基于Curvelet变换的地震资料信噪分离技术
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摘要
在地震资料中,噪声干扰严重影响了有效信号的提取,为此必须进行信噪分离处理.本文提出一种基于Curvelet变换和KL变换相结合的软硬阈值折衷处理方法.首先对地震数据进行Curvelet变换,然后对各尺度系数选取适当阈值压制噪声干扰,再利用KL变换提取数据中的相干有效信号,最后重构得到去噪后的记录.经合成记录和实际地震资料处理实验证明,该方法与小波变换法相比较,更能有效进行信噪分离,提高地震剖面信噪比和分辨率.
In seismic data, noises seriously affect the extraction of significant signals, so the denoising processing is necessary. A method of signal noise separation is proposed based on a combination of Curvelet transform and KL transform. This paper first uses the Curvelet method to decompose seismic data. The soft and hard thresholds on scales of the Curvelet domain are selected for attenuation of noises, and then we makes use of KL transform to extract correlative significant signals. Lastly we reconstruct the seismic data processed. The synthetic and real seismic data processing experiments show that the method in this paper can efficiently separate signal and noise, and improve seismic section signal-to-noise ratio and seismic resolution compared with the wavelet method.
In seismic data, noises seriously affect the extraction of significant signals, so the denoising processing is necessary. A method of signal noise separation is proposed based on a combination of Curvelet transform and KL transform. This paper first uses the Curvelet method to decompose seismic data. The soft and hard thresholds on scales of the Curvelet domain are selected for attenuation of noises, and then we makes use of KL transform to extract correlative significant signals. Lastly we reconstruct the seismic data processed. The synthetic and real seismic data processing experiments show that the method in this paper can efficiently separate signal and noise, and improve seismic section signal-to-noise ratio and seismic resolution compared with the wavelet method.
引文
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[2] Candes E J,Guo F.New multiscale transforms,minimum total rariation systhesis: Applications to edge-prserving image reconstruction [J].Signal Processing,2002,82,1519-1543．
[3] CandesE J,Donoho D L.Continuous curvelet transform Ⅱ: discretization and frames [J].Appl.Comput.Harmon.Anal.,2005 ,19:198-222．
[4] Candes E J,Donoho D L.Recovering edges in Ⅲ-posed problems: optimality of curvelet frames[J].Ann.Statist.,2000,30: 784．
[5] Candes E J,Roberg J,Tao T.Stable signal recovery from incomplete and inaccurate measurements[J].Comm.Pare Appl.Math.,2006,59(8) :1207-1223．
[6] Candes E J,Demanet S L,Donoho D L,Ying L.Fast discrete curvelet transforms,SIAM muhiscale Model [J].Simul.,2006． 5(3) : 861-899．
[7] Starck J L,Candes E J,Donoho D L.The curvelet transform for image denoising [J].IEEE Transactions on Image Processing,2002,11(6) : 670-684．
[8] Herrmann F,Hennenfent G,Moghaddam P.Seismic imaging and processing with curvelets,the 69th Annual Meeting,Extended Abastracts[J].EAGE.
