基于改进Curvelet变换的地震数据重建方法
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摘要
由于采集环境及仪器性能的限制,采集到的地震勘探数据经常是不规则和不完整的,进而影响到地震数据后续处理及反演,因此在对地震数据进行下一步分析处理前有必要先重建出完整的地震数据,提出了一种基于改进的Curvelet域的地震数据压缩重建算法。首先在压缩感知理论的框架下,利用Curvelet的稀疏特性,建立缺失地震数据重建模型;然后在CRSI(Curvelet Recovery by Sparsity-Promoting Inversion,CRSI)算法框架基础上,采用改进的指数阈值方法,对缺失地震数据进行恢复重建。使用了4层水平均匀介质模型和Marmousi模型模拟的地震数据进行了随机稀疏采样和重建的数值实验。实验结果表明,与传统重建算法比较,该方法不仅加快了原有算法的收敛速度,同时保证了重建数据的高信噪比,验证了所提方法的可行性和有效性。
As a result of the acquisition of environment and instrument performance constraints,seismic data collected are often irregular and incomplete.Thus it is necessary to reconstruct the complete seismic data before proceeding to the next step in the seismic data analysis. The authors present a modified Curvelet algorithm for image reconstruction based on seismic compression.First in the framework of compressed sensing theory,using the sparse characteristic of Curvelet,a missing data reconstruction model is built,and then using the CRSI(Curvelet Recovery by sparsity-promoting Inversion,CRSI) algorithm framework,adopting improved exponential threshold algorithm,the missing seismic data are restored and reconstructed.In this paper,the authors use four level homogeneous medium model and the seismic data simulated by Marmousi model to carry out numerical experiments of random sparse sampling and reconstruction.The result of the experiment shows that compared with the traditional recon-struction algorithm,the proposed method not only accelerates the convergence speed of the original algorithm,but also guarantees a high SNR of the reconstructed data,which verifies the feasibility and effectiveness of the proposed method.
As a result of the acquisition of environment and instrument performance constraints,seismic data collected are often irregular and incomplete.Thus it is necessary to reconstruct the complete seismic data before proceeding to the next step in the seismic data analysis. The authors present a modified Curvelet algorithm for image reconstruction based on seismic compression.First in the framework of compressed sensing theory,using the sparse characteristic of Curvelet,a missing data reconstruction model is built,and then using the CRSI(Curvelet Recovery by sparsity-promoting Inversion,CRSI) algorithm framework,adopting improved exponential threshold algorithm,the missing seismic data are restored and reconstructed.In this paper,the authors use four level homogeneous medium model and the seismic data simulated by Marmousi model to carry out numerical experiments of random sparse sampling and reconstruction.The result of the experiment shows that compared with the traditional recon-struction algorithm,the proposed method not only accelerates the convergence speed of the original algorithm,but also guarantees a high SNR of the reconstructed data,which verifies the feasibility and effectiveness of the proposed method.
引文
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[21]张华,陈小宏.基于jitter采样和曲波变换的三维地震数据重建[J].地球物理学报,2013,56(5):1637-1649.ZHANG Hua,CHEN Xiaohong. Seismic data reconstruction based on jittered sampling and curvelet transform[J]. Geophysics,2013,56(5):1637-1649.
[22] GAO J J,CHEN X H,LI J Y,et al.Irregular seismic data reconstruction based on exponential threshold model of POCS method[J].Applied Geophysics,2010,7(3):229-238.
[23]周亚同,王丽莉,蒲青山.压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J].石油地球物理勘探,2014,49(4):652-660.ZHOU Yatong,WANG Lili,PU Qingshan.Based on K-singular value decomposition dictionary learning based seismic data reconstruction[J]. Petroleum Geophysical Exploration,2014,49(4):652-660.
[2] WANG Jiachen,WU Renlun,ZHANG Peng.Characteristics and applications of gas desorption with excavation disturbances in coal mining[J]. International Journal of Coal Science&Technology,2015,2(1):30-37.
[3] LIU Yu,ZHU Yanming. Comparison of pore characteristics in the coal and shale reservoirs of Taiyuan Formation,Qinshui Basin,China[J]. International Journal of Coal Science&Technology,2016,3(3):330-338.
[4] DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[5] HERRMANN F J,HENNENFENT G.Non-parametric seismic data recovery with curvelet frames[J]. Geophysical Journal of the Royal Astronomical Society,2010,173(1):233-248.
[6] CANDS E J,DONOHO D L.New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities[J].Communications on Pure&Applied Mathematics,2004,57(2):219-266.
[7] DAUBECHIES I,DEFRISE M,DE MOL C.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure&Applied Mathematics,2003,57(11):1413-1457.
[8] MA J,PLONKA G. The curvelet transform[J]. Signal Processing Magazine IEEE,2010,27(2):118-133.
[9] YIN W.Analysis and generalizations of the linearized bregman method[J].Siam Journal on Imaging Sciences,2010,3(4):856-877.
[10] CANDS E J,ROMBERG J,TAO T.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory,2004,52(2):489-509.
[11] BARANIUK R.Compressive sensing[A].Information Sciences and Systems,2008[C].2008.
[12] CANDS E J.The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique,2008,346(9-10):589-592.
[13]白兰淑,刘伊克,卢回忆,等.基于压缩感知的Curvelet域联合迭代地震数据重建[J].地球物理学报,2014,57(9):2937-2945.BAI Lanshu,LIU Yinke,LU Huiyi,et al. Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing[J].Chinese Journal of Geophysics,2014,57(9):2937-2945.
[14] CHEN S S,DONOHO D L,SAUNDERS M A.Atomic decomposition by basis Pursuit[J].SIAM Rev.,2001,43(1):129-159.
[15] MALLAT S G,ZHANG Z. Matching pursuits with time-frequency dictionaries[J]. IEEE Trans on Signal Processing,1993,41(12):3397-3415.
[16]唐刚.基于压缩感知和稀疏表示的地震数据重建与去噪[D].北京:清华大学,2010:42.TANG Gang. Seismic data reconstruction and denoising based on compressed sensing and sparse representation[D].Beijing:Tsinghua University,2010:42.
[17] HERRMANN F J,WANG D,HENNENFENT G.Multiple prediction from incomplete data with the focused curvelet transform[J].Society of Exploration Geophysicists,2007(1):2505.
[18] BREGMAN L M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming[J]. Ussr Computational Mathematics&Mathematical Physics,1967,7(3):200-217.
[19] LANDWEBER L. An iteration formula for fredholm integral equations of the first kind[J].American Journal of Mathematics,1951,73(3):615-624.
[20] PATI Y C,REZAIIFAR R,KRISHNAPRASAD P S. Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition[A]. Signals,Systems and Computers,1993,Conference Record of The Twenty-Seventh Asilomar Conference on[C].IEEE,2002:40-44.
[21]张华,陈小宏.基于jitter采样和曲波变换的三维地震数据重建[J].地球物理学报,2013,56(5):1637-1649.ZHANG Hua,CHEN Xiaohong. Seismic data reconstruction based on jittered sampling and curvelet transform[J]. Geophysics,2013,56(5):1637-1649.
[22] GAO J J,CHEN X H,LI J Y,et al.Irregular seismic data reconstruction based on exponential threshold model of POCS method[J].Applied Geophysics,2010,7(3):229-238.
[23]周亚同,王丽莉,蒲青山.压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J].石油地球物理勘探,2014,49(4):652-660.ZHOU Yatong,WANG Lili,PU Qingshan.Based on K-singular value decomposition dictionary learning based seismic data reconstruction[J]. Petroleum Geophysical Exploration,2014,49(4):652-660.