基于Curvelet变换的高密度地震弱信号检测与去噪方法研究
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摘要
高密度地震技术是近年来国外发展较快的物探技术之一,使用该方法获得的地震资料较好地解决了压制噪音、提高分辨率和保真度等难题。但同时也存在着高频段信噪比低、弱信号被混杂或淹没在噪声里的严重问题。如果不经过弱信号与噪声的分离处理,直接用它来进行叠加、速度分析、动校正、偏移等处理,最终的资料质量会大打折扣,不易发挥出高密度资料的潜在优势。因此,加强高密度地震弱信号的检测与去噪方法的研究,着力提高高密度地震资料信噪比的研究具有十分重要的意义。
Curvelet变换是在小波变换基础上发展起来的一种新的多尺度变换。Curvelet变换对图像的边缘,如曲线、直线等几何特征的表达更加优于小波,这一特点使得Curvelet变换在图像去噪中取得较为广泛的研究成果。本文将Curvelet变换引入高密度地震技术领域,重点讨论了Curvelet变换在高密度地震弱信号检测与去噪方面的应用。
文章以第二代离散Curvelet变换为工具,讨论了Curvelet变换在不含弱信号和含有弱信号情况下的实现方法:在不含弱信号情况下,通过Curvelet硬阈值法就能达到较好的保幅去噪效果;在含有弱信号的情况下分别讨论了各种阈值处理方法在弱信号识别方面的效果,综合对比选择了对弱信号识别更有效的半软阈值法,并通过采用降低阈值门限的方法改进弱信号识别效果。
对于降低阈值门限后出现的Curvelet域系数滤除不干净,时域中出现野值的问题,通过在Curvelet域采用均值滤波方法加以平滑,经模型试验和实际资料验证,此方法相对于小波变换、Curvelet硬阈值方法对弱信号的检测和识别更加有效。经试验,本文算法最高可分辨埋没于2倍于信号幅值的噪声中的弱信号。
High-density seismic technology was one of the geophysical exploration technologies which had developed rapidly in recent years. The high-density seismic data had solved the problems such as suppressing noise, enhancing resolution and keeping fidelity. Meanwhile there were also some critical problems, such as low SNR and sophistication weak signals with noise. The quantity of the final data wouldn’t be perfect if we used the original data without denoising for stacking, velocity analyzing, NMO correcting and migrating. It’s difficult to exert the potential advantages of high-density data if we used the original data without denoising. Therefore, it’s of great importance to research on weak signal detection and denoising of high-density seismic wave and find out how to improve SNR of high-density seismic data.
Curvelet transform was a new multi-scale transformation which developed on the basis of wavelet transform. Curvelet transform worked better in display the edge of graphics, such as curves, straight lines and other geometric features, this feature made Curvelet transform achieve abundant research results in investigation. Curvelet transform was introduced into the field of density seismic technology in this paper. The usage of Curvelet transformation in high density seismic weak signal detection and denoising was emphasized discussed.
In this paper, Fast Discrete Curvelet Transform was used as a basic tool to discuss how to deal with seismic data contains weak signal or not. In case of no weak signal in seismic data, denoising with hard threshold value method may achieve good effect. While weak signal was contained in the data, lots of threshold value methods were used to evaluate in weak signal identification separately. The semi-soft threshold method was chosen which had better effect than hard threshold and other methods, and the effect of the weak signal identification was improved through reducing the threshold.
To overcome the problem of filtering coefficients thoroughly in Curvelet domain and singular points in time domain, the mean filter method was used in Curvelet domain. Model and real data tests verified that this process achieved better effects than other methods, such as Wavelet transform and hard threshold method in Curvelet transform. This algorithm could discern the weak signal buried under 2 times the noise signal amplitude.
