杨氏模量和泊松比反射系数近似方程及叠前地震反演
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摘要
杨氏模量和泊松比等岩石弹性参数是表征页岩气储集体岩石脆性、评价储层含气特征的重要特征参数,而叠前地震反演是从地震资料中获取此类参数的有效途径.地震波反射系数方程是叠前反演的基础.首先,在平面波入射等假设条件下推导了基于杨氏模量(Y)、泊松比(σ)和密度(D)的纵波反射系数线性近似方程(YPD反射系数近似方程),该方程建立了地震纵波反射系数与杨氏模量反射系数、泊松比反射系数和密度反射系数的线性关系;其次,对该方程的精度和适用条件进行了分析,模型分析表明,在入射角为40°时,该方程具有较高的计算精度;最后,建立了一种稳定获取杨氏模量和泊松比的叠前地震直接反演方法.模型试算和实际资料试处理表明,基于新方程的反演方法能够稳定合理的直接从叠前地震资料中获取杨氏模量和泊松比参数,提供了一种高可靠性的页岩气"甜点"地震识别方法.
Young′s modulus and Poisson ratio are two important rock parameters to indicate the "sweet spot" in gas shale.Pre-stack inversion based on reflection coefficient equation with different model parameterization is an efficient approach to obtain these parameters.Firstly,we derive the reflection coefficient approximate equation in terms of Young′s modulus,Poisson ratio and density(YPD approximate equation) with the hypothesis of incident planar wave,which establishes the linear relationship between the reflection coefficient and Young′s modulus reflectivity,Poisson ratio reflection reflectivity and density reflectivity.Secondly,we analyze the precision and applicable condition of the novel reflection coefficient equation,and the model test shows that this equation is as accurate as the exact equation until the incident angle approaches to 40 degree.Finally,a robust AVA inversion procedure is introduced to test the possibility to invert for Young′s modulus and Poisson ratio directly.Model and real data tests show that the introduced inversion method can obtain reasonable inversion results even with moderate Gaussian noise,which offers an efficient method to identify "sweet spot" with seismic data.
Young′s modulus and Poisson ratio are two important rock parameters to indicate the "sweet spot" in gas shale.Pre-stack inversion based on reflection coefficient equation with different model parameterization is an efficient approach to obtain these parameters.Firstly,we derive the reflection coefficient approximate equation in terms of Young′s modulus,Poisson ratio and density(YPD approximate equation) with the hypothesis of incident planar wave,which establishes the linear relationship between the reflection coefficient and Young′s modulus reflectivity,Poisson ratio reflection reflectivity and density reflectivity.Secondly,we analyze the precision and applicable condition of the novel reflection coefficient equation,and the model test shows that this equation is as accurate as the exact equation until the incident angle approaches to 40 degree.Finally,a robust AVA inversion procedure is introduced to test the possibility to invert for Young′s modulus and Poisson ratio directly.Model and real data tests show that the introduced inversion method can obtain reasonable inversion results even with moderate Gaussian noise,which offers an efficient method to identify "sweet spot" with seismic data.
引文
[1]彭苏萍,高云峰,杨瑞召等.AVO探测煤层瓦斯富集的理论探讨和初步实践——以淮南煤田为例.地球物理学报,2005,48(6):1475-1486.Peng S P,Gao Y F,Yang R Z,et al.Theory and applicationof AVO for detection of coalbed methane——A case from theHuainan coalfield.Chinese J.Geophys.(in Chinese),2005,48(6):1475-1486.
[2]牛滨华,文鹏飞,温宁等.基于BSR的AVO正演估算水合物含量方法的研究.地球物理学报,2006,49(1):143-152.Niu B H,Wen P F,Wen N,et al.Estimation of hydrateconcentration based on AVO modeling of BSR.Chinese J.Geophys.(in Chinese),2006,49(1):143-152.
[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]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.(in Chinese),2005,48(4):902-908.
[5]陈建江,印兴耀.基于贝叶斯理论的AVO三参数波形反演.地球物理学报,2007,50(4):1251-1260.Chen J J,Yin X Y.Three-parameter AVO waveforminversion based on Bayesian theorem.Chinese J.Geophys.(in Chinese),2007,50(4):1251-1260.
[6]Aki K,Richards P G.Quantitative Seismology(2ed).SanFrancisco:W.H.Freeman,1980:158-164.
[7]Shuey R T.A simplification of the Zoeppritz equations.Geophysics,1985,50(4):609-614.
[8]Fatti J L,Smith G C,Vail P J,et al.Detection of gas insandstone reservoirs using AVO analysis:A 3-D seismic casehistory using the Geostack technique.Geophysics,1994,59(9):1362-1376.
