基于广义高斯分布的地震盲反褶积方法研究
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摘要
Bussgang算法是针对褶积盲源分离问题提出的,本文将其用于地震盲反褶积处理.由于广义高斯概率密度函数具有逼近任意概率密度函数的能力,从反射系数序列的统计特征出发,引入广义高斯分布来体现反射系数序列超高斯分布特征.依据反射系数序列的统计特征和Bussgang算法原理,建立以Kullback-Leibler距离为非高斯性度量的目标函数,并导出算法中涉及到的无记忆非线性函数,最终实现了地震盲反褶积.模型试算和实际资料处理结果表明,该方法能较好地适应非最小相位系统,能够同时实现地震子波和反射系数估计,有效地提高地震资料分辨率.
Deconvolution is an effective and essential method to improve seismic resolution.Traditional deconvolution techniques assume that the wavelet is minimum phase and the reflection coefficients have a white Gaussian noise distribution.The assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible;however,a non-Gaussian distribution in theory allows recovery of the phase.It is generally recognized that primary reflection coefficients typically have a non-Gaussian amplitude distribution,and the purpose of deconvolution is to recover the non-Gaussian distribution feature of the reflectivity.Blind deconvolution differs from conventional deconvolution in that the reflection coefficients have a non-Gaussian amplitude distribution and we do not make a priori assumption about the wavelet phase.Bussgang algorithm was proposed for convolutive blind source separation problem,in this paper,it was applied to seismic blind deconvolution process.Because the generalized Gaussian probability density function has the capacity for approximating any probability density function,in accordance with the statistical characteristics of the reflectivity,it was introduced in to reflect the super-Gaussian distribution characteristics of the reflectivity.On the basis of the statistical characteristics of the reflectivity and the principle of Bussgang algorithm,a corresponding objective function which utilizing Kullback-Leibler distance as non-Gaussian measure was established,and then,the memoryless nonlinearity involved in Bussgang algorithm was derived.finally,the seismic blind deconvolution technique based on generalized Gaussian distribution was realized.The results of model test showed that the conventional deconvolution methods,such as spiking deconvolution,estimate the wavelet characteristics from the autocorrelation,unfortunately,there is no information about the phase of the wavelet in the autocorrelation,so the deconvolution result is incorrect.However,testing results showed that the deconvolution method in this paper can be better adapt to non-minimum phase systems,the seismic wavelet and reflectivity can be estimated at the same time,the phase of wavelet can be correctly recovered,and the method is robust in the presence of noise.Then,the method was used to process the field data,in contrast with the spiking deconvolution result,the blind deconvolution technique not only improved the resolution of the profile,the phase axis superimposed together were separated,but also highlights the weak reflection information between the strong reflection axis.As an effective means to improve seismic resolution,the blind deconvolution technique can broaden the effective band of seismic records,and will play an important role in seismic exploration and exploitation.
Deconvolution is an effective and essential method to improve seismic resolution.Traditional deconvolution techniques assume that the wavelet is minimum phase and the reflection coefficients have a white Gaussian noise distribution.The assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible;however,a non-Gaussian distribution in theory allows recovery of the phase.It is generally recognized that primary reflection coefficients typically have a non-Gaussian amplitude distribution,and the purpose of deconvolution is to recover the non-Gaussian distribution feature of the reflectivity.Blind deconvolution differs from conventional deconvolution in that the reflection coefficients have a non-Gaussian amplitude distribution and we do not make a priori assumption about the wavelet phase.Bussgang algorithm was proposed for convolutive blind source separation problem,in this paper,it was applied to seismic blind deconvolution process.Because the generalized Gaussian probability density function has the capacity for approximating any probability density function,in accordance with the statistical characteristics of the reflectivity,it was introduced in to reflect the super-Gaussian distribution characteristics of the reflectivity.On the basis of the statistical characteristics of the reflectivity and the principle of Bussgang algorithm,a corresponding objective function which utilizing Kullback-Leibler distance as non-Gaussian measure was established,and then,the memoryless nonlinearity involved in Bussgang algorithm was derived.finally,the seismic blind deconvolution technique based on generalized Gaussian distribution was realized.The results of model test showed that the conventional deconvolution methods,such as spiking deconvolution,estimate the wavelet characteristics from the autocorrelation,unfortunately,there is no information about the phase of the wavelet in the autocorrelation,so the deconvolution result is incorrect.However,testing results showed that the deconvolution method in this paper can be better adapt to non-minimum phase systems,the seismic wavelet and reflectivity can be estimated at the same time,the phase of wavelet can be correctly recovered,and the method is robust in the presence of noise.Then,the method was used to process the field data,in contrast with the spiking deconvolution result,the blind deconvolution technique not only improved the resolution of the profile,the phase axis superimposed together were separated,but also highlights the weak reflection information between the strong reflection axis.As an effective means to improve seismic resolution,the blind deconvolution technique can broaden the effective band of seismic records,and will play an important role in seismic exploration and exploitation.