Curvelet变换是在小波变换基础上发展起来的一种新的多尺度变换。Curvelet变换对图像的边缘,如曲线、直线等几何特征的表达更加优于小波,这一特点使得Curvelet变换在图像去噪中取得较为广泛的研究成果。本文将Curvelet变换引入高密度地震技术领域,重点讨论了Curvelet变换在高密度地震弱信号检测与去噪方面的应用。
文章以第二代离散Curvelet变换为工具,讨论了Curvelet变换在不含弱信号和含有弱信号情况下的实现方法:在不含弱信号情况下,通过Curvelet硬阈值法就能达到较好的保幅去噪效果;在含有弱信号的情况下分别讨论了各种阈值处理方法在弱信号识别方面的效果,综合对比选择了对弱信号识别更有效的半软阈值法,并通过采用降低阈值门限的方法改进弱信号识别效果。
对于降低阈值门限后出现的Curvelet域系数滤除不干净,时域中出现野值的问题,通过在Curvelet域采用均值滤波方法加以平滑,经模型试验和实际资料验证,此方法相对于小波变换、Curvelet硬阈值方法对弱信号的检测和识别更加有效。经试验,本文算法最高可分辨埋没于2倍于信号幅值的噪声中的弱信号。
High-density seismic technology was one of the geophysical exploration technologies which had developed rapidly in recent years. The high-density seismic data had solved the problems such as suppressing noise, enhancing resolution and keeping fidelity. Meanwhile there were also some critical problems, such as low SNR and sophistication weak signals with noise. The quantity of the final data wouldn’t be perfect if we used the original data without denoising for stacking, velocity analyzing, NMO correcting and migrating. It’s difficult to exert the potential advantages of high-density data if we used the original data without denoising. Therefore, it’s of great importance to research on weak signal detection and denoising of high-density seismic wave and find out how to improve SNR of high-density seismic data.
Curvelet transform was a new multi-scale transformation which developed on the basis of wavelet transform. Curvelet transform worked better in display the edge of graphics, such as curves, straight lines and other geometric features, this feature made Curvelet transform achieve abundant research results in investigation. Curvelet transform was introduced into the field of density seismic technology in this paper. The usage of Curvelet transformation in high density seismic weak signal detection and denoising was emphasized discussed.
In this paper, Fast Discrete Curvelet Transform was used as a basic tool to discuss how to deal with seismic data contains weak signal or not. In case of no weak signal in seismic data, denoising with hard threshold value method may achieve good effect. While weak signal was contained in the data, lots of threshold value methods were used to evaluate in weak signal identification separately. The semi-soft threshold method was chosen which had better effect than hard threshold and other methods, and the effect of the weak signal identification was improved through reducing the threshold.
To overcome the problem of filtering coefficients thoroughly in Curvelet domain and singular points in time domain, the mean filter method was used in Curvelet domain. Model and real data tests verified that this process achieved better effects than other methods, such as Wavelet transform and hard threshold method in Curvelet transform. This algorithm could discern the weak signal buried under 2 times the noise signal amplitude.
引文
[1]王喜双,谢文导,邓志文.高密度空间采样地震勘探技术发展与展望.中国石油勘探,2007,12(1):49-53.
[2]周求湛,胡峰晔,张利平.弱信号检测与估计.北京:北京航空航天大学出版社,2007
[3]杨三女,秦刚平等.基于弱信号分离技术的频谱属性计算.CPS/SEG Beijing 2009 International Geophysical Conference & Exposition.
[4]王正蕾.基于小波变换的微地震信号检测方法研究.勘探地球物理进展,2009,32(3):182-185.
[5]李月,杨宝俊等.混沌振子检测系统的弱有效地震信号检测能力.科学通报,2006(51):13-17.
[6]刘学伟,尹军杰,王德志等.基于地震数据处理的三维地震观测系统设计—泌阳凹陷南部陡坡带三维地震观测系统设计实例.石油地球物理勘探,2004,39(4): 375-380.
