地震波反射系数偏导矩阵的精确解及对近似计算的精度分析
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摘要
目前叠前反演方法大多是基于Zoeppritz方程近似式实现的,它仅适应于弱反射介质界面、中小角度(或小偏移距)的地震数据反演,不能满足勘探开发的地质需求.本文建立了基于zoeppritz方程精确求解反射系数的梯度矩阵,分析了矩阵特点和精度,为研究利用反射系数梯度精确解反演地震参数奠定了基础.
Most of the current pre-stack inversion methods are based on approximate equations of the Zoeppritz equation which only adapt to seismic data with weak reflection media interface and small angle(or small offset),and cannot meet the demand of geological exploration and development in Shengli Oilfield.A gradient matrix of reflection coefficient based on the Zoeppritz equation is established,and the characteristics and accuracy of the matrix are analyzed in this paper.The foundation are laid for the study of seismic parameters inversion utilizing the exact solutions of the reflection coefficient gradient.
Most of the current pre-stack inversion methods are based on approximate equations of the Zoeppritz equation which only adapt to seismic data with weak reflection media interface and small angle(or small offset),and cannot meet the demand of geological exploration and development in Shengli Oilfield.A gradient matrix of reflection coefficient based on the Zoeppritz equation is established,and the characteristics and accuracy of the matrix are analyzed in this paper.The foundation are laid for the study of seismic parameters inversion utilizing the exact solutions of the reflection coefficient gradient.
引文
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[20]Zhang W P,Guo P,Hu T Y.Study and practice of wide-angleseismic data processing.Applied Geophysics,2004,1(1):31-37.
[21]Fruehn J,White R S,Fliedner M,et al.Large-apertureseismic:Imaging beneath high-velocity strata.World Oil,1999,220(1):109-113.
[22]刘福平,李瑞忠,杨长春等.非均匀P—偏振电磁波在导电界面的类全反射横向偏移.地球物理学报,2007,50(2):556-566.Liu F P,Zhang H M,Yang C C,et al.The quasi totalreflected lateral shift of inhomogeneous p-polarizedelectromagnetic wave on the interface of conductive media.Chinese J.Geophys.(in Chinese),2007,50(2):556-566.
[23]Liu F P,Wang A L,Chen Q,et al.The research progress onlateral shift of reflected electromagnetic wave at the interfaceof two conductive media.Chinese Science Bulletin,2008,53(7):961-968.
[24]胡中平,管路平,顾连兴等.高速屏蔽层下广角地震波场分析及成像方法.地球物理学报,2004,47(1):88-94.Hu Z P,Guan L P,Gu L X,et al.Wide angle seismic wavefield analysis and imaging method below the high velocityshield layers.Chinese J.Geophys.(in Chinese),2004,47(1):88-94.
[25]李怀胜.广角反射在塔中地区的应用.石油物探,2005,44(3):292-295.Li H S.The application of wide-angle reflection method incentral Tarim basin.Geophysical prospecting for petroleum(in Chinese),2005,44(3):292-295.
[26]王志,贺振华,黄德济等.高速屏蔽层下弱反射层地震勘探——广角反射.勘探地球物理进展,2002,25(5):23-27.Wang Z,He Z H,Huang D J,et al.A seismic survey methodfor weak reflectors below shielded layer of high velocity:Wideangle reflection.Progress in Exploration Geophysics(inChinese),2002,25(5):23-27.
[27]孙成禹,倪长宽,李胜军等.广角地震反射数据特征及校正方法研究,石油地球物理勘探,2007,42(1):24-29.Sun C Y,Ni C K,Li S J,et al.Feature of wide-angle reflectiondata and correction method.Oil Geophysical Prospecting(inChinese),2007,42(1):24-29.
[28]王志,贺振华,黄德济等.广角反射波场特征研究及正演模拟分析.地球物理学进展,2003,18(1):116-121.Wang Z,He Z H,Huang D J,et al.The wave-field featuresresearching of wide-angle reflection and the analyzing offorward modeling.Progress in Geophysics,2003,18(1):116-121.
[29]徐文君,於文辉,胡中平.广角反射波的特征及正演模拟.石油地球物理勘探,2006,41(4):390-395.Xu WJ,Yu W H,Hu Z P.Feature and forward simulation ofwide-angle Reflection.Oil Geophysical Prospecting(inChinese),2006,41(4):390-395.
