Stretch correction method based on Curvelet sparse transform
LIU Shi-You1(), ZHANG Ming-Lin2, SONG Wei-Qi2
1. Hainan Branch of CNOOC (China) Co.,Ltd., Haikou 570311, China 2. School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China
NMO correction is an important step in seismic data processing, but it will produce the wavelet stretching distortion effect in the process of correction. With the increase of offset, the dominant frequency will decrease and the amplitude will increase.Due to stretch distortion, the in-phase axis is not leveled, leading to non-in-phase stacking, which will lead to frequency distortion and resolution decrease of horizontal stacking profile. Therefore, stretch correction is the key to improve the resolution of horizontal stacking profile.The stretching distortion of wavelet is incoherent in the curved sparse domain, and the stretching correction can be regarded as a nonlinear optimization process.By measuring the sparsity of the data in the sparse domain, a fast and effective algorithm is used to optimize the nonlinear problem generated by the wavelet stretching distortion, and finally the purpose of eliminating the wavelet stretching distortion is realized.The curved sparse transform stretching correction method can eliminate the wavelet stretching distortion caused by NMO correction, recover the high frequency information at the far offset and level the in-phase axis.Combining model data and actual data processing, the curved wave sparse stretch correction method can significantly improve the resolution of horizontal superposition profile.
Xia H R, Ge C Q, Zou S F. Analysis and elimination of stretch phenomenon in dynamic school[J]. Geophysical Prospecting for Petroleum, 2005,44(3):220-224.
Zhao X L, Wu G C. Angle domain prestack gather detuning method based on unsteady matching[J]. Geophysical and Geochemical Exploration, 2017,41(1):141-146.
Cui B W, Wang W H. Study on spectrum substitution non stretching NMO method[J]. Progress in Geophysics, 2007,22(3):960-965.
[9]
Kazemi N, Siahkoohi H R. Local stretch zeroing NMO correction[J]. Geophysical Journal International, 2014,188(1):123-130.
doi: 10.1111/gji.2012.188.issue-1
[10]
Zhang B, Zhang K, Guo S, et al. Nonstretching NMO correction of prestack time-migrated gathers using a matching-pursuit algorithm[J]. Geophysics, 2013,78(1):U9-U18.
doi: 10.1190/geo2011-0509.1
[11]
Abedi M M, Riahi M A. Nonhyperbolic stretch-free normal moveout correction[J]. Geophysics, 2016,81(6):U87-U95.
doi: 10.1190/geo2016-0078.1
[12]
Zhang F, Lan N. Seismic gather wavelet stretching correction based on multi-wavelet decomposition algorithm[J]. Geophysics, 2020,85(5):1-33.
doi: 10.1190/geo2018-0881.1
[13]
Barnes A E. Another look at NMO stretch[J]. Geophysics, 2012,57(5):749.
doi: 10.1190/1.1443289
[14]
Buchholtz H. A note on signal distortion due to dynamic (NMO) corrections[J]. Geophysical Prospecting, 1972,20(2):395-402.
doi: 10.1111/gpr.1972.20.issue-2
[15]
Candes E, Romberg J, Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Comm. Pure Appl. Math., 2005,59(8):1-15.
doi: 10.1002/(ISSN)1097-0312
Luo Y, Mao H B, Yang X H, et al. Random noise attenuation method for seismic data based on double sparse representation[J]. Geophysical and Geochemical Exploration, 2018,42(3):608-615.
[17]
Herrmann F J, Moghaddam P, Stolk C C. Sparsity- and continuity-promoting seismic image recovery with curvelet frames[J]. Applied & Computational Harmonic Analysis, 2008,24(2):150-173.
[18]
Gholami A. Residual statics estimation by sparsity maximization[J]. Geophysics, 2013,78(1):V11-V19.
doi: 10.1190/geo2012-0035.1
[19]
Gholami A, Hosseini S M. A general framework for sparsity based denoising and inversion[J]. IEEE Transactions on Signal Processing, 2011,59(11):5202-5211.
doi: 10.1109/TSP.2011.2164074
