基于高阶统计约束实现同态盲地震反褶积
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摘要
本文通过引入高阶统计学的独立变量分析算法(ICA),利用双谱估计出的地震子波作为约束条件来实现同态盲地震反褶积。首先在无噪声的条件下,将地震记录由时间域变换到同态域,利用相邻两道地震道作为组合,将地震褶积模型转换为线性混合ICA模型;然后,利用高阶统计学中的双谱估计地震子波,利用估计出的地震子波信息作为约束条件应用于快速独立变量分析算法(FastICA)中,实现地震子波和反射系数在同态域的分离;最后将分离的地震子波和反射系数再反变换到时间域,即可得到反射系数和地震子波。模拟和实际地震数据的数值算例均表明,在不对反射系数作高斯白噪假设及子波最小相位假设的条件下,基于高阶统计约束的同态盲反褶积方法能够取得较好的反褶积效果。
A high order statistical method,so called,in-dependent components analysis(ICA)with constraint of seismic wavelet estimated from bispectrum of seismic traces,is introduced in this paper to improve the traditional homomorphic seismic deconvolution method.In the noise-free condition,seismic records are converted from the time domain to the complex cepstrum domain in order to transform the common seismic model to the basic ICA model.By applying FastICA algorithm,reflectivity series and the seismic wavelet can be produced in complex cepstrum domain and converted back to the time domain subsequently.Model and real seismic data numerical examples show that this method can blindly and effectively inverse the wavelet and the reflectivity at the same time without the assumptions of Gauss reflectivity white noise and wavelet minimum phase.The algorithm referred here is an updated version of homomorphic deconvolution methods for seismic signal blind deconvolution and merits more researches.
A high order statistical method,so called,in-dependent components analysis(ICA)with constraint of seismic wavelet estimated from bispectrum of seismic traces,is introduced in this paper to improve the traditional homomorphic seismic deconvolution method.In the noise-free condition,seismic records are converted from the time domain to the complex cepstrum domain in order to transform the common seismic model to the basic ICA model.By applying FastICA algorithm,reflectivity series and the seismic wavelet can be produced in complex cepstrum domain and converted back to the time domain subsequently.Model and real seismic data numerical examples show that this method can blindly and effectively inverse the wavelet and the reflectivity at the same time without the assumptions of Gauss reflectivity white noise and wavelet minimum phase.The algorithm referred here is an updated version of homomorphic deconvolution methods for seismic signal blind deconvolution and merits more researches.
引文
[1]刘喜武,刘洪.地震盲反褶积综述.地球物理学进展,2003,18(2):203～209Liu Xiwu,Liu Hong.Survey on seismic blind decon-volution.Progress in Geophysics,2003,18(2):203～209
[2]刘喜武,刘洪.实现稀疏反褶积的预条件共轭梯度法.物探化探计算技术,2003,18(3):215～219Liu Xiwu,Liu Hong.The preconditional dual conju-gate gradient algorithm for sparse deconvolution.Computing Techniques for Geophysical and Geo-chemical Exploration,2003,18(3):215～219