[30]王彦飞.反演问题的计算方法及其应用—当代科学前沿论丛.北京:高等教育出版社,2007:31-84.Wang Y F.Computational Methods for Inverse Problem andTheir Applications(in Chinese).Beijing:Higher EducationPress,2007:31-84.
[31]刘福平,孟宪军,王玉梅等.介质密度反演偏导矩阵的精确计算方法.地球物理学报,2010,53(9):2189-2195.Liu F P,Meng X J,Wang Y M,et al.Accurate method forcalculating derivative matrix in medium density ratioinversion.Chinese J.Geophys.(in Chinese),2010,53(9):2189-2195.
[2]Han D H,Nur A,Morgan D.Effects of porosity and claycontent on wave velocities in sandstones.Geophysics,1986,51(11):2093-2107.
[3]Keys R G,Xu S Y.An approximation for the Xu-Whitevelocity model.Geophysics,2002,67(5):1406-1414.
[4]Kuster G T,Toks?z M N.Velocity and attenuation of seismicwaves in two phase media:Part I:Theoretical formulations.Geophysics,1974,39(5):587-606.
[5]White L,Castagna J.Stochastic fluid modulus inversion.Geophysics,2002,67(6):1853-1843.
[6]Xu S,White R E.A new velocity model for clay-sand mixtures.Geophysical Prospecting,1995,43(1):91-118.
[7]Hilterman F J H.地震振幅解释.孙夕平,赵良武译,北京:石油工业出版社,2006:18-39Hilterman F J H.Amplitude Interpretation(in Chinese).SunX P,Zhao L W,(translation).Beinjing:Petroleum IndustryPress,2006:18-39.
[8]陆基孟.地震勘探原理(上,下).山东东营:石油大学出版社,1993,上:20-30,下:123-194,267.Lu J M.Seismic Exploration Principle(the first and secondvolumes,in Chinese),Shandong Dongying:Petroleum ofUniversity Press,1993,the first volume:20-30,the secondvolume:123-194.
[9]Xu S,White R E.A physical model for shear-wave velocityprediction.Geophysical Prospecting,1996,44(4):687-717.
[10]Shuey R T.A simplification of the Zoeppritz-equations.Geophysics,1985,50(3):609-614.
[11]马在田.P-SV反射波的倾角时差校正(DMO)方法研究.地球物理学报,1996,39(2):243-250.Ma Z T.DMO for P-SV converted reflection.Chinese J.Geophys.(in Chinese),1996,39(2):243-250.
[12]李景叶,陈小宏,郝振江等.多波时移地震AVO反演研究.地球物理学报,2005,48(4):902-908.Li J Y,Chen X H,Hao Z J,et al.A study on multiple time-lapse seismic AVO inversion.Chinese J.Geophys.(inChinese),2005,48(4):902-908.
[13]孟宪军,姜秀娣,黄捍东等.叠前AVA广义非线性纵横波速度反演.石油地球物理勘探,2004,39(6):645-650.Meng X J,Jiang X D,Huang H D,et al.Generalized non-linear P wave and S wave velocity inversion of prestack AVA.Oil Geophysical Prospecting(in Chinese),2004,39(6):645-650.
[14]Shou H,Liu H,Gao J H.AVO inversion based on commonshot migration.Applied Geophysics,2006,3(2):99-104.
[15]顾汉明,王家映,江涛等.海底多波多分量AVO蕴含弹性参数信息的定量分析.石油地球物理勘探,2000,35(1):56-63.Gu H M,Wang J Y,Jiang T,et al.Quantitative analysis ofelastic parameter information contained in AVO of sea-bottommulti-wave multi-component seismic data.Oil GeophysicalProspecting(in Chinese),2000,35(1):56-63.
[16]陈建江,印兴耀,张广智.层状介质AVO叠前反演.石油地球物理勘探,2006,41(6):656-662.Chen J J,Yin XY,Zhang G H.Prestack AVO inversion oflayered medium.Oil Geophysical Prospecting(in Chinese),2006,41(6):656-662.