[9] Herrmann FJ,Moghaddam P,Stolk C.Sparsity-and continuity-promoting seismic image recovery with curvelets frames [J].Applied and Computational Harmonic Analysis,2007．
[10] Donoho D.De-noising by soft-thresholding [J].IEEE.Trans.On IT,1995,3:613-627．
[11] Mallat S G,Hang W L.Singuluarity detection and processing with wavelets[J].IEEE Trans on Information Theory,1992,38(2) :617-643．
[12] Yu Y,Weaver J B,et al.Wavelet transform domain filters: a spatial selective noise filteration technique[J].IEEE Trans Image Processing,Nov 1994,3(6) : 747-757．
[13] Mallat S,Hang W L.Sigularity detection and processing with wavelets[J].IEEE Trans.On Information Theory,1992,38(2) ,617-643．
[14] Donoho D L,De-noising by soft-thresholding [J].IEEE.Trans Inform Theory,1995,41:613-627．
[15] Stephane Mt.A Wavelet Tour of Signal Processing [M].Second Edition,Academic Press,1999
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[17] 包乾宗,高静怀,陈文超.Curvelet域垂直地震剖面波场分离[J].西安交通大学学报,2007,41(6) :650-654． Bao Q Z,Gao J H,Chen W C.Wave field separation of vertical seismic profiling m Curvelet Domain[J].Journal of Xi'An Jiaotong University,2007,41(6) :650-654．
[18] 吴芳平,狄红卫.基于Curvelet变换的软硬阈值折衷图像去噪[J].光学技术,2007． 33(5) :688-690． Wu F P,Di H W.A image denoising method between soft and hard thresholding based on Curvelet transform [J]. Optical technique,2007,33(5) :688-690．
[19] 柳建新.韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2) :541-545． Liu J X,Han S L,Ma J.Application of wavelet analysis in seismic data denoising [J].Progress in Geophysics (in Chinese),2006,21(2) : 541-545．
[20] 张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法技术综合评述[J].地球物理学进展,2006,21(2) :546-553． Zhang J H,L(u|¨) N,Tian L Y,Lu W Z,Zhong L.An overview of the methods and techniques for seismic data noise attenuation[J].Progress in Geophystcs(in Chinese),2006,21(2) : 546-553．
[21] 冯象初,甘小冰,宋国乡.数值泛涵与小波理论[M].西安:西安电子科技大学出版社.2003． Feng X C,Gan X B,Song G X.Numerical function and wavelet theory[M].Xi'An: XiDian university press,2003．
[22] 包乾宗,高静怀,陈文超.面波压制的Ridgelet域方法[J].地球物理学报,2007,50(4) :1210-1215． Bao Q Z,Gao J H,Chen W C,Ridgelet domain method of ground-roll suppression [J].Chinese J.Geophys.(in Chinese),2007,50(4) :1210-1215．
[23] 高静怀,毛剑,满蔚仕,等.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报,2006,49(4) :1155-1163． Gao J H,Mao J,Man W S,et al.On the denoising method of prestack seismic data in wavelet domain[J].Chinese J.Geophys.(in Chinese),2006,49(4) :1155-1163．
[24] 彭才,朱仕军,孙建库,等.小波变换域K-L变换及其去噪效果分析[J].石油物探.2007,46(2) :112-114． Peng C,Zhu S j,Sun J k,et al.K-L transformation in wavelet conversion and the analysis of de-noise effect[J].Geophysical Prospecting For Petroleum,2007,46(2) :112-114．
[2] Candes E J,Guo F.New multiscale transforms,minimum total rariation systhesis: Applications to edge-prserving image reconstruction [J].Signal Processing,2002,82,1519-1543．
[3] CandesE J,Donoho D L.Continuous curvelet transform Ⅱ: discretization and frames [J].Appl.Comput.Harmon.Anal.,2005 ,19:198-222．
[4] Candes E J,Donoho D L.Recovering edges in Ⅲ-posed problems: optimality of curvelet frames[J].Ann.Statist.,2000,30: 784．
[5] Candes E J,Roberg J,Tao T.Stable signal recovery from incomplete and inaccurate measurements[J].Comm.Pare Appl.Math.,2006,59(8) :1207-1223．
[6] Candes E J,Demanet S L,Donoho D L,Ying L.Fast discrete curvelet transforms,SIAM muhiscale Model [J].Simul.,2006． 5(3) : 861-899．
[7] Starck J L,Candes E J,Donoho D L.The curvelet transform for image denoising [J].IEEE Transactions on Image Processing,2002,11(6) : 670-684．
[8] Herrmann F,Hennenfent G,Moghaddam P.Seismic imaging and processing with curvelets,the 69th Annual Meeting,Extended Abastracts[J].EAGE.
