基于快速非支配排序遗传算法的VTI介质多分量叠前联合反演
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摘要
在VTI介质中,由于引入了各向异性参数使得多分量多参数地震反演问题的非线性程度显著增加,因此采用传统的权重加权法构建单目标函数进行反演得到的反演结果往往并不理想.本文以反射率法为基础,结合快速非支配排序遗传算法研究了一种VTI介质的多分量叠前联合反演方法.该方法以反射率法为正演方程,应用互相关原理构建PP波和PSV波的多目标函数,进而采用快速非支配排序遗传算法全局寻优获得VTI介质的厚度、纵横波速度、密度和各向异性参数等多个参数.在正演的过程中,反射率法可以考虑几何扩散、吸收衰减、透射损失、多次波以及纵横波旅行时不匹配等地震波传播效应,更能精确地描述地震波在地下地层中的真实传播情况;在反演的过程中,快速非支配排序遗传算法可以在不引入权重系数的条件下同时优化多个目标函数,获得联合反演问题的Pareto最优解,既不添加权重系数影响又充分利用多分量地震数据.模型测试结果验证了该反演方法的有效性和可行性.
Because introducing anisotropic parameters markedly increases the nonlinearity of the multicomponent or multiparameter prestack joint inversion for VTI media,the conventional weighted stacking inversion method of objective functions which is aimed at constructing a singleobjective function is usually unsuitable.Based on the reflectivity method,a multicomponent prestack joint inversion method for VTI media is studied by using a fast nondominated sorting genetic algorithm(NSGA Ⅱ)in this paper.This approach first uses the reflectivity method as forward equation and establishes a multi-objective function of PP and PSV waves based on the cross-correlation approach,and then uses the NSGA Ⅱto estimate multiple parameters including thickness,P-and S-wave velocity,density and anisotropic parameters by inverting PP and PSV wave seismic records jointly.In the process of forward modeling,the reflectivity method canaccurately describe the propagation characteristics of seismic wave because some wave-propagation effects are considered,such as geometric spreading,absorption attenuation,transmission loss,multiples and travel time mismatching of P-wave and S-wave.In the process of inversion,the NSGA Ⅱ can simultaneously optimize more than one objective function to obtain the Pareto-optimal solutions of the joint inversion problem without introducing weight coefficients,which eliminates the influence of weight coefficients on inversion results and makes full use of multicomponent seismic records.Model tests verify the effectiveness and feasibility of the proposed inversion method.
Because introducing anisotropic parameters markedly increases the nonlinearity of the multicomponent or multiparameter prestack joint inversion for VTI media,the conventional weighted stacking inversion method of objective functions which is aimed at constructing a singleobjective function is usually unsuitable.Based on the reflectivity method,a multicomponent prestack joint inversion method for VTI media is studied by using a fast nondominated sorting genetic algorithm(NSGA Ⅱ)in this paper.This approach first uses the reflectivity method as forward equation and establishes a multi-objective function of PP and PSV waves based on the cross-correlation approach,and then uses the NSGA Ⅱto estimate multiple parameters including thickness,P-and S-wave velocity,density and anisotropic parameters by inverting PP and PSV wave seismic records jointly.In the process of forward modeling,the reflectivity method canaccurately describe the propagation characteristics of seismic wave because some wave-propagation effects are considered,such as geometric spreading,absorption attenuation,transmission loss,multiples and travel time mismatching of P-wave and S-wave.In the process of inversion,the NSGA Ⅱ can simultaneously optimize more than one objective function to obtain the Pareto-optimal solutions of the joint inversion problem without introducing weight coefficients,which eliminates the influence of weight coefficients on inversion results and makes full use of multicomponent seismic records.Model tests verify the effectiveness and feasibility of the proposed inversion method.
引文
Auld B A.1973.Acoustic resonators.∥Acoustic Fields and Waves in Solids.2nd ed.New York:John Willey and Sons.
Banik N C.1987.An effective anisotropy parameter in transversely isotropic media.Geophysics,52(12):1654-1664.
Daley P F,Hron F.1977.Reflection and transmission coefficients for transversely isotropic media.Bulletin of the Seismological Society of America,67(3):661-675.
Deb K,Agrawal R B.1995.Simulated binary crossover for continuous search space.Complex Systems,9(3):115-148.