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[9]詹毅,周熙襄.小波包分析与奇异值分解(SVD)叠前去噪方法.石油地球物理勘探,2004,39(4):394-397.
[10]钟本善,何昌礼,杨忠民.复杂构造地区的SVD去噪技术.成都理工学院学报,2000,27(1):93-95.
[11]谭善文,秦树人,汤宝平.Hilbert-Huang变换的滤波特性及其应用.重庆大学学报,2004,27(2):9-12.
[12]王毅,牛亦龙,陈海洋.独立分量分析的基本问题与研究进展.计算机工程与应用,2005,41(27):55-58.
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[17]周开明.小波变换及其在去噪中的应用.石油地球物理勘探,1994,29(3):274-285.
[18]李庆武,陈小刚.小波阈值去噪的一种改进方法.光学技术,2006,32(6):831-833.
[19] Gao Hong-Ye, Bruce A G. Wave shrink and semisoft shrinkage. StaSci Research Report, 1995(39).
[20]倪林.一种更适合图像处理的多尺度变换-Curvelet变换.计算机工程与应用,2004,6(28):21-26.
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[22]黄薇.Curvelet变换及其在图像处理中的应用[D].西安:西安理工大学,2007.
[23]赵心.基于Curvelet变换的图像去噪方法研究与应用[D].青岛:山东科技大学,2007.
[24] Meyer F G, Coifman R, Brushlets. A tool for directional image analysis and image compressin. Applied and Computational Harmonic Analysis, 1997, 5: 147– 187.
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[31] Do M N, Vetterli M, Contourlets J, Stoeckler G, Welland V. Beyond wavelets, Academic Press, 2002.
[32] Velisavljevic V, Beferull-Lozano B, Vetterli M, and Dragotti P L. Directionlets: Anisotropic muti-directional representation with separable filtering, IEEE Trans. on Image Processing, 2006, 15(7):1916-1933.
[33] Labate D, Lim W Q, Kutyniok G, and Weiss G. Sparse multidimensional representation using shearlets, Wavelets XI(SanDiege,CA,2005), SPIE Proc, 5914, SPIE, Bellingham,WA,2005.
[34] Candes E J, Donoho D L. New tight frames of Curvelets and optimal representations of objects with C2 Singularities. Communion Pure and Appl. Math, 2002, 57(2):219-266.
[35] Bovike A C, Clark M. Multichannel texture analysis using localized spatial filters. IEEE, PAMI,1990,12(1):55-72.
[36] Herrmann F J, Verschuur E. Curvelet-domain multiple elimination with sparseness constraints. Society of exploration geophysicists, Expanded Abstracts, 1333-1336, 2004.
[37] Hennenfent G, Herrmann F J. Three-term amplitude-versus-offset(AVO)inverse on revisited by Curvelet and Wavelet transforms. Society of exploration geophysicists, Expanded Abstracts, 211-214, 2004.
[38] Huub D, Maarten V. Wave-character preserving pre-stack map migration using curvelets. Society of exploration geophysicists, Expanded Abstracts, 961-964, 2004.
[39] Herrmann F J, Deli Wang, Hennenfent G, et al. Seismic data processing with curvelets: A multiscale and nonlinear approach. Society of exploration geophysicists, Expanded Abstracts, 2220-2224, 2007.
[40] Ramesh N, Domimique G, Mohamed T, et al. Coherent and random noise attenuation using the curvelet transform. The leading Edge, 2008, 27(2):240-248.
[41]何劲,李宏伟,张帆.基于Curvelet变换的图像消噪.现代电子技术,2008(2):140-144.
[42]刘国高,周建东,符进祥.Curvelet变换及其在图像去噪中的应用研究.电子测量技术,2008(7):7-11.
[43]卢成武,宋国乡.带曲波域约束的全变差正则化抑噪方法[J].2008,36(4):646-649.
[44]吴芳平,狄红卫.基于Curvelet变换的软硬阈值折衷图像去噪.光学技术,2007,33(5):688-690.