[9]Bill G,Chen T W,Downton J.Improved AVO fluiddetection and lithology discrimination using Lame′s petro-physical parameters:“λρ”,“μρ”,&“λ/μfluid stack”,fromP and S inversions.SEG Technical Program ExpandedAbstracts,1997,16(1):183-186.
[10]Russell B H,Gray D,Hampson D P.Linearized AVO andporoelasticity.Geophysics,2011,76(3):C19-C29.
[11]Simmons J L,Backus M M.Waveform-based AVO inversionand AVO prediction-error.Geophysics,1996,61(6):1575-1588.
[12]Gardner G H F,Gardner L W G,Gregory A R.Formationvelocity and density-the diagnostic basics for stratigraphictraps.Geophysics,1974,39(6):770-780.
[13]Castagna J,Batzle M,Eastwood R L.Relationships betweencompressional-wave and shear-wave velocities in clasticsilicate rocks.Geophysics,1985,50(4):571-581.
[14]Arild B,More H.Bayesian linearized AVO inversion.Geophysics,2003,68(1):185-198.
[15]Yin X Y,Yang P J,Zhang G Z.A novel prestack AVOinversion and its application.SEG Technical ProgramExpanded Abstracts,2008,27(1):2041-2045.
[16]Connolly P.Elastic impedance.The Leading Edge,1999,18(4):438-452.
[17]Guillaume C.AVO inversion and elastic impedance.SEGTechnical Program Expanded Abstracts,2000,19(1):142-145.
[18]Yin X Y,Yuan S H,Zhang F C.Rock elastic parameterscalculated from elastic impedance.CPS/SEG TechnicalProgram Expanded Abstracts,2004:538-542.
[19]Wang B L,Yin X Y,Zhang F C.Laméparameters inversionbased on elastic impedance and its application.AppliedGeophysics,2006,3(3):174-178.
[20]Gray D,Verttas D G C.Elastic inversion for Lameparameters.SEG Technical Program Expanded Abstracts,2002,21(1):213-216.
[21]Sena A,Gabino C,Chesser K,et al.Seismic reservoircharacterization in resource shale plays:“Sweet spot”discrimination and optimization of horizontal well placement.SEG Technical Program Expanded Abstracts,2011,30(1):1744-1748.
[22]Goodway B,Perez M,Varsek J,et al.Seismic petrophysicsand isotropic-anisotropic AVO methods for unconventionalgas exploration.The Leading Edge,2010,29(12):1500-1508.
[23]Zong Z Y,Yin X Y,Wu G C.Robust AVO inversion forelastic modulus and its application in fluid factor calculation.SEG Technical Program Expanded Abstracts,2011,30(1):406-411.
[24]Mavko G,Mukerji T,Dvorkin J.The Rock PhysicsHandbook:Tools for Seismic Analysis in Porous Media.Cambridge:Cambridge University Press,2009:21-25.
[25]Wubshet A,Sacchi M D.High-resolution three-term AVOinversion by means of a Trivariate Cauchy probabilitydistribution.Geophysics,2011,76(3):R43-R55.
[26]杨培杰,印兴耀.非线性二次规划贝叶斯叠前反演.地球物理学报,2008,51(6):1876-1882.Yang P J,Yin X Y.Non-linear quadratic programmingBayesian prestack inversion.Chinese J.Geophys.(in Chinese),2008,51(6):1876-1882.
[27]Daubechies I,Devore R,Fornasier M,et al.Iterativelyreweighted least squares minimization for sparse recovery.Communications on Pure and Applied Mathematics,2010,63(1):1-38.
[28]Lines L R.Density contrast is difficult to determine fromAVO.Canadian Journal of Exploration Geophysics,1998.
[29]Downton J E.Seismic parameter estimation from AVOinversion[Ph.D.thesis].Canada:University of Calgary,2005:87.
[30]宗兆云,印兴耀,吴国忱.基于叠前地震纵横波模量直接反演的流体检测方法.地球物理学报,2012,55(1):284-292.Zong Z Y,Yin X Y,Wu G C.Fluid identification methodbased on compressional and shear modulus direct inversion.Chinese J.Geophys.(in Chinese),2012,55(1):284-292.
[2]牛滨华,文鹏飞,温宁等.基于BSR的AVO正演估算水合物含量方法的研究.地球物理学报,2006,49(1):143-152.Niu B H,Wen P F,Wen N,et al.Estimation of hydrateconcentration based on AVO modeling of BSR.Chinese J.Geophys.(in Chinese),2006,49(1):143-152.
[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]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.(in Chinese),2005,48(4):902-908.
[5]陈建江,印兴耀.基于贝叶斯理论的AVO三参数波形反演.地球物理学报,2007,50(4):1251-1260.Chen J J,Yin X Y.Three-parameter AVO waveforminversion based on Bayesian theorem.Chinese J.Geophys.(in Chinese),2007,50(4):1251-1260.