[17]王保丽,印兴耀,张繁昌.基于Gray近似的弹性波阻抗方程及反演.石油地球物理勘探,2007,42(4):435-439.Wang B L,Yin X Y,Zhang F C.Gray approximation-basedelastic wave impedance equation and inversion.OilGeophysical Prospecting(in Chinese),2007,42(4):435-439.
[18]丁继才,常旭,刘伊克等.基于声波方程的井间地震数据快速WTW反演方法.地球物理学报,2007,50(5):1527-1533.Ding J C,Chang X,Liu Y K,et al.Rapid method for acousticwave-equation WTW inversion of cross-hole seismic data.Chinese J.Geophys.(in Chinese),2007,50(5):1527-1533.
[19]Brittan J,W arner M.W ide-angle seismic velocities inheterogeneous crust.Geophysics Journal International,1997,129(2):269-280.
[20]Zhang W P,Guo P,Hu T Y.Study and practice of wide-angleseismic data processing.Applied Geophysics,2004,1(1):31-37.
[21]Fruehn J,White R S,Fliedner M,et al.Large-apertureseismic:Imaging beneath high-velocity strata.World Oil,1999,220(1):109-113.
[22]刘福平,李瑞忠,杨长春等.非均匀P—偏振电磁波在导电界面的类全反射横向偏移.地球物理学报,2007,50(2):556-566.Liu F P,Zhang H M,Yang C C,et al.The quasi totalreflected lateral shift of inhomogeneous p-polarizedelectromagnetic wave on the interface of conductive media.Chinese J.Geophys.(in Chinese),2007,50(2):556-566.
[23]Liu F P,Wang A L,Chen Q,et al.The research progress onlateral shift of reflected electromagnetic wave at the interfaceof two conductive media.Chinese Science Bulletin,2008,53(7):961-968.
[24]胡中平,管路平,顾连兴等.高速屏蔽层下广角地震波场分析及成像方法.地球物理学报,2004,47(1):88-94.Hu Z P,Guan L P,Gu L X,et al.Wide angle seismic wavefield analysis and imaging method below the high velocityshield layers.Chinese J.Geophys.(in Chinese),2004,47(1):88-94.
[25]李怀胜.广角反射在塔中地区的应用.石油物探,2005,44(3):292-295.Li H S.The application of wide-angle reflection method incentral Tarim basin.Geophysical prospecting for petroleum(in Chinese),2005,44(3):292-295.
[26]王志,贺振华,黄德济等.高速屏蔽层下弱反射层地震勘探——广角反射.勘探地球物理进展,2002,25(5):23-27.Wang Z,He Z H,Huang D J,et al.A seismic survey methodfor weak reflectors below shielded layer of high velocity:Wideangle reflection.Progress in Exploration Geophysics(inChinese),2002,25(5):23-27.
[27]孙成禹,倪长宽,李胜军等.广角地震反射数据特征及校正方法研究,石油地球物理勘探,2007,42(1):24-29.Sun C Y,Ni C K,Li S J,et al.Feature of wide-angle reflectiondata and correction method.Oil Geophysical Prospecting(inChinese),2007,42(1):24-29.
[28]王志,贺振华,黄德济等.广角反射波场特征研究及正演模拟分析.地球物理学进展,2003,18(1):116-121.Wang Z,He Z H,Huang D J,et al.The wave-field featuresresearching of wide-angle reflection and the analyzing offorward modeling.Progress in Geophysics,2003,18(1):116-121.
[29]徐文君,於文辉,胡中平.广角反射波的特征及正演模拟.石油地球物理勘探,2006,41(4):390-395.Xu WJ,Yu W H,Hu Z P.Feature and forward simulation ofwide-angle Reflection.Oil Geophysical Prospecting(inChinese),2006,41(4):390-395.
[30]王彦飞.反演问题的计算方法及其应用—当代科学前沿论丛.北京:高等教育出版社,2007:31-84.Wang Y F.Computational Methods for Inverse Problem andTheir Applications(in Chinese).Beijing:Higher EducationPress,2007:31-84.
[31]刘福平,孟宪军,王玉梅等.介质密度反演偏导矩阵的精确计算方法.地球物理学报,2010,53(9):2189-2195.Liu F P,Meng X J,Wang Y M,et al.Accurate method forcalculating derivative matrix in medium density ratioinversion.Chinese J.Geophys.(in Chinese),2010,53(9):2189-2195.
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