基于改进反射系数近似方程的纵横波阻抗同步反演
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摘要
基于地震波反射系数近似公式的叠前反演是油气勘探的重要工具.本文在已有研究的基础上,推导了一个改进的射线参数域地震纵波反射系数近似方程.该方程建立了地震纵波反射系数与纵波阻抗和横波阻抗的非线性关系,在中、小角度的范围内较现有的反射系数线性近似公式精度更高.另外,由于该方程仅包含纵波和横波阻抗反射系数项,因此基于新方程的反演能够有效地降低同步反演纵波速度、横波速度、密度三个参数的不适定性.在此基础上,结合广义线性反演法(GLI)理论和贝叶斯理论,相应地发展了一种叠前地震同步反演方法.模型测试和实际资料的应用表明,基于新方程的反演方法能够利用有限角度(偏移距)的数据稳定地反演纵波和横波阻抗,由于在反演过程中,不需要假设纵横波速度为常数,因此该方法还能有效地提高反演结果的精度.
Prestack inversion utilizing approximate formulas of reflection coefficients is an important tool for exploration of oil and gas.In this paper,we derivate an improved approximation of reflection coefficients in the ray parameter domain.This equation provides a nonlinear relationship between seismic reflection coefficients and P-and S-wave impedance reflectivity,and is more accurately than the conventional linearized equations in the range of small and middle incident angles.Besides,because the new equation contains only the terms of P-and S-wave impedances,the inversion utilizing this equation can efficiently reduce the ill-posedness of the simultaneous inversion of Pwave velocity,S-wave velocity and density.We then develop aprestack seismic inversion methodby combining the generalized linear inversion(GLI)method and the Bayes theory.Both of synthetic and real data tests show the feasibility of this inversion scheme,and for the reason of the assumption that P-and S-wave velocity ratio is constant does not use in the inversion process,the accuracy of inverted results is improved effectively.
Prestack inversion utilizing approximate formulas of reflection coefficients is an important tool for exploration of oil and gas.In this paper,we derivate an improved approximation of reflection coefficients in the ray parameter domain.This equation provides a nonlinear relationship between seismic reflection coefficients and P-and S-wave impedance reflectivity,and is more accurately than the conventional linearized equations in the range of small and middle incident angles.Besides,because the new equation contains only the terms of P-and S-wave impedances,the inversion utilizing this equation can efficiently reduce the ill-posedness of the simultaneous inversion of Pwave velocity,S-wave velocity and density.We then develop aprestack seismic inversion methodby combining the generalized linear inversion(GLI)method and the Bayes theory.Both of synthetic and real data tests show the feasibility of this inversion scheme,and for the reason of the assumption that P-and S-wave velocity ratio is constant does not use in the inversion process,the accuracy of inverted results is improved effectively.
引文
Aki K I,Richards P G.1980.Quantitative Seismology:Theory and Methods.New York:W.H.Freeman&Co.
Avseth P,Mukerji T and Mavko G.2005.Quantitative seismic intrepretation.
Alemie W,Sacchi M D.2011.High-resolution three-term AVOinversion by means of a Trivariate Cauchy probability distribution.Geophysics,76(3):R43-R55.
Bogdanov A,Knudsen L R,Leander G,et al.2007.PRESENT:An ultra-lightweight block cipher.∥International Workshop on Cryptographic Hardware and Embedded Systems.Berlin Heidelberg:Springer,450-466.
Bortfeld R.1961.Approximations to the reflection and transmission coefficients of plane longitudinal and transverse waves.Geophysical Prospecting,9(4):485-502.
Castagna J P,Batzle M L,Eastwood R L.1985.Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks.Geophysics,50(4):571-581.
Cooke D A,Schneider W A.1983.Generalized linear inversion of reflection seismic data.Geophysics,48(6):665-676.
Downton J E,Pickford S,Lines L R.2001.Constrained three parameter AVO inversion and uncertainty analysis.∥71st Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,251-254.
Fatti J L,Smith G C,Vail P J,et al.1994.Detection of gas in sandstone reservoirs using AVO analysis:A 3-D seismic case history using the Geostack technique.Geophysics,59(9):1362-1376.
Gardner G H F,Gardner L W,Gregory A R.1974.Formation velocity and density-The diagnostic basics for stratigraphic traps.Geophysics,39(6):770-780.
Goodway B,Chen T W,Downton J.1997.Improved AVO fluid detection and lithology discrimination using Lamépetrophysical parameters;“λρ”,“μρ”,and“λ/μfluid stack”,from P and Sinversions.∥67th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,183-186.
Gray D,Goodway B,Chen T.1999.Bridging the gap-Using AVOto detect changes in fundamental elastic constants.∥61st Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,852-855.
Li C,Yin X Y,Zhang G Z,et al.2014.Prestack AVA inversion for pore fluid modulus.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,533-537.
Ma J F.2003.Forward modeling and inversion methods based on generalized elastic impedance in seismic exploration.Chinese Journal of Geophysics,46(1):159-168.
