基于PSO的地震盲反褶积方法
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摘要
本文基于地层反射系数非高斯的统计特性,在反褶积输出单位方差约束下,将反褶积输出的负熵表示为非多项式函数,作为盲反褶积的目标函数,然后采用粒子群算法优化目标函数寻找最佳反褶积算子,实现地震信号的盲反褶积.数值模拟和实际资料处理结果表明,与传统反褶积方法相比,本文方法同时适应于最小相位子波及混合相位子波的反褶积,能够更好地从地震数据中估计反射系数,有效拓宽地震资料的频谱,得到高分辨率的地震资料.
The deconvolution of seismic data is to estimate reflectivity so that the resolution can be improved.In most cases,reflectivity exhibits the non-Gaussian statistical character.The information theory criterion—negentropy is a good measure tool of non-Gaussian character.When the negentropy of deconvolution output attains maximum,deconvolution output can be thought as the optimal estimation of reflectivity.In this paper,based on the non-Gaussian statistical character of reflectivity,the negentropy of deconvolution output is expressed as non-polynomial functions to build objective function for blind deconvolution under the unit variance constraint of deconvolution output.Then Particle Swarm Optimization is applied to search for optimum deconvolution operator in order to achieve deconvolution of seismic data.Numerical simulations and actual seismic data processing results prove that,in contrast to the conventional deconvolution methods,the proposed method is suitable for both minimum-phase and mixed-phase wavelet,can obtain a good estimation of reflectivity from seismic data,and can broaden the spectrum of seismic data effectively resulting in the improved resolution.
The deconvolution of seismic data is to estimate reflectivity so that the resolution can be improved.In most cases,reflectivity exhibits the non-Gaussian statistical character.The information theory criterion—negentropy is a good measure tool of non-Gaussian character.When the negentropy of deconvolution output attains maximum,deconvolution output can be thought as the optimal estimation of reflectivity.In this paper,based on the non-Gaussian statistical character of reflectivity,the negentropy of deconvolution output is expressed as non-polynomial functions to build objective function for blind deconvolution under the unit variance constraint of deconvolution output.Then Particle Swarm Optimization is applied to search for optimum deconvolution operator in order to achieve deconvolution of seismic data.Numerical simulations and actual seismic data processing results prove that,in contrast to the conventional deconvolution methods,the proposed method is suitable for both minimum-phase and mixed-phase wavelet,can obtain a good estimation of reflectivity from seismic data,and can broaden the spectrum of seismic data effectively resulting in the improved resolution.
引文
[1]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.
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[3]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 Bussgang seismic blinddeconvolution method based on negentropy.Oil GeophysicalProspecting(in Chinese),2007,42(5):499-505.
[4]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.
[5]戴永寿,王俊岭,王伟伟等.基于高阶累积量ARMA模型线性非线性结合的地震子波提取方法研究.地球物理学报,2008,51(6):1851-1859.Dai Y S,Wang J L,Wang W W,et al.Seismic waveletextraction via cumulant-based ARMA model approach withlinear and nonlinear combination.Chinese J.Geophys.(inChinese),2008,51(6):1851-1859.
[6]高少武,赵波,贺振华等.地震子波提取方法研究进展.地球物理学进展,2009,24(4):1384-1391.Gao S W,Zhao B,He Z H,et al.Research progress of seismicwavelet extraction.Progress in Geophysics(in Chinese),2009,24(4):1384-1391.
[7]Baan M V D,Pham D T.Robust wavelet estimation and blinddeconvolution of noisy surface seismics.Geophysics,2008,73(5):37-46.
[8]戴永寿,彭星,牛慧.一种基于信息反馈的高精度地震子波提取方法.地球物理学进展,2011,26(3):1004-1009.Dai Y S,Peng X,Niu H.Research on high precision seismicwavelet estimation based on information feedback.Progress inGeophysics(in Chinese),2011,26(3):1004-1009.
[9]岳碧波,彭真明,洪余刚等.基于粒子群优化算法的叠前角道集子波反演.地球物理学报,2009,52(12):3116-3123.Yue B B,Peng Z M,Hong Y G,et al.Wavelet inversion of pre-stack seismic angle-gather based on particle swarmoptimization algorithm.Chinese J.Geophys.(in Chinese),2009,52(12):3116-3123.
[10]章珂,刘贵忠.用遗传算法实现地震信号反褶积.地球物理学报,1997,40(4):550-560.Zhang K,Liu G Z.Deconvolution of seismic signal usinggenetic algorithms.Chinese J.Geophys.(in Chinese),1997,40(4):550-560.
[11]Rosec O,Boucher J M,Nsiri B,et al.Blind marine seismicdeconvolution using statistical MCMC methods.IEEE Journalof Oceanic Engineering(in Chinese),2003,28(3):502-512.