[3]刘喜武,刘洪,李幼铭.反射系数和子波同时迭代反演的预条件共轭梯度法.物探化探计算技术,2006,21(3):211～215Liu Xiwu,Liu Hong,Li Youming.The precondi-tional conjugate gradient algorithm for inversion of re-flectivity and wavelet by simultaneous iteration.Com-puting Techniques for Geophysical and GeochemicalExploration,2006,21(3):211～215
[4]胡启宇.用于同态反褶积的最小相位变换.石油地球物理勘探,1984,19(2):126～139Hu Qiyu.Minimum phase transform used to makehomomorphic deconvolution.OGP,1984,19(2):126～139
[5]周兴元.应用同态理论估算地震子波.石油地球物理勘探,1983,18(6):510～521Zhou Xingyuan.The estimation of seismic wavelet byhomomorphic theory.OGP,1983,18(6):510～521
[6]Oppenheim A V.Supperposition in a Class of Non-linear Systems.Technical Report No.432,ReaearchLaboratory of Electronics,MIT,Cambridge,Mars,1965
[7]Schafer R W.Echo Removal Discrete GeneralizedLinear Filtering.Technical Report No.466,Re-search Laboratory of Electronics,MIT,Cambridge,Mars,1969
[8]Stoffa P L et al.The application of homomorphic de-convolution to shallow-water marine seismology—PartⅠ:models.Geophysics,1974,39(4):401～416
[9]Stoffa P L et al.The application of homomorphic decon-volution to shallow-water marine seismology—PartⅡ:real data.Geophysics,1974,39(4):417～426
[10]俞寿朋.相位谱及其计算.石油地球物理勘探,1981,16(5):1～14Yu Shoupeng.The phase spectrum and it's calcula-tion.OGP,1981,16(5):1～14
[11]凌云,俞寿朋,周熙襄.零相位同态反褶积.石油地球物理勘探,1995,30(3):299～309LingYun,Yu Shoupeng and Zhou Xixiang.Zero-phase homomorphic deconvolution.OGP,1995,30(3):299～309
[12]王君,周兴元,曹孟起.同态反褶积的改进与应用.石油地球物理勘探,2003,28(增刊):27～30
[13]杨红卫,杨丽,王炳锡.一种基于ICA的同态盲反卷积算法.计算机工程与应用,2005,41(17):30～32Yang Hongwei,Yang Li and Wang Bingxi.An algo-rithm for homomorphic blind deconvolution based onICA.Computer Engineering and Applications,2005,41(17):30～32
[14]Gao Wei,Liu Huaishan and Zhang Jin.ICA with ho-momorphic deconvolution based seismic blind decon-volution.IFCSTA,2009 International Forum onComputer Science Technology and Applications,2009,2:421～424
[15]杨培杰,印兴耀.地震子波提取方法综述.石油地球物理勘探,2008,43(1):123～128Yang Peijie,Yin Xingyao.Summary of seismic wave-let pick-up.OGP,2008,43(1):123～128
[16]谢桂生,石玉梅,尹成.高阶累积量法子波估计预处理.石油物探,2000,39(4):19～25Xie Guisheng Shi Yumei and Yin Cheng.Wavelet es-timation and processing using high-order accumulationmethod.GPP,2000,39(4):19～25
[17]尹成,唐斌,谢桂生.地震子波估计——高阶累积量矩阵方程法.信号处理,2000,16(增刊1):83～87,62Yin Cheng,Tang Bin and Xie Guisheng.Seismicwavelet estimation:matrix-equation method of high-order cumulants.Signal Processing,2000,16(Sup1):83～87,62
[18]唐斌,尹成.基于高阶统计的非最小相位地震子波恢复.地球物理学报,2001,44(3):404～410Tang Bin,Yin Cheng.Non-minimum phase seismicwavelet reconstruction based on higher order statis-tics.Chinese Journal of Geophysics,2001,44(3):404～410
