基于α稳定分布的地震反演方法
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摘要
本文介绍了α稳定分布的统计特征,并对比分析了实际地震信号与α稳定分布的动态样本方差特征,提出地震信号服从非高斯α稳定分布的假设.在此基础上,利用地震记录估计误差的p阶统计量作为代价函数,提出了基于非高斯α稳定分布的最小p范数地震反演方法.将该方法应用到单道反射系数理论模型及实际叠前弹性阻抗反演实例中,均取得了良好的反演效果.实际反演结果验证了本文提出的地震信号服从非高斯α稳定分布假设的合理性,以及最小p范数地震反演方法的可行性和有效性.
This paper briefly introduced the statistic characteristics of α-stable distribution,analyzed the dynamic sample variance of α-stable distribution and seismic signals comparatively,and proposed that seismic signals follow α-stable distribution.Based on this,the cost function was built with the p-order statistics of seismic data estimated error.The least p-norm seismic inversion algorithm was proposed and applied to single-channel reflectivity inversion and real pre-stack elastic impedance inversion.Both of the applications obtained good results,which demonstrated that the seismic signals follow non-Gaussian α-stable distribution and the least p-norm seismic inversion algorithm was efficient and feasible.
This paper briefly introduced the statistic characteristics of α-stable distribution,analyzed the dynamic sample variance of α-stable distribution and seismic signals comparatively,and proposed that seismic signals follow α-stable distribution.Based on this,the cost function was built with the p-order statistics of seismic data estimated error.The least p-norm seismic inversion algorithm was proposed and applied to single-channel reflectivity inversion and real pre-stack elastic impedance inversion.Both of the applications obtained good results,which demonstrated that the seismic signals follow non-Gaussian α-stable distribution and the least p-norm seismic inversion algorithm was efficient and feasible.
引文
[1]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 ofpre-stack seismic angle-gather based on particle swarmoptimization algorithm.Chinese J.Geophys.(in Chinese),2009,52(12):3116-3123.
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[3]彭真明,李亚林,魏文阁等.粒子滤波非线性AVO反演方法.地球物理学报,2008,51(4):1218-1225.Peng Z M,Li Y L,Wei W G,et al.Nonlinear AVOinversion using particle filter.Chinese J.Geophys.(inChinese),2008,51(4):1218-1225.
[4]Liu J,Lu W K.An improved predictive deconvolution basedon maximization of non-Gaussianity.Applied Geophysics,2008,5(3):189-196.
[5]陈建江.AVO三参数反演方法研究[博士论文].山东:中国石油大学,2007.Chen J J.Study of three-term AVO inversion method[Ph.D.thesis](in Chinese).Shandong:China University ofPetroleum,2007.
[6]Godfrey B,Claerbout J F.Two methods of deconvolution:power spectrum smoothing and parsimonious deconvolution.Stanford Exploration Project,1978,14:207-226.
[7]孙永梅,邱天爽.α稳定分布噪声下自适应信号处理的研究进展.信号处理,2004,20(6):618-622.Sun Y M,Qiu T S.The development of adaptive signalprocessing in alpha-stable noise environments.SignalProcessing(in Chinese),2004,20(6):618-622.
[8]张军保.基于对称alpha平稳分布的SAR图像复原算法研究[硕士论文].北京:中国科学院电子学研究所,2005.Zhang J B.Synthetic Aperture Radar(SAR)image recoveringwith improving symmetric alpha-stable distribution method[Master′s thesis](in Chinese).Beijing:Institute ofElectronics,Chinese Academy of Sciences,2005.
[9]胡睿,孙进平,王文光.基于α稳定分布的SAR图像目标检测算法.中国图像图形学报,2009,14(1):25-29.Hu R,Sun J P,Wang W G.Target detection of SAR imagesusing alpha stable distribution.Journal of Image andGraphics(in Chinese),2009,14(1):25-29.
[10]郭文强.稳定分布噪声下的盲信号处理方法及应用研究[博士论文].大连:大连理工大学,2007.Guo W Q.Study on method and applications of blind signalprocessing in stable noise[Ph.D.thesis](in Chinese).Dalian:Dalian University of Technology,2007.
[11]Shuey R T.A simplification of the Zoeppritz equations.Geophysics,1985,50(4):609-614.
[12]Tsihrintzis G A,Nikias C L.Evaluation of fractional,lower-order statistics-based detection algorithms on real radar sea-clutter data.IEE Proceedings-Radar,Sonar and Navigation,1997,144(1):29-38.
[13]Shao M,Nikias C L.Signal processing with fractional lowerorder moments:stable processes and their applications.Proceeding of the IEEE,1993,81(7):986-1010.
[14]Gonzalez J G,Paredes J L,Arce G R.Zero-order statistics:a mathematical framework for the processing and characterizationof very impulsive signals.IEEE Transactions on Signal Processing,2006,54(10):3939-3851.
[15]Joon L T.System Identification Using Novel Adaptive FilterStructures.Cambridge:University of Cambridge,1995.