引文
[1]Kjetil F K,Tofinn T.Multichannel blind deconvolution of seismicsignals.Geophysics,1998,63(6):2093-2107.
[2]Luo H,Li Y D.The application of blind channel identificationtechniques to prestack seismic deconvolution.Proceeding ofThe IEEE,1998,86(10):2082-2089.
[3]刘喜武,刘洪.地震盲反褶积综述.地球物理学进展,2003,18(2):203-209.Liu X W,Liu H.Survey on seismic blind deconvolution.Progress in Geophysics(in Chinese),2003,18(2):203-209.
[4]王西文,胡自多,田彦灿等.地震子波处理的二步法反褶积方法研究.地球物理学进展,2006,21(4):1167-1179.Wang X W,Hu Z D,Tian Y C,et al.Study of seismic waveletprocessing method in two step deconvolution.Progress inGeophysics(in Chinese),2006,21(4):1167-1179.
[5]患晓宇,刘洪,李幼铭.预条件共轭梯度反褶积的改进及其应用.地球物理学进展,2006,21(4):1192-1197.Xi X Y,Liu H,Li Y M.The improvement and application ofpreconditional conjugate gradient deconvolutions.Progress inGeophysics(in Chinese),2006,21(4):1192-1197.
[6]吴庆举,李永华,张瑞青等.用多道反褶积方法测定台站接收函数.地球物理学报,2007,50(3):791-796.Wu Q J,Li Y H,Zhang R Q,et al.Receiver function estimatedby multi-channel deconvolution.Chinese J.Geophys.(inChinese),2007,50(3):791-796.
[7]陈宝书,梅金顺,王润秋.褶积与反褶积的一种计算方法.地球物理学进展,2009,24(2):501-506.Chen B S,Mei J S,Wang R Q.A new convolutional anddeconvolutional method.Progress in Geophysics(in Chinese),2009,24(2):501-506.
[8]刘喜武,高伟,张宁等.基于带状混合矩阵ICA实现地震盲反褶积.地球物理学进展,2007,22(4):1153-1163.Liu X W,Gao W,Zhang N,et al.ICA with banded mixingmatrix based seismic blind deconvolution.Progress inGeophysics(in Chinese),2007,22(4):1153-1163.
[9]Baan M V,Pham D T.Robust wavelet estimation and blinddeconvolution of noisy surface seismics.Geophysics,2008,73(5):V37-V46.
[10]张繁昌,刘杰,印兴耀等.修正柯西约束地震盲反褶积方法.石油地球物理勘探,2008,43(4):391-396.Zhang F C,Liu J,Yin X Y and Yang P J.Modified Cauchy-constrained seismic blind deconvolution.Oil GeophysicalProspecting(in Chinese),2008,43(4):391-396.
[11]Walden A T.Non-Gaussian reflectivity,entropy,and deconvolution.Geophysics,1985,50(12):2862-2888.
[12]Hy¨υarinen A,Karhunen J,Oja E.Independent ComponentAnalysis.New York:John Wiley&Sons,Inc.,2001:355-369.
[13]印兴耀,刘杰,杨培杰.一种基于负熵的Bussgang地震盲反褶积方法.石油地球物理勘探,2007,42(5):499-505.Yin X Y,Liu J,Yang P J.A negative entropy-based Bussgangseismic blind de-convolotion.Oil Geophysical Prospecting(inChinese),2007,42(5):499-505.
