基于广义S变换、经验模态分解叠前去噪方法的比较
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摘要
高频噪声压制是高分辨率地震数据处理中的关键性问题.基于广义S变换、经验模态分解的时频域地震去噪技术具有时变、分频和高保真特性,可有效处理非平稳地震信号,但二者在去噪原理、去噪效果、保真度、计算效率等方面尚存差异.对比分析表明:两种算法在提高地震信号信噪比的同时,可保持地震信号的保真度,保护陡倾角反射界面能量;基于广义S变换的叠前去噪方法以人工交互方式确定不同时刻的高频压制范围,以满足地震信号的时变和空变特性,但其计算效率较慢;基于经验模态分解的叠前去噪方法通过频率-空间域内的短窗口筛分出高频、高波数的本征模量函数,以消除高频、高波数噪声,但其高频噪声压制范围不能随时间变化,存在模态混叠的缺陷.
It is a key issue that high frequency noise is suppressed in high resolution seismic data processing.The time-frequency domain denoising technique based on generalized S transform,empirical mode decomposition have some characters such as time-varying,frequency decomposition,high fidelity.Therefore they can effectively deal with the nonstationary signal.However,there are some differences between two algorithms in the denoising" principle, denoising effect,fidelity of signal and computational efficiency.It is shown that two algorithms not only can enhance the signal-noise ratio but also can effectively reserve the fidelity of seismic signal and protect the steeply dipping reflect event.The denoising method based on generalized S transform can reasonably determined the high frequency suppressed scope by interaction between man and computer in order to meet the need of time-varying and spatialvarying of seismic signal.But the computational efficiency of this method is relatively low.Moreover,the denoising method based on empirical mode decomposition can extract the high frequency and high wavenumber intrinsic mode function from the sliding time window in the frequency-spatial domain so it can restrain the high frequency noise.But the scope of high frequency noise suppression of this method can't vary with time and there is a drawback of mode mixing in this method.
It is a key issue that high frequency noise is suppressed in high resolution seismic data processing.The time-frequency domain denoising technique based on generalized S transform,empirical mode decomposition have some characters such as time-varying,frequency decomposition,high fidelity.Therefore they can effectively deal with the nonstationary signal.However,there are some differences between two algorithms in the denoising" principle, denoising effect,fidelity of signal and computational efficiency.It is shown that two algorithms not only can enhance the signal-noise ratio but also can effectively reserve the fidelity of seismic signal and protect the steeply dipping reflect event.The denoising method based on generalized S transform can reasonably determined the high frequency suppressed scope by interaction between man and computer in order to meet the need of time-varying and spatialvarying of seismic signal.But the computational efficiency of this method is relatively low.Moreover,the denoising method based on empirical mode decomposition can extract the high frequency and high wavenumber intrinsic mode function from the sliding time window in the frequency-spatial domain so it can restrain the high frequency noise.But the scope of high frequency noise suppression of this method can't vary with time and there is a drawback of mode mixing in this method.
引文
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[18]陈凯.基于经验模式分解的去噪方法[J].石油地球物理勘探, 2009,44(5):603-608. Chen K.A new denoising method based on Empirical Mode Decomposition(EMD)[J].Oil Geophysical Prospecting(in Chinese),2009,44(5):603 - 608.
[19]Bekara M,van der Baan M.Random and coherent noise attenuation by empirical mode decomposition[J].Geophysics,2009,74: V89-V98.
[20]Stockwell,R G,Mansinha,L,Lowe,R P.Localization of the complex spectrum:The S transform[J].IEEE Trans,signal Process.,1996,44(4):998-1001.
[21]Pinnegar,R C,Mansinha,L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003,68(1 ): 381-385.
[22]李雪英,侯相辉.基于广义s变换的叠前高频噪声压制[J].石油地球物理勘探,2011,46(4):545-549. Li X Y,Hou X H.Prestack high frequency noise suppression based on generalized S transform[J].Oil Geophysical Prospecting(in Chinese),2011,46(4):545- 549.