[6]Aki K,Richards P G.Quantitative Seismology(2ed).SanFrancisco:W.H.Freeman,1980:158-164.
[7]Shuey R T.A simplification of the Zoeppritz equations.Geophysics,1985,50(4):609-614.
[8]Fatti J L,Smith G C,Vail P J,et al.Detection of gas insandstone reservoirs using AVO analysis:A 3-D seismic casehistory using the Geostack technique.Geophysics,1994,59(9):1362-1376.
[9]Bill G,Chen T W,Downton J.Improved AVO fluiddetection and lithology discrimination using Lame′s petro-physical parameters:“λρ”,“μρ”,&“λ/μfluid stack”,fromP and S inversions.SEG Technical Program ExpandedAbstracts,1997,16(1):183-186.
[10]Russell B H,Gray D,Hampson D P.Linearized AVO andporoelasticity.Geophysics,2011,76(3):C19-C29.
[11]Simmons J L,Backus M M.Waveform-based AVO inversionand AVO prediction-error.Geophysics,1996,61(6):1575-1588.
[12]Gardner G H F,Gardner L W G,Gregory A R.Formationvelocity and density-the diagnostic basics for stratigraphictraps.Geophysics,1974,39(6):770-780.
[13]Castagna J,Batzle M,Eastwood R L.Relationships betweencompressional-wave and shear-wave velocities in clasticsilicate rocks.Geophysics,1985,50(4):571-581.
[14]Arild B,More H.Bayesian linearized AVO inversion.Geophysics,2003,68(1):185-198.
[15]Yin X Y,Yang P J,Zhang G Z.A novel prestack AVOinversion and its application.SEG Technical ProgramExpanded Abstracts,2008,27(1):2041-2045.
[16]Connolly P.Elastic impedance.The Leading Edge,1999,18(4):438-452.
[17]Guillaume C.AVO inversion and elastic impedance.SEGTechnical Program Expanded Abstracts,2000,19(1):142-145.
[18]Yin X Y,Yuan S H,Zhang F C.Rock elastic parameterscalculated from elastic impedance.CPS/SEG TechnicalProgram Expanded Abstracts,2004:538-542.
[19]Wang B L,Yin X Y,Zhang F C.Laméparameters inversionbased on elastic impedance and its application.AppliedGeophysics,2006,3(3):174-178.
[20]Gray D,Verttas D G C.Elastic inversion for Lameparameters.SEG Technical Program Expanded Abstracts,2002,21(1):213-216.
[21]Sena A,Gabino C,Chesser K,et al.Seismic reservoircharacterization in resource shale plays:“Sweet spot”discrimination and optimization of horizontal well placement.SEG Technical Program Expanded Abstracts,2011,30(1):1744-1748.
[22]Goodway B,Perez M,Varsek J,et al.Seismic petrophysicsand isotropic-anisotropic AVO methods for unconventionalgas exploration.The Leading Edge,2010,29(12):1500-1508.
[23]Zong Z Y,Yin X Y,Wu G C.Robust AVO inversion forelastic modulus and its application in fluid factor calculation.SEG Technical Program Expanded Abstracts,2011,30(1):406-411.
[24]Mavko G,Mukerji T,Dvorkin J.The Rock PhysicsHandbook:Tools for Seismic Analysis in Porous Media.Cambridge:Cambridge University Press,2009:21-25.
[25]Wubshet A,Sacchi M D.High-resolution three-term AVOinversion by means of a Trivariate Cauchy probabilitydistribution.Geophysics,2011,76(3):R43-R55.
[26]杨培杰,印兴耀.非线性二次规划贝叶斯叠前反演.地球物理学报,2008,51(6):1876-1882.Yang P J,Yin X Y.Non-linear quadratic programmingBayesian prestack inversion.Chinese J.Geophys.(in Chinese),2008,51(6):1876-1882.
[27]Daubechies I,Devore R,Fornasier M,et al.Iterativelyreweighted least squares minimization for sparse recovery.Communications on Pure and Applied Mathematics,2010,63(1):1-38.
[28]Lines L R.Density contrast is difficult to determine fromAVO.Canadian Journal of Exploration Geophysics,1998.
[29]Downton J E.Seismic parameter estimation from AVOinversion[Ph.D.thesis].Canada:University of Calgary,2005:87.
[30]宗兆云,印兴耀,吴国忱.基于叠前地震纵横波模量直接反演的流体检测方法.地球物理学报,2012,55(1):284-292.Zong Z Y,Yin X Y,Wu G C.Fluid identification methodbased on compressional and shear modulus direct inversion.Chinese J.Geophys.(in Chinese),2012,55(1):284-292.
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