地震偏移成像不确定性分析初探
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摘要
勘探地球物理领域存在大量宏观动力学过程的物理数学表达及尚待深入探索的不确定性事实,其中一类是源自对偶量的不可交换性或不可对易性.本文从地震偏移成像中的不确定性分析入手,探讨偏移成像中受到波场延拓过程不确定性的影响.文中给出了若干深度偏移算法对Marmousi模型的偏移不确定度分布表达及图像显示;文中还对若干波场延拓方法,从不确定性估计的角度进行了比较.笔者认为对应用技术领域中的宏观不确定性分析,将有益于深化对宏观动力学过程的理性认识,也为偏移算法评价提供一种途径;重要的是,进行不确定性分析将有利于把握所用偏移算法的不确定度分布,继而有针对性地采取相应的改善措施,以期提高算法的整体确定性程度.
In exploration geophysics realm,there are abundant mathematical physics expressions for macro-dynamic procedures and many concerning uncertainty facts need to be probed among which there exists a certain uncertainty originating from the non-interchangeability of dual variables.Starting from the uncertainty analysis in seismic migration imaging,the effects due to uncertainty of wavefield extrapolation procedure in migration imaging are analyzed in this paper.The uncertainty distribution expression and its image display for some depth migration algorithms with Marmousi model are presented so as to compare,from the viewpoint of uncertainty evaluation,their performances in imaging.We hold macro uncertainty analysis in applicable technological fields can help us to deepen the rational understanding about macro-dynamic procedure also provide us an evaluation approach for migration algorithm.Moreover,we can benefit from uncertainty analysis to obtain the uncertainty degree distribution of adopted migration algorithm,then accordingly to rectify that algorithm with improving measures so as to increase its global certainty.
In exploration geophysics realm,there are abundant mathematical physics expressions for macro-dynamic procedures and many concerning uncertainty facts need to be probed among which there exists a certain uncertainty originating from the non-interchangeability of dual variables.Starting from the uncertainty analysis in seismic migration imaging,the effects due to uncertainty of wavefield extrapolation procedure in migration imaging are analyzed in this paper.The uncertainty distribution expression and its image display for some depth migration algorithms with Marmousi model are presented so as to compare,from the viewpoint of uncertainty evaluation,their performances in imaging.We hold macro uncertainty analysis in applicable technological fields can help us to deepen the rational understanding about macro-dynamic procedure also provide us an evaluation approach for migration algorithm.Moreover,we can benefit from uncertainty analysis to obtain the uncertainty degree distribution of adopted migration algorithm,then accordingly to rectify that algorithm with improving measures so as to increase its global certainty.
引文
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[2]曾谨言.量子力学[M].北京:科学出版社,2000.Zeng J Y.Quantum Mechanics(in Chinese)[M].Beijing:Science Press,2000.
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[12]杨辉,刘洪,李幼铭.单程波方程偏移算子高阶辛格式[J].地球物理学报,2003,46(4):533~538.Yang H,Liu H,Li Y M.High order symplectic scheme forone-way wave equation operator[J].Chinese J.Geophys.(in Chinese),2003,46(4):533~538.
[13]张致付,刘洪,陈景波.地震偏移的最优可分近似算法实现[J].地球物理学报,2005,48(6):1422~1427.Zhang Z F,Liu H,Chen J B.Implement of optimal separableapproximation in seismic migration[J].Chinese J.Geophys.(in Chinese),2005,48(6):1422~1427.
[14]吕小林,刘洪.波动方程深度偏移波场延拓算子的快速重建[J].地球物理学进展,2005,20(1):24~28.Lu X L,Liu H.Fast reconstruction of wave-field propagatorin wave-equation depth migration[J].Progress in Geophysics(in Chinese),2005,20(1):24~28.
[15]肖明耀.误差理论与应用[M].北京:计量出版社,1985.Xiao M Y.Error Theory and Its Application(in Chinese)[M].Beijing:Legal Metrology Press,1985.
[16]刘光鼎,张丽莉,祝靓谊.试论复杂地质体的油气地震勘探[J].地球物理学进展,2006,21(3):683~686.Liu G D,Zhang L L,Zhu L Y.Seismic prospecting for oiland gas on the complex geological bodies[J].Progress in Ge-ophysics(in Chinese),2006,21(3):683~686.
[17]李幼铭.面向油气勘探开发提升地震偏移及属性刻划水平[J].地球物理学进展,2002,17(2):198~210.Li Y M.Improving the level of seismic wave’s migration andattribute’s description in face of exploration and exploitation[J].Progress in Geophysics(in Chinese),2002,17(2):198~210.