[19]李鲲鹏,李衍达,张学工,许建华.基于谱模拟技术的混合相位地震子波估计方法.石油物探,2001,40(2):21～28Li Kunpeng,Li Yanda,Zhang Xuegong and Xu Jian-hua.The mixed-phase wavelet estimate method basedon spectral modeling.GPP,2001,40(2):21～28
[20]尹成,伍志明,邓怀群.高阶统计量方法在地震勘探中的应用.地球物理学进展,2003,18(3):546～550Yin Cheng,Wu Zhiming and Deng Huaiqun.Appli-cation of high-order statistics in seismic exploration.Progress in Geophysics,2003,18(3):546～550
[21]李大卫,田继东,成竹,杨旭明.基于高阶统计的混合相位子波估计及其处理.勘探地球物理进展,2005,28(2):117～121Li Dawei,Tian Jidong,Cheng Zhu and Yang Xum-ing.Estimation of mixed-phase wavelet base on high-er-order statistics.Progress in Exploration Geophy-sics,2005,28(2):117～121
[22]李大卫,尹成,熊晓军,马洪艳.高阶谱混合方法地震子波估计及处理.地球物理学进展,2005,20(1):29～33Li Dawei,Yin Cheng,Xiong Xiaojun and Ma Hong-yan.A hybrid high-order spectrum method for seis-mic wavelet estimation and processing.Progress inGeophysics,2005,20(1):29～33
[23]戴永寿,郑德玲,魏磊,霍志勇.高阶统计量地震子波估计建模.石油地球物理勘探,2006,41(5):514～518Dai Yongshou,Zheng Deling,Wei Lei and HuoZhiyong.Estimation of high-order statistic seismicwavelet.OGP,2006,41(5):514～518
[24]彭才,朱仕军,黄中玉,孙建库.基于动态褶积模型的动态子波估计.石油物探,2007,46(4):324～329Peng Cai,Zhu Shijun,Huang Zhongyu and Sun Jianku.Dynamic wavelet estimation based on the dynamic convo-lution model.GPP,2007,46(4):324～329
[25]李亚峻,李月,高颖.基于双谱幅值和相位重构的地震子波提取.地球物理学进展,2007,22(3):947～952Li Yajun,Li Yue and Gao Ying.A method of extrac-ting seismic wavelet based on bispectrum amplitudeand phase reconstruction.Progress in Geophysics,2007,22(3):947～952
[26]彭才,曾涛,常智,朱仕军.混合相位动态子波估计.油气地球物理,2008,6(1):21～24Peng Cai,Zeng Tao,Chang Zhi and Zhu Shijun.Es-timation of mixed-phase nonstationary wavelet.Pe-troleum Geophysics,2008,6(1):21～24
[27]王荐,朱仕军,文中平等.基于高阶累积量拟合及混合蚁群算法的地震子波估计.勘探地球物理进展,2009,32(5):330～333Wang Jian,Zhu Shijun,Wen Zhongping et al.Seis-mic wavelet estimation using high-order cumulantmatching method and hybrid ant colony algorithm.Progress in Exploration Geophysics,2009,32(5):330～333
[28]Yu Yongcai,Wang Shangxu,Yuan Sanyi and QiPengfei.Phase estimation in bispectral domain basedon conformal mapping and applications in seismicwavelet estimation.Applied Geophysics,2011,18(1):36～47
[29]张贤达.时间序列分析——高阶统计量方法.北京:清华大学出版社,1999,6～20
[30]Sundaramoorthy G,Raghuveer M R,Dianat S A.Bis-pectral reconstruction of signals in noise:amplitudereconstruction issues.IEEE Trans Acoustics Speech,Signal Processing,1990,38(7):1297～1306
[31]Brillinger D R.An introduction topolyspectra.AnnMath Statist,1965,36(1):1351～1374
[32]Rosenblatt M,Van Ness J W.Estimation of the bi-spectrum.Ann Math Statist,1965,36(1):1120～1136
[33]Velis D R,Ulrych T J.Simulated annealing waveletestimation via fourth-order cumulant matching.Geo-physics,1996,61(6):1939～1948
[2]刘喜武,刘洪.实现稀疏反褶积的预条件共轭梯度法.物探化探计算技术,2003,18(3):215～219Liu Xiwu,Liu Hong.The preconditional dual conju-gate gradient algorithm for sparse deconvolution.Computing Techniques for Geophysical and Geo-chemical Exploration,2003,18(3):215～219