Mallick S.1993.A simple approximation to the P-wave reflection coefficient and its implication in the inversion of amplitude variation with offset data.Geophysics,58(4):544-552.
Potter C C,Dey A K,Stewart R R.1998.Density prediction using P-and S-wave sonic velocities.∥68th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,320-320.
Richards P G,Frasier C W.1976.Scattering of elastic waves from depth-dependent inhomogeneities.Geophysics,41(3):441-458.
Russell B H,Gray D,Hampson D P.2011.Linearized AVO and poroelasticity.Geophysics,76(3):C19-C29.
Shuey R T.1985.A simplification of the Zoeppritz equations.Geophysics,50(4):609-614.
Simmons J L Jr,Backus M M.1996.Waveform-based AVOinversion and AVO prediction-error.Geophysics,61(6):1575-1588.
Smith G C,Gidlow P M.1987.Weighted stacking for rock property estimation and detection of gas.Geophysical Prospecting,35(9):993-1014.
Wang Y.2003.Seismic Amplitude Inversion in Reflection Tomography.Amsterdam:Elsevier.
Wang Y H.1999.Approximations to the Zoeppritz equations and their use in AVO analysis.Geophysics,64(6):1920-1927.
Wiggins R,Kenny G S,McClure C D.1983.A method for determiningand displaying the shear-velocity reflectivities of a geologic formation.European Patent Application 0113944.
Yang P J,Yin X Y.2008.Non-linear quadratic programming Bayesian prestack inversion.Chinese Journal of Geophysics(in Chinese),51(6):1876-1882.
Yin X Y,Zong Z Y,Wu G C.2013.Improving seismic interpretation:a high-contrast approximation to the reflection coefficient of a plane longitudinal wave.Petroleum Science,10(4):466-476.
Yin X Y,Zong Z Y,Wu G C.2014.Seismic wave scattering inversion for fluid factor of heterogeneous media.Science China Earth Sciences,57(3):542-549.
Yin X Y,Zhang S X.2014.Bayesian inversion for effective porefluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation.Geophysics,79(5):R221-R232.
Zoeppritz K.1919.Erdbebenwellen VIII B,Uber Reflexion und Durchgang seismischer Wellen durch Unstetigkeitsflachen.Gottinger Nachr,1:66-84.
Zong Z,Yin X.2016.Direct inversion of Young′s and Poisson impedances for fluid discrimination.Geofluids,16(5):1006-1016.
Zong Z Y,Yin X Y,Wu G C.2012a.AVO inversion and poroelasticity
with P-and S-wave moduli.Geophysics,77(6):N17-N24.
Zong Z Y,Yin X Y,Zhang F,et al.2012.Reflection coefficient equation and pre-stack seismic inversion with Young's modulus and Poisson ratio.Chinese Journal of Geophysics(in Chinese),55(11):3786-3794,doi:10.6038/j.issn.0001-5733.2012.11.025.
Zong Z Y,Yin X Y,Wu G C.2012b.Elastic impedance parameterization and inversion with Young′s modulus and Poisson′s ratio.Geophysics,78(6):N35-N42.
Zong Z Y,Yin X Y,Wu G C.2013.Direct inversion for a fluid factor and its application in heterogeneous reservoirs.Geophysical Prospecting,61(5):998-1005.
Zong Z Y,Yin X Y,Wu G C.2015.Geofluid discrimination incorporating poroelasticity and seismic reflection inversion.Surveys in Geophysics,36(5):659-681.
杨培杰,印兴耀.2008.非线性二次规划贝叶斯叠前反演.地球物理学报,51(6):1876-1882.
宗兆云,印兴耀,张峰等.2012.杨氏模量和泊松比反射系数近似方程及叠前地震反演.地球物理学报,55(11):55(11):3786-3794,doi:10.6038/j.issn.0001-5733.2012.11.025.
Avseth P,Mukerji T and Mavko G.2005.Quantitative seismic intrepretation.
Alemie W,Sacchi M D.2011.High-resolution three-term AVOinversion by means of a Trivariate Cauchy probability distribution.Geophysics,76(3):R43-R55.
Bogdanov A,Knudsen L R,Leander G,et al.2007.PRESENT:An ultra-lightweight block cipher.∥International Workshop on Cryptographic Hardware and Embedded Systems.Berlin Heidelberg:Springer,450-466.
Bortfeld R.1961.Approximations to the reflection and transmission coefficients of plane longitudinal and transverse waves.Geophysical Prospecting,9(4):485-502.
Castagna J P,Batzle M L,Eastwood R L.1985.Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks.Geophysics,50(4):571-581.
Cooke D A,Schneider W A.1983.Generalized linear inversion of reflection seismic data.Geophysics,48(6):665-676.
Downton J E,Pickford S,Lines L R.2001.Constrained three parameter AVO inversion and uncertainty analysis.∥71st Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,251-254.