[14]Nadarajah S.A generalized normal distribution.Journal ofApplied Statistics,2005,32(7):685-694.
[15]Bellini S.Bussgang techniques for blind equalization.//IEEEGlobal Telecommunication Conference Records.1986:1634-1640.
[16]Bellini S.Blind Equalization.Alta Frequenza,1988,57:445-450.
[17]Tenorio L.Modeling Non-Gaussian reflectivities:generalizingWiener-Levinson deconvolution.Geophysics,2001,66(6):1913-1920.
[18]傅予力,谢胜利,何昭水.稀疏信号的参数分析.武汉大学学报(工学版),2006,39(6):10-104.Fu Y L,Xie S L,He Z S.Parametric analysis of SparseSignals.Engineering Journal of Wuhan University(inChinese),2006,39(6):101-104.
[19]何昭水,傅予力,谢胜利.信号的稀疏性分析.自然科学进展,2006,16(9):1167-1173.He Z S,Fu Y L,Xie S L.Analysis of sparse signals.Progressin Natural Science(in Chinese),2006,16(9):1167-1173.
[20]Donoho D L.On Minimum Entropy Deconvolution.//Proc2nd Applied Time Series Symp.,1981,109(6):565-608.
[21]杨福生,洪波.独立分量分析的原理与应用.北京:清华大学出版社,2006:20-22.Yang F S,Hon B.Independent Component Analysis Theoryand Application(in Chinese).Beijing:Tsinghua UniversityPress,2006:20-22.
[22]Varanasi M K,Aazhang B.Parametric generalized Gaussiandensity estimation.The Journal of the Acoustical Society ofAmerica,1989,86(4):1404-1415.
[23]Kamran S,Alberto L G.Estimation of shape parameter forgeneralized Gaussian distributions in subband decompositionsof video.IEEE Trans.on Circuits and Systems for VideoTechnology,1995,5(1):52-56.
[24]Krupiński R,Purczyński J.Approximated fast estimator forthe shape parameter of Generalized Gaussian distribution.Journal of Signal Processing,2005,86(2):205-211.
[25]Dahyot R,Wilson S.Robust scale estimation for thegeneralized gaussian probability density function.MetodoloskiZvezki,2006,3(1):21-37.
[26]汪太月,李志明.一种广义高斯分布的参数快速估计法.工程球物理学报,2006,3(3):172-176.Wang T Y,Li Z M.A fast parameter estimation of generalizedGaussian distribution.Chinese Journal of EngineeringGeophysics(in Chinese),2006,3(3):172-176.
[2]Luo H,Li Y D.The application of blind channel identificationtechniques to prestack seismic deconvolution.Proceeding ofThe IEEE,1998,86(10):2082-2089.
[3]刘喜武,刘洪.地震盲反褶积综述.地球物理学进展,2003,18(2):203-209.Liu X W,Liu H.Survey on seismic blind deconvolution.Progress in Geophysics(in Chinese),2003,18(2):203-209.
[4]王西文,胡自多,田彦灿等.地震子波处理的二步法反褶积方法研究.地球物理学进展,2006,21(4):1167-1179.Wang X W,Hu Z D,Tian Y C,et al.Study of seismic waveletprocessing method in two step deconvolution.Progress inGeophysics(in Chinese),2006,21(4):1167-1179.
[5]患晓宇,刘洪,李幼铭.预条件共轭梯度反褶积的改进及其应用.地球物理学进展,2006,21(4):1192-1197.Xi X Y,Liu H,Li Y M.The improvement and application ofpreconditional conjugate gradient deconvolutions.Progress inGeophysics(in Chinese),2006,21(4):1192-1197.
[6]吴庆举,李永华,张瑞青等.用多道反褶积方法测定台站接收函数.地球物理学报,2007,50(3):791-796.Wu Q J,Li Y H,Zhang R Q,et al.Receiver function estimatedby multi-channel deconvolution.Chinese J.Geophys.(inChinese),2007,50(3):791-796.
[7]陈宝书,梅金顺,王润秋.褶积与反褶积的一种计算方法.地球物理学进展,2009,24(2):501-506.Chen B S,Mei J S,Wang R Q.A new convolutional anddeconvolutional method.Progress in Geophysics(in Chinese),2009,24(2):501-506.