[3]刘喜武,刘洪,李幼铭.反射系数和子波同时迭代反演的预条件共轭梯度法.物探化探计算技术,2006,21(3):211～215Liu Xiwu,Liu Hong,Li Youming.The precondi-tional conjugate gradient algorithm for inversion of re-flectivity and wavelet by simultaneous iteration.Com-puting Techniques for Geophysical and GeochemicalExploration,2006,21(3):211～215
[4]胡启宇.用于同态反褶积的最小相位变换.石油地球物理勘探,1984,19(2):126～139Hu Qiyu.Minimum phase transform used to makehomomorphic deconvolution.OGP,1984,19(2):126～139
[5]周兴元.应用同态理论估算地震子波.石油地球物理勘探,1983,18(6):510～521Zhou Xingyuan.The estimation of seismic wavelet byhomomorphic theory.OGP,1983,18(6):510～521
[6]Oppenheim A V.Supperposition in a Class of Non-linear Systems.Technical Report No.432,ReaearchLaboratory of Electronics,MIT,Cambridge,Mars,1965
[7]Schafer R W.Echo Removal Discrete GeneralizedLinear Filtering.Technical Report No.466,Re-search Laboratory of Electronics,MIT,Cambridge,Mars,1969
[8]Stoffa P L et al.The application of homomorphic de-convolution to shallow-water marine seismology—PartⅠ:models.Geophysics,1974,39(4):401～416
[9]Stoffa P L et al.The application of homomorphic decon-volution to shallow-water marine seismology—PartⅡ:real data.Geophysics,1974,39(4):417～426
[10]俞寿朋.相位谱及其计算.石油地球物理勘探,1981,16(5):1～14Yu Shoupeng.The phase spectrum and it's calcula-tion.OGP,1981,16(5):1～14
[11]凌云,俞寿朋,周熙襄.零相位同态反褶积.石油地球物理勘探,1995,30(3):299～309LingYun,Yu Shoupeng and Zhou Xixiang.Zero-phase homomorphic deconvolution.OGP,1995,30(3):299～309
[12]王君,周兴元,曹孟起.同态反褶积的改进与应用.石油地球物理勘探,2003,28(增刊):27～30
[13]杨红卫,杨丽,王炳锡.一种基于ICA的同态盲反卷积算法.计算机工程与应用,2005,41(17):30～32Yang Hongwei,Yang Li and Wang Bingxi.An algo-rithm for homomorphic blind deconvolution based onICA.Computer Engineering and Applications,2005,41(17):30～32
[14]Gao Wei,Liu Huaishan and Zhang Jin.ICA with ho-momorphic deconvolution based seismic blind decon-volution.IFCSTA,2009 International Forum onComputer Science Technology and Applications,2009,2:421～424
[15]杨培杰,印兴耀.地震子波提取方法综述.石油地球物理勘探,2008,43(1):123～128Yang Peijie,Yin Xingyao.Summary of seismic wave-let pick-up.OGP,2008,43(1):123～128
[16]谢桂生,石玉梅,尹成.高阶累积量法子波估计预处理.石油物探,2000,39(4):19～25Xie Guisheng Shi Yumei and Yin Cheng.Wavelet es-timation and processing using high-order accumulationmethod.GPP,2000,39(4):19～25
[17]尹成,唐斌,谢桂生.地震子波估计——高阶累积量矩阵方程法.信号处理,2000,16(增刊1):83～87,62Yin Cheng,Tang Bin and Xie Guisheng.Seismicwavelet estimation:matrix-equation method of high-order cumulants.Signal Processing,2000,16(Sup1):83～87,62
[18]唐斌,尹成.基于高阶统计的非最小相位地震子波恢复.地球物理学报,2001,44(3):404～410Tang Bin,Yin Cheng.Non-minimum phase seismicwavelet reconstruction based on higher order statis-tics.Chinese Journal of Geophysics,2001,44(3):404～410