[23]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstaionary time series analysis[J].Proc.R.Soc.Lond, 1998,454(1971):903-995.
[24]Huang N E,Zheng S,Long S R.A new view of nonlinear water waves;the Hilbert spectrum[J].Annu.Rev.Fluid Mech,1999,31:417-457.
[25]Huang N E,Wu M L C,Long S R,et al.A confidence limit for the empirical mode decomposition and Hilbert spectrum analysis[J].Proc.R.Soc.Lond,SERIESA,2003,459(2073): 2317-2345.
[26]Battista B M,Knapp C,McGee T,et al.Application of the empirical mode decompositionand Hilbert-Huang transform to seismic reflection data[J].Geophysics,2007,72(5):H29- H37.
[27]Wu Z,Huang N E.A study of the characteristics of white noise using empirical mode decomposition[J].Proc.R.Soc. Lond,SERIESA,2004,460(2046):1587- 1611.
[28]钱昌松,刘代志,刘志刚等.基于递归高通滤波的经验模态分解及其在地震信号分析中的应用[J].地球物理学报,2010,53 (5):1215-1225. Qian C S,Liu D Z,Liu Z G,et al.EMD based on recursive high-pass filter and its application on seismic signal analysis [J].Chinese J.Geophys.(in Chinese),2010,53(5):1215 - 1225.
[2]Liu Y,Liu C,Wang D.A 1D time-varying median filter for seismic random,spike-like noise elimination[J].Geophysics, 2009,74(1):V17-V24.
[3]刘洋,王典,刘财等.局部相关加权中值滤波技术及其在叠后随机噪声衰减中的应用[J].地球物理学报,2011,5d(2):358- 367. Liu Y,Wang D,Liu C,et al.Weighted median filter based on local correlation and its application to poststack random noise attenuation[J].Chinese J.Geophys.(in Chinese),2011,54(2 ): 358-367.
[4]刘伟,杨凯,王征等.基于SVD的正交多项式变换及基在地震资料处理中的应用[J].二程地球物理学报,2010,7(4):433- 437. Liu W,Yang K,Wang Z,et al.Orthogonal polynomials transform based on SVD and its application in seismic data processing[J].Chinese Journal of Engineering Geophysics, 2010,7(4):433-437.
[5]钟伟,杨宝俊,张智.多项式拟合技术在强噪声地震资料中的应用研究[J].地球物理学进展,2006,21(1):184-189. Zhong W,Yang B J,Zhang Z.Research on application of polynomial fitting technique in highly noisy seismic data[J]. Grogress in Geophys.(in Chinese),2006,21(1):184-189.
[6]俞寿朋,蔡希铃.用地震信号多项式拟合提高叠加剖面信噪比[J].石油地球物理勘探,1988,23(2):131-139. Yu S P,Cai X L.Improvement of signal-noise ratio of stack section using polynomial fitting of seismic signal[J].Oil Geophysical Prospecting(in Chinese),1988,23(2):131-139.
[7]Canales L.Random noise reduction[M].54~(th)Annual International Meeting,SEG,Expanded Abstracts,1984,525-527.
[8]Galbraith M.Random noise attenuation by f-x prediction:A tutorial[M].61st Annual International Meeting,SEG, Expanded Abstracts,1991,1428-1431.
[9]Harris P E and White R E.Improving the performance of f-x prediction filter at low signal-to-noise ratios[J].Geophysical Prospecting,1997,45(2):269 -302.
[10]刘洋,Fomel Sergey,刘财等.高阶seislet变换及其在随机噪声消除中的应用[J].地球物理学报,2009,52(8):2142- 2151. Liu Y,Fomel Sergey,Liu C,et al.High-order seislet transform and its application of random noise attenuation[J]. Chinese J.Geophys.(in Chinese),2009,52(8):2142-2151.
[11]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.
