Curvelet域面波衰减方法研究
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摘要
在面波压制方法中,常规面波消除方法都是单一的利用面波某种特性,如Fourier变换域方法利用波组的频率差异等,难以有效地压制面波,并且根据单一的波组特征差异进行面波消除很容易损伤有效波信息。Curvelet变换可以对时空信号进行最稀疏表达,能够获得最优的非线性逼近。分析地震信号面波与有效反射波在Curvelet域(j,θ,k)三维空间的特征差异,将空间域波组方向与Curvelet域角度变量联系起来,指出可以在Curvelet域利用波组的频率、角度和空间位置差异实现波场分离,并设计非线性阈值函数对面波系数进行衰减,避免传统软、硬阈值函数的不足。研究结果表明:基于Curvelet域的面波压制方法受随机噪声的影响较小,它可以有效地压制面波干扰,同时对有效波信息的保真度高。
The traditional methods can suppressing the surface wave to some extent,but they only use single characteristic.For instance,Fourier transform methods use the frequency characteristic between surface wave and effective wave.When these methods are employed to attenuate surface wave,the signal components may be harmed.Curvelet transform is characterized by optimum sparseness constraint condition that it can deal with line-like phenomena in high dimension.The signal characteristic in(j,θ,k) of Curvelet domain between surface wave and desirable signal was analyzed,and the Curvelet angle was linked with the direction of wave group,so surface wave will be separated from effective wave based on the differences in frequency,angle and position characteristics.And besides,a non-linear thresholding was designed to suppress the surface wave coefficients which can avoid the discontinuity caused by the hard or soft thresholding.The results show its feasibility and effectiveness in attenuating surface wave,and it can provide superior surface wave attenuation with minimal impact on the desirable signal components.
The traditional methods can suppressing the surface wave to some extent,but they only use single characteristic.For instance,Fourier transform methods use the frequency characteristic between surface wave and effective wave.When these methods are employed to attenuate surface wave,the signal components may be harmed.Curvelet transform is characterized by optimum sparseness constraint condition that it can deal with line-like phenomena in high dimension.The signal characteristic in(j,θ,k) of Curvelet domain between surface wave and desirable signal was analyzed,and the Curvelet angle was linked with the direction of wave group,so surface wave will be separated from effective wave based on the differences in frequency,angle and position characteristics.And besides,a non-linear thresholding was designed to suppress the surface wave coefficients which can avoid the discontinuity caused by the hard or soft thresholding.The results show its feasibility and effectiveness in attenuating surface wave,and it can provide superior surface wave attenuation with minimal impact on the desirable signal components.
引文
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[20]Herrmann F J,Hennenfent G,Non-parametric seismic datarecovery with Curvelet frames[J].Geophysics J Int,2008,173(1):233-248.
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[23]张恒磊,张云翠,宋双,等.基于Curvelet域的叠前地震资料去噪方法[J].石油地球物理勘探,2008,43(5):508-513.ZHANG Heng-lei,ZHANG Yun-cui,SONG Shuang,et al.Curvelet domain-based prestack seismic data denoise method[J].Oil Geophysical Prospecting,2008,43(5):508-513.
[2]刘法启,张关泉.小波变换与F-K算法在滤波中的应用[J].石油地球物理勘探,1996,31(6):782-791.LIU Fa-qi,ZHANG Guan-quan.Application of wavelettransform and F-K algorithm in filtering[J].Oil GeophysicalProspecting,1996,31(6):782-791.
[3]Herrmann R B,Russell D R.Ground roll:Rejection usingadaptive phase-matched filters[J].Geophysics,1990,55(6):776-781.
[4]夏洪瑞,周开明.地震资料处理中相干干扰消除方法分析[J].石油物探,2003,42(4):526-528.XIA Hong-run,ZHOU Kai-ming.Elimination of coherentinterference in seismic data processing[J].GeophysicalProspecting for Petroleum,2003,42(4):526-528.