[19]李鲲鹏,李衍达,张学工,许建华.基于谱模拟技术的混合相位地震子波估计方法.石油物探,2001,40(2):21～28Li Kunpeng,Li Yanda,Zhang Xuegong and Xu Jian-hua.The mixed-phase wavelet estimate method basedon spectral modeling.GPP,2001,40(2):21～28
[20]尹成,伍志明,邓怀群.高阶统计量方法在地震勘探中的应用.地球物理学进展,2003,18(3):546～550Yin Cheng,Wu Zhiming and Deng Huaiqun.Appli-cation of high-order statistics in seismic exploration.Progress in Geophysics,2003,18(3):546～550
[21]李大卫,田继东,成竹,杨旭明.基于高阶统计的混合相位子波估计及其处理.勘探地球物理进展,2005,28(2):117～121Li Dawei,Tian Jidong,Cheng Zhu and Yang Xum-ing.Estimation of mixed-phase wavelet base on high-er-order statistics.Progress in Exploration Geophy-sics,2005,28(2):117～121
[22]李大卫,尹成,熊晓军,马洪艳.高阶谱混合方法地震子波估计及处理.地球物理学进展,2005,20(1):29～33Li Dawei,Yin Cheng,Xiong Xiaojun and Ma Hong-yan.A hybrid high-order spectrum method for seis-mic wavelet estimation and processing.Progress inGeophysics,2005,20(1):29～33
[23]戴永寿,郑德玲,魏磊,霍志勇.高阶统计量地震子波估计建模.石油地球物理勘探,2006,41(5):514～518Dai Yongshou,Zheng Deling,Wei Lei and HuoZhiyong.Estimation of high-order statistic seismicwavelet.OGP,2006,41(5):514～518
[24]彭才,朱仕军,黄中玉,孙建库.基于动态褶积模型的动态子波估计.石油物探,2007,46(4):324～329Peng Cai,Zhu Shijun,Huang Zhongyu and Sun Jianku.Dynamic wavelet estimation based on the dynamic convo-lution model.GPP,2007,46(4):324～329
[25]李亚峻,李月,高颖.基于双谱幅值和相位重构的地震子波提取.地球物理学进展,2007,22(3):947～952Li Yajun,Li Yue and Gao Ying.A method of extrac-ting seismic wavelet based on bispectrum amplitudeand phase reconstruction.Progress in Geophysics,2007,22(3):947～952
[26]彭才,曾涛,常智,朱仕军.混合相位动态子波估计.油气地球物理,2008,6(1):21～24Peng Cai,Zeng Tao,Chang Zhi and Zhu Shijun.Es-timation of mixed-phase nonstationary wavelet.Pe-troleum Geophysics,2008,6(1):21～24
[27]王荐,朱仕军,文中平等.基于高阶累积量拟合及混合蚁群算法的地震子波估计.勘探地球物理进展,2009,32(5):330～333Wang Jian,Zhu Shijun,Wen Zhongping et al.Seis-mic wavelet estimation using high-order cumulantmatching method and hybrid ant colony algorithm.Progress in Exploration Geophysics,2009,32(5):330～333
[28]Yu Yongcai,Wang Shangxu,Yuan Sanyi and QiPengfei.Phase estimation in bispectral domain basedon conformal mapping and applications in seismicwavelet estimation.Applied Geophysics,2011,18(1):36～47
[29]张贤达.时间序列分析——高阶统计量方法.北京:清华大学出版社,1999,6～20
[30]Sundaramoorthy G,Raghuveer M R,Dianat S A.Bis-pectral reconstruction of signals in noise:amplitudereconstruction issues.IEEE Trans Acoustics Speech,Signal Processing,1990,38(7):1297～1306
[31]Brillinger D R.An introduction topolyspectra.AnnMath Statist,1965,36(1):1351～1374
[32]Rosenblatt M,Van Ness J W.Estimation of the bi-spectrum.Ann Math Statist,1965,36(1):1120～1136
[33]Velis D R,Ulrych T J.Simulated annealing waveletestimation via fourth-order cumulant matching.Geo-physics,1996,61(6):1939～1948
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