[12]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,et al.Modified Cauchy-constrainedseismic blind deconvolution.Oil Geophysical Prospecting(inChinese),2008,43(4):391-396.
[13]曾锐,刘洪,陈世军等.柯西约束盲反褶积技术在井间地震的应用.地球物理学进展,2004,19(1):166-172.Zeng R,Liu H,Chen S J,et al.Application of cauchy-constraint blind deconvolution in cross-hole seismic dataprocessing.Progress in Geophysics(in Chinese),2004,19(1):166-172.
[14]葸晓宇,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.
[15]刘喜武,宁俊瑞,张改兰.Cauchy稀疏约束Bayesian估计地震盲反褶积框架与算法研究.石油物探,2009,48(5):459-464.Liu X W,Ning J R,Zhang G L.Cauchy sparse constrainedBayesian estimation based seismic blind deconvolution frameand algorithm.Geophysical Prospecting for Petroleum(inChinese),2009,48(5):459-464.
[16]Larue A,Mars J I,Jutten C.Frequency-domain blinddeconvolution based on mutual information rate.IEEETransactions on Signal Processing,2006,54(5):1771-1780.
[17]高静怀,张明,张兵.一种改进的基于互信息率的盲反褶积方法.地球物理学进展,2011,26(2):540-548.Gao J H,Zhang M,Zhang B.An improved blind deconvolutionbased on mutual information rate.Progress in Geophysics(inChinese),2011,26(2):540-548.
[18]Hani A F M,Younis M S,Halim M F M.A HOS-based blinddeconvolution algorithm for the improvement of timeresolution of mixed phase low SNR seismic data.Journal ofGeophysics and Engineering,2009,6(1):87-100.
[19]Santamaría-Caballero I,Pantaleón-Prieto C J,Artés-RodríguezA.Sparse deconvolution using adaptive mixed-Gaussianmodels.Signal Processing,1996,54(2):161-172.
[20]王锐,孙成禹.有限熵反褶积.石油地球物理勘探,2005,40(6):638-641.Wang R,Sun C Y.Finite entropy deconvolution.OilGeophysical Prospecting(in Chinese),2005,40(6):638-641.
[21]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.
[22]刘喜武,刘洪,李幼铭.独立分量分析及其在地震信息处理中应用初探.地球物理学进展,2003,18(1):90-96.Liu X W,Liu H,Li Y M.Independent component analysis andits testing application on seismic signal processing.Progress inGeophysics(in Chinese),2003,18(1):90-96.
[23]Trelea I C.The particle swarm optimization algorithm:convergence analysis and parameter selection.InformationProcessing Letters,2003,85(6):317-325.
[24]朱童,李小凡,李一琼等.基于改进粒子群算法的地震标量波方程反演.地球物理学报,2011,54(11):2951-2959.Zhu T,Li X F,Li Y Q,et al.Seismic scalar wave equationinversion based on an improved particle swarm optimizationalgorithm.Chinese J.Geophys.(in Chinese),2011,54(11):2951-2959.
[25]Walden A T.Non-Gaussian reflectivity,entropy,anddeconvolution.Geophysics,1985,50(12):2862-2888.
[26]Kaplan S T,Ulrych T J.Blind deconvolution and ICA with abanded mixing matrix.Japan:4th International Symposium onIndependent Component Analysis and Blind SourceSeparation,2003.
[2]安西峰,刘平,张旭.地表一致性反褶积在地震勘探中的应用及效果.地球物理学进展,2010,25(6):2125-2129.An X F,Liu P,Zhang X.Application of surface consistentdeconvolution to seismic prospecting and its effect.Progress inGeophysics(in Chinese),2010,25(6):2125-2129.
[3]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 Bussgang seismic blinddeconvolution method based on negentropy.Oil GeophysicalProspecting(in Chinese),2007,42(5):499-505.
[4]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.
[5]戴永寿,王俊岭,王伟伟等.基于高阶累积量ARMA模型线性非线性结合的地震子波提取方法研究.地球物理学报,2008,51(6):1851-1859.Dai Y S,Wang J L,Wang W W,et al.Seismic waveletextraction via cumulant-based ARMA model approach withlinear and nonlinear combination.Chinese J.Geophys.(inChinese),2008,51(6):1851-1859.
[6]高少武,赵波,贺振华等.地震子波提取方法研究进展.地球物理学进展,2009,24(4):1384-1391.Gao S W,Zhao B,He Z H,et al.Research progress of seismicwavelet extraction.Progress in Geophysics(in Chinese),2009,24(4):1384-1391.