[8]刘喜武,高伟,张宁等.基于带状混合矩阵ICA实现地震盲反褶积.地球物理学进展,2007,22(4):1153-1163.Liu X W,Gao W,Zhang N,et al.ICA with banded mixingmatrix based seismic blind deconvolution.Progress inGeophysics(in Chinese),2007,22(4):1153-1163.
[9]Baan M V,Pham D T.Robust wavelet estimation and blinddeconvolution of noisy surface seismics.Geophysics,2008,73(5):V37-V46.
[10]张繁昌,刘杰,印兴耀等.修正柯西约束地震盲反褶积方法.石油地球物理勘探,2008,43(4):391-396.Zhang F C,Liu J,Yin X Y and Yang P J.Modified Cauchy-constrained seismic blind deconvolution.Oil GeophysicalProspecting(in Chinese),2008,43(4):391-396.
[11]Walden A T.Non-Gaussian reflectivity,entropy,and deconvolution.Geophysics,1985,50(12):2862-2888.
[12]Hy¨υarinen A,Karhunen J,Oja E.Independent ComponentAnalysis.New York:John Wiley&Sons,Inc.,2001:355-369.
[13]印兴耀,刘杰,杨培杰.一种基于负熵的Bussgang地震盲反褶积方法.石油地球物理勘探,2007,42(5):499-505.Yin X Y,Liu J,Yang P J.A negative entropy-based Bussgangseismic blind de-convolotion.Oil Geophysical Prospecting(inChinese),2007,42(5):499-505.
[14]Nadarajah S.A generalized normal distribution.Journal ofApplied Statistics,2005,32(7):685-694.
[15]Bellini S.Bussgang techniques for blind equalization.//IEEEGlobal Telecommunication Conference Records.1986:1634-1640.
[16]Bellini S.Blind Equalization.Alta Frequenza,1988,57:445-450.
[17]Tenorio L.Modeling Non-Gaussian reflectivities:generalizingWiener-Levinson deconvolution.Geophysics,2001,66(6):1913-1920.
[18]傅予力,谢胜利,何昭水.稀疏信号的参数分析.武汉大学学报(工学版),2006,39(6):10-104.Fu Y L,Xie S L,He Z S.Parametric analysis of SparseSignals.Engineering Journal of Wuhan University(inChinese),2006,39(6):101-104.
[19]何昭水,傅予力,谢胜利.信号的稀疏性分析.自然科学进展,2006,16(9):1167-1173.He Z S,Fu Y L,Xie S L.Analysis of sparse signals.Progressin Natural Science(in Chinese),2006,16(9):1167-1173.
[20]Donoho D L.On Minimum Entropy Deconvolution.//Proc2nd Applied Time Series Symp.,1981,109(6):565-608.
[21]杨福生,洪波.独立分量分析的原理与应用.北京:清华大学出版社,2006:20-22.Yang F S,Hon B.Independent Component Analysis Theoryand Application(in Chinese).Beijing:Tsinghua UniversityPress,2006:20-22.
[22]Varanasi M K,Aazhang B.Parametric generalized Gaussiandensity estimation.The Journal of the Acoustical Society ofAmerica,1989,86(4):1404-1415.
[23]Kamran S,Alberto L G.Estimation of shape parameter forgeneralized Gaussian distributions in subband decompositionsof video.IEEE Trans.on Circuits and Systems for VideoTechnology,1995,5(1):52-56.
[24]Krupiński R,Purczyński J.Approximated fast estimator forthe shape parameter of Generalized Gaussian distribution.Journal of Signal Processing,2005,86(2):205-211.
[25]Dahyot R,Wilson S.Robust scale estimation for thegeneralized gaussian probability density function.MetodoloskiZvezki,2006,3(1):21-37.
[26]汪太月,李志明.一种广义高斯分布的参数快速估计法.工程球物理学报,2006,3(3):172-176.Wang T Y,Li Z M.A fast parameter estimation of generalizedGaussian distribution.Chinese Journal of EngineeringGeophysics(in Chinese),2006,3(3):172-176.
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