[5]高静怀,汪文秉,朱光明,等.地震资料处理中小波函数的选取研究[J].地球物理学报,1996,39(3):389-397.GAO Jing-huai,WANG Wen-bing,ZHU Guang-ming,et al.Onthe choice of wavelet functions for seismic data processing[J].Chinese J Geophys,1996,39(3):389-397.
[6]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 Jing-huai,MAO Jian,MAN Wei-shi,et al.On thedenoising method of prestack seismic data in wavelet domain[J].Chinese J Geophys,2006,49(4):1155-1163.
[7]Deighan A J,Watts D R.Ground-roll suppressing using thewavelet transform[J].Geophysics,1997,62(6):1896-1903.
[8]张三宗,徐义贤.地震记录小波域高阶相关叠加技术[J].地球物理学报,2006,49(2):554-560.ZHANG San-zong,XU Yi-xian.Higher-order correlativestacking for seismic data in the wavelet domain[J].Chinese JGeophys,2006,49(2):554-560.
[9]Mallat S.A theory for multiresolution signal decomposition:Thewavelet representation[J].IEEE Transactions on Pattern Analysisand Machine Intelligence,1989,11(7):674-693.
[10]Candès E J,Donoho D L.Ridgelets:A key to high-dimensionalintermittency[J].Phil Trans Roy Soc London A,1999,357(1760):2495-2509.
[11]Donoho D L.Orthonormal Ridgelets and linear singularities[J].SIAM J Math Anal,1998,31(5):1030-1061.
[12]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 Qian-zong,GAO Jing-huai,CHEN Wen-chao.Ridgeletdomain method of ground-roll suppression[J].Chinese JGeophys,2007,50(4):1210-1215.
[13]Arivazhagan S,Ganesan L,Subash Kumar T G.Textureclassification using Ridgelet transform[J].Pattern RecognitionLetters,2006,27(16):1875-1883.
[14]ZHANG Heng-lei,LIU Tian-you,ZHANG Yun-cui.Denoisingof seismic data via multi-scale Ridgelet transform[J].EarthquakeScience,2009,22(5):493-498.
[15]Candès E J,Donoho D L.Curvelets:A surprisingly effectivenonadattive representation for objects with edges[C]//Cohen A,Rabut C,Schumaker L L.Curves and Surface Fitting.Nashville:Vanderbilt University Press,2000:105-120.
[16]Candès E J,Donoho D L.Continuous curvelet transform[J].Appl Comput Harmon Anal,2005,19(2):198-222.
[17]Starck J L,Fadili M J.Curvelets and ridgelets[EB/OL].[2007-10-24].http://jstarck.free.fr/curvencyclop09.pdf.
[18]Starck J L,Candès E J,Donoho D L.The curvelet transform forimage denoising[J].IEEE Transactions on Image Processing,2002,11(6):67-684.
[19]Neelamani R,Baumstein A I,Gillard D G,et al.Coherent andrandom noise attenuation using the Curvelet transform[J].TheLeading Edge,2008,27(2):240-248.
[20]Herrmann F J,Hennenfent G,Non-parametric seismic datarecovery with Curvelet frames[J].Geophysics J Int,2008,173(1):233-248.
[21]Herrmann F J,Wang D L,Hennenfent G,et al.Curvelet-basedseismic data processing:A multiscale and nonlinear approach[J].Geophysics,2008,73(1):A1-A5.
[22]Douma H,de Hoop M.Leading-order seismic imaging usingCurvelets[J].Geophysics,2007,72(6):S231-S248.
[23]张恒磊,张云翠,宋双,等.基于Curvelet域的叠前地震资料去噪方法[J].石油地球物理勘探,2008,43(5):508-513.ZHANG Heng-lei,ZHANG Yun-cui,SONG Shuang,et al.Curvelet domain-based prestack seismic data denoise method[J].Oil Geophysical Prospecting,2008,43(5):508-513.
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