[16]Stuck B W.Minimum error dispersion linear filtering ofscalar symmetric stable processes.IEEE Transactions onAutomatic Control,1978,23(3):507-509.
[17]邱天爽,杨志春,李小兵等.α稳定分布下的加权平均最小p-范数算法.电子与信息学报,2007,29(2):410-413.Qiu T S,Yang Z C,Li X B,et al.A weighted average leastp-norm algorithm under alpha stable noise conditions.Journal of Electronics&Information Technology(inChinese),2007,29(2):410-413.
[18]彭真明,李亚林,巫盛洪等.碳酸盐岩储层多角度弹性阻抗流体识别方法.地球物理学报,2008,51(3):881-885.Peng Z M,Li Y L,Wu S H,et al.Discriminating gas andwater using multi-angle extended elastic impedance inversionin carbonate reservoirs.Chinese J.Geophys.(in Chinese),2008,51(3):881-885.
[2]Walden A T.Non-Gaussian reflectivity,entropy,anddeconvolution.Geophysics,1985,50(12):2862-2888.
[3]彭真明,李亚林,魏文阁等.粒子滤波非线性AVO反演方法.地球物理学报,2008,51(4):1218-1225.Peng Z M,Li Y L,Wei W G,et al.Nonlinear AVOinversion using particle filter.Chinese J.Geophys.(inChinese),2008,51(4):1218-1225.
[4]Liu J,Lu W K.An improved predictive deconvolution basedon maximization of non-Gaussianity.Applied Geophysics,2008,5(3):189-196.
[5]陈建江.AVO三参数反演方法研究[博士论文].山东:中国石油大学,2007.Chen J J.Study of three-term AVO inversion method[Ph.D.thesis](in Chinese).Shandong:China University ofPetroleum,2007.
[6]Godfrey B,Claerbout J F.Two methods of deconvolution:power spectrum smoothing and parsimonious deconvolution.Stanford Exploration Project,1978,14:207-226.
[7]孙永梅,邱天爽.α稳定分布噪声下自适应信号处理的研究进展.信号处理,2004,20(6):618-622.Sun Y M,Qiu T S.The development of adaptive signalprocessing in alpha-stable noise environments.SignalProcessing(in Chinese),2004,20(6):618-622.
[8]张军保.基于对称alpha平稳分布的SAR图像复原算法研究[硕士论文].北京:中国科学院电子学研究所,2005.Zhang J B.Synthetic Aperture Radar(SAR)image recoveringwith improving symmetric alpha-stable distribution method[Master′s thesis](in Chinese).Beijing:Institute ofElectronics,Chinese Academy of Sciences,2005.
[9]胡睿,孙进平,王文光.基于α稳定分布的SAR图像目标检测算法.中国图像图形学报,2009,14(1):25-29.Hu R,Sun J P,Wang W G.Target detection of SAR imagesusing alpha stable distribution.Journal of Image andGraphics(in Chinese),2009,14(1):25-29.
[10]郭文强.稳定分布噪声下的盲信号处理方法及应用研究[博士论文].大连:大连理工大学,2007.Guo W Q.Study on method and applications of blind signalprocessing in stable noise[Ph.D.thesis](in Chinese).Dalian:Dalian University of Technology,2007.
[11]Shuey R T.A simplification of the Zoeppritz equations.Geophysics,1985,50(4):609-614.
[12]Tsihrintzis G A,Nikias C L.Evaluation of fractional,lower-order statistics-based detection algorithms on real radar sea-clutter data.IEE Proceedings-Radar,Sonar and Navigation,1997,144(1):29-38.
[13]Shao M,Nikias C L.Signal processing with fractional lowerorder moments:stable processes and their applications.Proceeding of the IEEE,1993,81(7):986-1010.
[14]Gonzalez J G,Paredes J L,Arce G R.Zero-order statistics:a mathematical framework for the processing and characterizationof very impulsive signals.IEEE Transactions on Signal Processing,2006,54(10):3939-3851.
[15]Joon L T.System Identification Using Novel Adaptive FilterStructures.Cambridge:University of Cambridge,1995.
[16]Stuck B W.Minimum error dispersion linear filtering ofscalar symmetric stable processes.IEEE Transactions onAutomatic Control,1978,23(3):507-509.
[17]邱天爽,杨志春,李小兵等.α稳定分布下的加权平均最小p-范数算法.电子与信息学报,2007,29(2):410-413.Qiu T S,Yang Z C,Li X B,et al.A weighted average leastp-norm algorithm under alpha stable noise conditions.Journal of Electronics&Information Technology(inChinese),2007,29(2):410-413.
[18]彭真明,李亚林,巫盛洪等.碳酸盐岩储层多角度弹性阻抗流体识别方法.地球物理学报,2008,51(3):881-885.Peng Z M,Li Y L,Wu S H,et al.Discriminating gas andwater using multi-angle extended elastic impedance inversionin carbonate reservoirs.Chinese J.Geophys.(in Chinese),2008,51(3):881-885.
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