Fatti J L,Smith G C,Vail P J,et al.1994.Detection of gas in sandstone reservoirs using AVO analysis:A 3-D seismic case history using the Geostack technique.Geophysics,59(9):1362-1376.
Gardner G H F,Gardner L W,Gregory A R.1974.Formation velocity and density-The diagnostic basics for stratigraphic traps.Geophysics,39(6):770-780.
Goodway B,Chen T W,Downton J.1997.Improved AVO fluid detection and lithology discrimination using Lamépetrophysical parameters;“λρ”,“μρ”,and“λ/μfluid stack”,from P and Sinversions.∥67th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,183-186.
Gray D,Goodway B,Chen T.1999.Bridging the gap-Using AVOto detect changes in fundamental elastic constants.∥61st Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,852-855.
Li C,Yin X Y,Zhang G Z,et al.2014.Prestack AVA inversion for pore fluid modulus.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,533-537.
Ma J F.2003.Forward modeling and inversion methods based on generalized elastic impedance in seismic exploration.Chinese Journal of Geophysics,46(1):159-168.
Mallick S.1993.A simple approximation to the P-wave reflection coefficient and its implication in the inversion of amplitude variation with offset data.Geophysics,58(4):544-552.
Potter C C,Dey A K,Stewart R R.1998.Density prediction using P-and S-wave sonic velocities.∥68th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,320-320.
Richards P G,Frasier C W.1976.Scattering of elastic waves from depth-dependent inhomogeneities.Geophysics,41(3):441-458.
Russell B H,Gray D,Hampson D P.2011.Linearized AVO and poroelasticity.Geophysics,76(3):C19-C29.
Shuey R T.1985.A simplification of the Zoeppritz equations.Geophysics,50(4):609-614.
Simmons J L Jr,Backus M M.1996.Waveform-based AVOinversion and AVO prediction-error.Geophysics,61(6):1575-1588.
Smith G C,Gidlow P M.1987.Weighted stacking for rock property estimation and detection of gas.Geophysical Prospecting,35(9):993-1014.
Wang Y.2003.Seismic Amplitude Inversion in Reflection Tomography.Amsterdam:Elsevier.
Wang Y H.1999.Approximations to the Zoeppritz equations and their use in AVO analysis.Geophysics,64(6):1920-1927.
Wiggins R,Kenny G S,McClure C D.1983.A method for determiningand displaying the shear-velocity reflectivities of a geologic formation.European Patent Application 0113944.
Yang P J,Yin X Y.2008.Non-linear quadratic programming Bayesian prestack inversion.Chinese Journal of Geophysics(in Chinese),51(6):1876-1882.
Yin X Y,Zong Z Y,Wu G C.2013.Improving seismic interpretation:a high-contrast approximation to the reflection coefficient of a plane longitudinal wave.Petroleum Science,10(4):466-476.
Yin X Y,Zong Z Y,Wu G C.2014.Seismic wave scattering inversion for fluid factor of heterogeneous media.Science China Earth Sciences,57(3):542-549.
Yin X Y,Zhang S X.2014.Bayesian inversion for effective porefluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation.Geophysics,79(5):R221-R232.
Zoeppritz K.1919.Erdbebenwellen VIII B,Uber Reflexion und Durchgang seismischer Wellen durch Unstetigkeitsflachen.Gottinger Nachr,1:66-84.
Zong Z,Yin X.2016.Direct inversion of Young′s and Poisson impedances for fluid discrimination.Geofluids,16(5):1006-1016.
Zong Z Y,Yin X Y,Wu G C.2012a.AVO inversion and poroelasticity
with P-and S-wave moduli.Geophysics,77(6):N17-N24.
Zong Z Y,Yin X Y,Zhang F,et al.2012.Reflection coefficient equation and pre-stack seismic inversion with Young's modulus and Poisson ratio.Chinese Journal of Geophysics(in Chinese),55(11):3786-3794,doi:10.6038/j.issn.0001-5733.2012.11.025.
Zong Z Y,Yin X Y,Wu G C.2012b.Elastic impedance parameterization and inversion with Young′s modulus and Poisson′s ratio.Geophysics,78(6):N35-N42.
Zong Z Y,Yin X Y,Wu G C.2013.Direct inversion for a fluid factor and its application in heterogeneous reservoirs.Geophysical Prospecting,61(5):998-1005.
Zong Z Y,Yin X Y,Wu G C.2015.Geofluid discrimination incorporating poroelasticity and seismic reflection inversion.Surveys in Geophysics,36(5):659-681.
杨培杰,印兴耀.2008.非线性二次规划贝叶斯叠前反演.地球物理学报,51(6):1876-1882.
宗兆云,印兴耀,张峰等.2012.杨氏模量和泊松比反射系数近似方程及叠前地震反演.地球物理学报,55(11):55(11):3786-3794,doi:10.6038/j.issn.0001-5733.2012.11.025.