[7]Baan M V D,Pham D T.Robust wavelet estimation and blinddeconvolution of noisy surface seismics.Geophysics,2008,73(5):37-46.
[8]戴永寿,彭星,牛慧.一种基于信息反馈的高精度地震子波提取方法.地球物理学进展,2011,26(3):1004-1009.Dai Y S,Peng X,Niu H.Research on high precision seismicwavelet estimation based on information feedback.Progress inGeophysics(in Chinese),2011,26(3):1004-1009.
[9]岳碧波,彭真明,洪余刚等.基于粒子群优化算法的叠前角道集子波反演.地球物理学报,2009,52(12):3116-3123.Yue B B,Peng Z M,Hong Y G,et al.Wavelet inversion of pre-stack seismic angle-gather based on particle swarmoptimization algorithm.Chinese J.Geophys.(in Chinese),2009,52(12):3116-3123.
[10]章珂,刘贵忠.用遗传算法实现地震信号反褶积.地球物理学报,1997,40(4):550-560.Zhang K,Liu G Z.Deconvolution of seismic signal usinggenetic algorithms.Chinese J.Geophys.(in Chinese),1997,40(4):550-560.
[11]Rosec O,Boucher J M,Nsiri B,et al.Blind marine seismicdeconvolution using statistical MCMC methods.IEEE Journalof Oceanic Engineering(in Chinese),2003,28(3):502-512.
[12]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,et al.Modified Cauchy-constrainedseismic blind deconvolution.Oil Geophysical Prospecting(inChinese),2008,43(4):391-396.
[13]曾锐,刘洪,陈世军等.柯西约束盲反褶积技术在井间地震的应用.地球物理学进展,2004,19(1):166-172.Zeng R,Liu H,Chen S J,et al.Application of cauchy-constraint blind deconvolution in cross-hole seismic dataprocessing.Progress in Geophysics(in Chinese),2004,19(1):166-172.
[14]葸晓宇,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.
[15]刘喜武,宁俊瑞,张改兰.Cauchy稀疏约束Bayesian估计地震盲反褶积框架与算法研究.石油物探,2009,48(5):459-464.Liu X W,Ning J R,Zhang G L.Cauchy sparse constrainedBayesian estimation based seismic blind deconvolution frameand algorithm.Geophysical Prospecting for Petroleum(inChinese),2009,48(5):459-464.
[16]Larue A,Mars J I,Jutten C.Frequency-domain blinddeconvolution based on mutual information rate.IEEETransactions on Signal Processing,2006,54(5):1771-1780.
[17]高静怀,张明,张兵.一种改进的基于互信息率的盲反褶积方法.地球物理学进展,2011,26(2):540-548.Gao J H,Zhang M,Zhang B.An improved blind deconvolutionbased on mutual information rate.Progress in Geophysics(inChinese),2011,26(2):540-548.
[18]Hani A F M,Younis M S,Halim M F M.A HOS-based blinddeconvolution algorithm for the improvement of timeresolution of mixed phase low SNR seismic data.Journal ofGeophysics and Engineering,2009,6(1):87-100.
[19]Santamaría-Caballero I,Pantaleón-Prieto C J,Artés-RodríguezA.Sparse deconvolution using adaptive mixed-Gaussianmodels.Signal Processing,1996,54(2):161-172.
[20]王锐,孙成禹.有限熵反褶积.石油地球物理勘探,2005,40(6):638-641.Wang R,Sun C Y.Finite entropy deconvolution.OilGeophysical Prospecting(in Chinese),2005,40(6):638-641.
[21]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.
[22]刘喜武,刘洪,李幼铭.独立分量分析及其在地震信息处理中应用初探.地球物理学进展,2003,18(1):90-96.Liu X W,Liu H,Li Y M.Independent component analysis andits testing application on seismic signal processing.Progress inGeophysics(in Chinese),2003,18(1):90-96.
[23]Trelea I C.The particle swarm optimization algorithm:convergence analysis and parameter selection.InformationProcessing Letters,2003,85(6):317-325.
[24]朱童,李小凡,李一琼等.基于改进粒子群算法的地震标量波方程反演.地球物理学报,2011,54(11):2951-2959.Zhu T,Li X F,Li Y Q,et al.Seismic scalar wave equationinversion based on an improved particle swarm optimizationalgorithm.Chinese J.Geophys.(in Chinese),2011,54(11):2951-2959.
[25]Walden A T.Non-Gaussian reflectivity,entropy,anddeconvolution.Geophysics,1985,50(12):2862-2888.
[26]Kaplan S T,Ulrych T J.Blind deconvolution and ICA with abanded mixing matrix.Japan:4th International Symposium onIndependent Component Analysis and Blind SourceSeparation,2003.
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