filtering cannot deal with the problem of recovering regularly missing data (up‐sampling) in the case of strongly aliased energy, because the regularly missing data will mix with signals in the singular spectrum. To solve this problem, it has been proposed to precondition the reconstruction of high‐frequency components using information from the low‐frequency components which are less aliased. In this paper, we further extend the de‐aliased Cadzow filtering approach to reconstruct regularly sampled seismic traces from the noisy observed data by modifying the reinserting operation, in which the high‐frequency components are projected onto the sub‐space spanned by several singular vectors of the low‐frequency components. At each iteration, the filtered data are weighted to the original data as a feedback. The weighting factor is related to the background noise level and changes with iteration. The feasibility of the proposed technique is validated via two‐dimensional, three‐dimensional and five‐dimensional synthetic data examples, as well as two‐dimensional post‐stack and three‐dimensional pre‐stack field data examples. The results demonstrate that the proposed technique can effectively interpolate regularly sampled data and is robust in noisy environments.

show abstract