[45]焦李成,侯彪,王爽,刘芳.图像多尺度几何分析理论与应用-后小波分析理论与应用.西安:西安电子科技大学出版社,2008.
[46]焦李成,谭山.图像的多尺度几何分析:回顾和展望.电子学报,2003,12A:1975-1981.
[47]张素芳,徐义贤,雷栋.基于Curvelet变换的多次波去除技术.石油地球物理勘探,2006,41(3):262-265.
[48]包乾宗,高静怀,陈文超.Curvelet域垂直地震剖面波场分离.西安交通大学学报,2007,41(6):650-654.
[49]彭才,常智,朱仕军.基于曲波变换的地震数据去噪方法.石油物探,2008,47(5):461-464.
[50]张恒磊,张云翠,宋双等.基于Curvelet域的叠前地震资料去噪方法.石油地球物理勘探,2008,43(5):508-513.
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[2]周求湛,胡峰晔,张利平.弱信号检测与估计.北京:北京航空航天大学出版社,2007
[3]杨三女,秦刚平等.基于弱信号分离技术的频谱属性计算.CPS/SEG Beijing 2009 International Geophysical Conference & Exposition.
[4]王正蕾.基于小波变换的微地震信号检测方法研究.勘探地球物理进展,2009,32(3):182-185.
[5]李月,杨宝俊等.混沌振子检测系统的弱有效地震信号检测能力.科学通报,2006(51):13-17.
[6]刘学伟,尹军杰,王德志等.基于地震数据处理的三维地震观测系统设计—泌阳凹陷南部陡坡带三维地震观测系统设计实例.石油地球物理勘探,2004,39(4): 375-380.
[7]熊翥.地震数据数字处理应用技术.北京:石油工业出版社,1993.
[8]陆基孟.地震勘探原理.东营:石油大学出版社,1993.
[9]詹毅,周熙襄.小波包分析与奇异值分解(SVD)叠前去噪方法.石油地球物理勘探,2004,39(4):394-397.
[10]钟本善,何昌礼,杨忠民.复杂构造地区的SVD去噪技术.成都理工学院学报,2000,27(1):93-95.
[11]谭善文,秦树人,汤宝平.Hilbert-Huang变换的滤波特性及其应用.重庆大学学报,2004,27(2):9-12.
[12]王毅,牛亦龙,陈海洋.独立分量分析的基本问题与研究进展.计算机工程与应用,2005,41(27):55-58.
[13]杨福生.小波变换的工程分析与应用.北京:科学出版社,1999.
[14] Mallat S. Multifrequency channel decompositions of images and wavelet models. IEEE Trans on acoustic speech and signal processing,1989,37(12),2091-2110.
[15]张军华,陆基孟.小波变换方法在地震资料去噪和提高分辨率中的应用.石油大学学报(自然科学版),1997,21(1):18-21.
[16]罗国安,杜世通.小波变换及信号重建在压制面波中的应用.石油地球物理勘探,1996,31(3):337-349.
[17]周开明.小波变换及其在去噪中的应用.石油地球物理勘探,1994,29(3):274-285.
[18]李庆武,陈小刚.小波阈值去噪的一种改进方法.光学技术,2006,32(6):831-833.
[19] Gao Hong-Ye, Bruce A G. Wave shrink and semisoft shrinkage. StaSci Research Report, 1995(39).
[20]倪林.一种更适合图像处理的多尺度变换-Curvelet变换.计算机工程与应用,2004,6(28):21-26.
[21] Pennec E L, Mallat S. Image compression with geometrical wavelets. In Proc. of ICIP’2000. Vancouver, Canada, September, 2000:661-664.
[22]黄薇.Curvelet变换及其在图像处理中的应用[D].西安:西安理工大学,2007.
[23]赵心.基于Curvelet变换的图像去噪方法研究与应用[D].青岛:山东科技大学,2007.