[18]李幼铭.对“油储”项目在大庆实施获得成果的概述及认识[J].地球物理学进展,2006,21(1):135~142.Li Y M.The outline and general comments about the advanceof the reservoir geophysics project implemented in daqing oil-field[J].Progress in Geophysics(in Chinese),2006,21(1):135~142.
[2]曾谨言.量子力学[M].北京:科学出版社,2000.Zeng J Y.Quantum Mechanics(in Chinese)[M].Beijing:Science Press,2000.
[3]罗伯特.马休斯.不可思议的世界[J].发明与创新,2004,(1):38~39.Matthews R.Enigmatical world[J].Invention&Innovation(in Chinese),2004,(1):38~39.
[4]史文中.空间数据与空间分析不确定性原理[M].北京:科学出版社,2005.Shi W Z.Principle of Modeling Uncertainties in Spatial Data andAnalysis(in Chinese)[M].Beijing:Science Press,2005.
[5]Cohen L.Time-Frequency Analysis-Theory and Applications[M].New York:Prentice Hall,1995.
[6]Shie Q.Introduction to Time-frequency and Wavelet Trans-forms[M].Beijing:Pearson Education Asia Limited and Chi-na Machine Press,2005.
[7]Jaffard S,Meyer Y,Ryan R D.Wavelets-Tools for Scienceand Technology[M].Philadelphia:SIAM,2001.
[8]齐民友,徐超江,王维克.现代偏微分方程引论[M].武汉:武汉大学出版社,2005.Qi M Y,Xu C J,Wang W K.Introduction of Modern PartialDifferential Equation(in Chinese)[M].Wuhan:Wuhan Uni-versity Press,2005.
[9]Gabor D.Theory of communication[J].Journal of IEEE,1946,93:429~457.
[10]杨长春,刘兴材,李幼铭,等.地震叠前深度偏移方法流程及应用[J].地球物理学报,1996,39(3):409~415.Yang C C,Liu X C,Li Y M,et al.A methodology for seis-mic prestack depth migration[J].Chinese J.Geophys.(inChinese),1996,39(3):409~415.
[11]刘洪,袁江华,陈景波,等.大步长波场深度延拓的理论[J].地球物理学报,2006,49(6):1779~1793.Liu H,Yuan J H,Chen J B,et al.The theory of large-stepwavefield depth extrapolation[J].Chinese J.Geophys.(inChinese),2006,49(6):1779~1793.
[12]杨辉,刘洪,李幼铭.单程波方程偏移算子高阶辛格式[J].地球物理学报,2003,46(4):533~538.Yang H,Liu H,Li Y M.High order symplectic scheme forone-way wave equation operator[J].Chinese J.Geophys.(in Chinese),2003,46(4):533~538.
[13]张致付,刘洪,陈景波.地震偏移的最优可分近似算法实现[J].地球物理学报,2005,48(6):1422~1427.Zhang Z F,Liu H,Chen J B.Implement of optimal separableapproximation in seismic migration[J].Chinese J.Geophys.(in Chinese),2005,48(6):1422~1427.
[14]吕小林,刘洪.波动方程深度偏移波场延拓算子的快速重建[J].地球物理学进展,2005,20(1):24~28.Lu X L,Liu H.Fast reconstruction of wave-field propagatorin wave-equation depth migration[J].Progress in Geophysics(in Chinese),2005,20(1):24~28.
[15]肖明耀.误差理论与应用[M].北京:计量出版社,1985.Xiao M Y.Error Theory and Its Application(in Chinese)[M].Beijing:Legal Metrology Press,1985.
[16]刘光鼎,张丽莉,祝靓谊.试论复杂地质体的油气地震勘探[J].地球物理学进展,2006,21(3):683~686.Liu G D,Zhang L L,Zhu L Y.Seismic prospecting for oiland gas on the complex geological bodies[J].Progress in Ge-ophysics(in Chinese),2006,21(3):683~686.
[17]李幼铭.面向油气勘探开发提升地震偏移及属性刻划水平[J].地球物理学进展,2002,17(2):198~210.Li Y M.Improving the level of seismic wave’s migration andattribute’s description in face of exploration and exploitation[J].Progress in Geophysics(in Chinese),2002,17(2):198~210.
[18]李幼铭.对“油储”项目在大庆实施获得成果的概述及认识[J].地球物理学进展,2006,21(1):135~142.Li Y M.The outline and general comments about the advanceof the reservoir geophysics project implemented in daqing oil-field[J].Progress in Geophysics(in Chinese),2006,21(1):135~142.
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