[9] Herrmann FJ,Moghaddam P,Stolk C.Sparsity-and continuity-promoting seismic image recovery with curvelets frames [J].Applied and Computational Harmonic Analysis,2007．
[10] Donoho D.De-noising by soft-thresholding [J].IEEE.Trans.On IT,1995,3:613-627．
[11] Mallat S G,Hang W L.Singuluarity detection and processing with wavelets[J].IEEE Trans on Information Theory,1992,38(2) :617-643．
[12] Yu Y,Weaver J B,et al.Wavelet transform domain filters: a spatial selective noise filteration technique[J].IEEE Trans Image Processing,Nov 1994,3(6) : 747-757．
[13] Mallat S,Hang W L.Sigularity detection and processing with wavelets[J].IEEE Trans.On Information Theory,1992,38(2) ,617-643．
[14] Donoho D L,De-noising by soft-thresholding [J].IEEE.Trans Inform Theory,1995,41:613-627．
[15] Stephane Mt.A Wavelet Tour of Signal Processing [M].Second Edition,Academic Press,1999
[16] 张素芳,徐义贤.雷栋.基于Curvelet变换的多次波去除技术[J].石油地球物理勘探,2006,41(3) :262-265． Zhang S F,Xu Y X,Lei D.Multiple-eliminated technique based on Curvelet transform [J].Oil Geophysical Prospecting,2006,41(3) :262-265．
[17] 包乾宗,高静怀,陈文超.Curvelet域垂直地震剖面波场分离[J].西安交通大学学报,2007,41(6) :650-654． Bao Q Z,Gao J H,Chen W C.Wave field separation of vertical seismic profiling m Curvelet Domain[J].Journal of Xi'An Jiaotong University,2007,41(6) :650-654．
[18] 吴芳平,狄红卫.基于Curvelet变换的软硬阈值折衷图像去噪[J].光学技术,2007． 33(5) :688-690． Wu F P,Di H W.A image denoising method between soft and hard thresholding based on Curvelet transform [J]. Optical technique,2007,33(5) :688-690．
[19] 柳建新.韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2) :541-545． Liu J X,Han S L,Ma J.Application of wavelet analysis in seismic data denoising [J].Progress in Geophysics (in Chinese),2006,21(2) : 541-545．
[20] 张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法技术综合评述[J].地球物理学进展,2006,21(2) :546-553． Zhang J H,L(u|¨) N,Tian L Y,Lu W Z,Zhong L.An overview of the methods and techniques for seismic data noise attenuation[J].Progress in Geophystcs(in Chinese),2006,21(2) : 546-553．
[21] 冯象初,甘小冰,宋国乡.数值泛涵与小波理论[M].西安:西安电子科技大学出版社.2003． Feng X C,Gan X B,Song G X.Numerical function and wavelet theory[M].Xi'An: XiDian university press,2003．
[22] 包乾宗,高静怀,陈文超.面波压制的Ridgelet域方法[J].地球物理学报,2007,50(4) :1210-1215． Bao Q Z,Gao J H,Chen W C,Ridgelet domain method of ground-roll suppression [J].Chinese J.Geophys.(in Chinese),2007,50(4) :1210-1215．
[23] 高静怀,毛剑,满蔚仕,等.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报,2006,49(4) :1155-1163． Gao J H,Mao J,Man W S,et al.On the denoising method of prestack seismic data in wavelet domain[J].Chinese J.Geophys.(in Chinese),2006,49(4) :1155-1163．
[24] 彭才,朱仕军,孙建库,等.小波变换域K-L变换及其去噪效果分析[J].石油物探.2007,46(2) :112-114． Peng C,Zhu S j,Sun J k,et al.K-L transformation in wavelet conversion and the analysis of de-noise effect[J].Geophysical Prospecting For Petroleum,2007,46(2) :112-114．
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