[24] Meyer F G, Coifman R, Brushlets. A tool for directional image analysis and image compressin. Applied and Computational Harmonic Analysis, 1997, 5: 147– 187.
[25] Candès E J, Ridgelets theory and applications Ph.D thesis, Department of Statistics, Stanford University,1998.
[26] Candès E J. Monoscale ridgelets for the representation of images with edges. Tech, Report, Department of Statistics.
[27] Candès E J, Donoho D L. Curvelets Tech Report, Deparment of Statitics, Stanford University, 1999.
[28] Donoho D L, Wedgelets. Nearly minimax estimation of Edges, Stanford University, Report, 1997.
[29] Donoho D L, Xiaoming Huo. Beamlet and multiscale image analysis, Stanford University, Report, 2001.
[30] Pennec E Le, Mallat S. Non linear image approximation with bandelets. Tech Report, CMAP Ecole Polytechnique, 2003.
[31] Do M N, Vetterli M, Contourlets J, Stoeckler G, Welland V. Beyond wavelets, Academic Press, 2002.
[32] Velisavljevic V, Beferull-Lozano B, Vetterli M, and Dragotti P L. Directionlets: Anisotropic muti-directional representation with separable filtering, IEEE Trans. on Image Processing, 2006, 15(7):1916-1933.
[33] Labate D, Lim W Q, Kutyniok G, and Weiss G. Sparse multidimensional representation using shearlets, Wavelets XI(SanDiege,CA,2005), SPIE Proc, 5914, SPIE, Bellingham,WA,2005.
[34] Candes E J, Donoho D L. New tight frames of Curvelets and optimal representations of objects with C2 Singularities. Communion Pure and Appl. Math, 2002, 57(2):219-266.
[35] Bovike A C, Clark M. Multichannel texture analysis using localized spatial filters. IEEE, PAMI,1990,12(1):55-72.
[36] Herrmann F J, Verschuur E. Curvelet-domain multiple elimination with sparseness constraints. Society of exploration geophysicists, Expanded Abstracts, 1333-1336, 2004.
[37] Hennenfent G, Herrmann F J. Three-term amplitude-versus-offset(AVO)inverse on revisited by Curvelet and Wavelet transforms. Society of exploration geophysicists, Expanded Abstracts, 211-214, 2004.
[38] Huub D, Maarten V. Wave-character preserving pre-stack map migration using curvelets. Society of exploration geophysicists, Expanded Abstracts, 961-964, 2004.
[39] Herrmann F J, Deli Wang, Hennenfent G, et al. Seismic data processing with curvelets: A multiscale and nonlinear approach. Society of exploration geophysicists, Expanded Abstracts, 2220-2224, 2007.
[40] Ramesh N, Domimique G, Mohamed T, et al. Coherent and random noise attenuation using the curvelet transform. The leading Edge, 2008, 27(2):240-248.
[41]何劲,李宏伟,张帆.基于Curvelet变换的图像消噪.现代电子技术,2008(2):140-144.
[42]刘国高,周建东,符进祥.Curvelet变换及其在图像去噪中的应用研究.电子测量技术,2008(7):7-11.
[43]卢成武,宋国乡.带曲波域约束的全变差正则化抑噪方法[J].2008,36(4):646-649.
[44]吴芳平,狄红卫.基于Curvelet变换的软硬阈值折衷图像去噪.光学技术,2007,33(5):688-690.
[45]焦李成,侯彪,王爽,刘芳.图像多尺度几何分析理论与应用-后小波分析理论与应用.西安:西安电子科技大学出版社,2008.
[46]焦李成,谭山.图像的多尺度几何分析:回顾和展望.电子学报,2003,12A:1975-1981.
[47]张素芳,徐义贤,雷栋.基于Curvelet变换的多次波去除技术.石油地球物理勘探,2006,41(3):262-265.
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