[12]夏洪瑞,葛川庆,彭涛.小波时空变阈值去噪方法在可控震源资料处理中的应用[J].石油地球物理勘探,2010,45(1):23- 27. Xia H R,Ge C Q,Peng T.Application of wavelet time-space-varying threshold denoising method in vibroseis seismic data processing[J].Oil Geophysical Prospecting(in Chinese), 2010,45(J):23-27.
[13]Wu A D W,Zhao X L.seismic denosing with curvelet shrinkage [J].Journal of Communication and Computer,2010,7(9):13 -17.
[14]Pinnegar,R C,Eaton,D W.Application of S transform to prestack noise attenuation filtering[J].J.Geophys.Res., 2003,108(Bg):1-10.
[15]王云专,兰金涛,龙玉沙.基于S变换的随机噪声压制方法[J].地球物理学进展,2010,25(2):562-567. Wang Y Z,Lan J T,Long Y S.The method for attenuating random noises based on S transform[J].Grogress in Genphys.(in Chinese),2010,25(2):562-567.
[16]赵淑红,朱光明.S变换时频滤波去噪方法[J].石油地球物理勘探,2007,42(4):402-406. Zhao S H,Zhu M G.Time frequency filtering to denoise by S transform[J].Oil Geophysical Prospecting(in Chinese), 2007,42(4):402- 406.
[17]焦叙明,刘怀山,童思友.广义S变换在叠前地震资料去噪中的应用[J].中国海洋大学学报,2007,37(增Ⅱ):177-180. Jiao S M,Liu H S,Tong S Y.application of generalized S transform for pre-stack seismic data denoising[J].Periodical of Ocean University of Chinas2007,37(Sup.Ⅱ):177-180.
[18]陈凯.基于经验模式分解的去噪方法[J].石油地球物理勘探, 2009,44(5):603-608. Chen K.A new denoising method based on Empirical Mode Decomposition(EMD)[J].Oil Geophysical Prospecting(in Chinese),2009,44(5):603 - 608.
[19]Bekara M,van der Baan M.Random and coherent noise attenuation by empirical mode decomposition[J].Geophysics,2009,74: V89-V98.
[20]Stockwell,R G,Mansinha,L,Lowe,R P.Localization of the complex spectrum:The S transform[J].IEEE Trans,signal Process.,1996,44(4):998-1001.
[21]Pinnegar,R C,Mansinha,L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003,68(1 ): 381-385.
[22]李雪英,侯相辉.基于广义s变换的叠前高频噪声压制[J].石油地球物理勘探,2011,46(4):545-549. Li X Y,Hou X H.Prestack high frequency noise suppression based on generalized S transform[J].Oil Geophysical Prospecting(in Chinese),2011,46(4):545- 549.
[23]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstaionary time series analysis[J].Proc.R.Soc.Lond, 1998,454(1971):903-995.
[24]Huang N E,Zheng S,Long S R.A new view of nonlinear water waves;the Hilbert spectrum[J].Annu.Rev.Fluid Mech,1999,31:417-457.
[25]Huang N E,Wu M L C,Long S R,et al.A confidence limit for the empirical mode decomposition and Hilbert spectrum analysis[J].Proc.R.Soc.Lond,SERIESA,2003,459(2073): 2317-2345.
[26]Battista B M,Knapp C,McGee T,et al.Application of the empirical mode decompositionand Hilbert-Huang transform to seismic reflection data[J].Geophysics,2007,72(5):H29- H37.
[27]Wu Z,Huang N E.A study of the characteristics of white noise using empirical mode decomposition[J].Proc.R.Soc. Lond,SERIESA,2004,460(2046):1587- 1611.
[28]钱昌松,刘代志,刘志刚等.基于递归高通滤波的经验模态分解及其在地震信号分析中的应用[J].地球物理学报,2010,53 (5):1215-1225. Qian C S,Liu D Z,Liu Z G,et al.EMD based on recursive high-pass filter and its application on seismic signal analysis [J].Chinese J.Geophys.(in Chinese),2010,53(5):1215 - 1225.
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