Deb K,Agrawal S.1999.A niched-penalty approach for constraint handling in genetic algorithms.∥Artificial Neural Nets and Genetic Algorithms.Vienna:Springer,235-243.
Deb K,Pratap A,Agarwal S,et al.2002.A fast and elitist multiobjective genetic algorithm:NSGA-II.IEEE Transactions on Evolutionary Computation,6(2):182-197.
Du B Y,Yang W Y,Wang E L,et al.2016.Joint pre-stack inversion of multiple waves based on Russell approximation.Chinese Journal of Geophysics(in Chinese),59(8):3016-3024,doi:10.6038/cjg20160824.
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.
Fryer G J,Frazer L N.1984.Seismic waves in stratified anisotropic media.Geophysical Journal of the Royal Astronomical Society,78(3):691-710.
Goldberg D E.1989.Genetic Algorithms in Search,Optimization,and Machine Learning.Boston:Addison-Wesley Professional.
Graebner M.1992.Plane-wave reflection and transmission coefficients for a transversely isotropic solid.Geophysics,57(11):1512-1519.
Heyburn R,Fox B.2010.Multi-objective analysis of body and surface waves from the Market Rasen(UK)earthquake.Geophysical Journal International,181(1):532-544.
Hou D J,Liu Y,Hu G Q,et al.2014a.Prestack multiwave joint inversion for elastic moduli based on Bayesian theory.Chinese Journal of Geophysics(in Chinese),57(4):1251-1264,doi:10.6038/cjg20140422.
Hou D J,Liu Y,Ren Z M,et al.2014b.Multi-wave prestack joint inversion in VTI media based on Bayesian theory.Geophysical Prospecting for Petroleum(in Chinese),53(3):294-303.
Kennett B L N.1983.Seismic Wave Propagation in Stratified Media.Cambridge:Cambridge University Press.
Kozlovskaya E,Vecsey L,PlomerováJ,et al.2007.Joint inversion of multiple data types with the use of multiobjective optimization:Problem formulation and application to the seismic anisotropy investigations.Geophysical Journal International,171(2):761-779.
Li Q,Li Q C,Zhang L.2014.Anisotropic parameter analysis of multi-component data in VTI media.Oil Geophysical Prospecting(in Chinese),49(3):503-507.
Li T,Mallick S.2015.Multicomponent,multi-azimuth pre-stack seismic waveform inversion for azimuthally anisotropic media using aparallel and computationally efficient non-dominated sorting genetic algorithm.Geophysical Journal International,200(2):1134-1152.
Liu Y Z,Wang G Y,Dong L G,et al.2014.Joint inversion of VTIparameters using nonlinear traveltime tomography.Chinese Journal of Geophysics(in Chinese),57(10):3402-3410,doi:10.6038/cjg20141026.
Liu Y Z,Wang G Y,Yang J Z,et al.2015.Multi-parameter fullwaveform inversion for VTI media based on Born sensitivity kernels.Chinese Journal of Geophysics(in Chinese),58(4):1305-1316,doi:10.6038/cjg20150418.
Mallick S,Frazer L N.1987.Practical aspects of reflectivity modeling.Geophysics,52(10):1355-1364.
Ostrander W J.1984.Plane-wave reflection coefficients for gas sands at non-normal angles of incidence.Geophysics,49(10):1637-1648.
Padhi A,Mallick S.2013.Accurate estimation of density from the inversion of multicomponent pre-stack seismic waveform data using a nondominated sorting genetic algorithm.The Leading Edge,32(1):94-98.
Padhi A,Mallick S.2014.Multicomponent pre-stack seismic waveform inversion in transversely isotropic media using a non-dominated sorting genetic algorithm.Geophysical Journal International,196(3):1600-1618.
Rüger A.1997.P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry.Geophysics,62(3):713-722.
Rüger A.1998.Variation of P-wave reflectivity with offset and azimuth in anisotropic media.Geophysics,63(3):935-947.
Singh V P,Duquet B,Léger M,et al.2008.Automatic wave-equation migration velocity inversion using multiobjective evolutionary algorithms.Geophysics,73(5):VE61-VE73.
Stewart R R.1990.Joint P and P-SV inversion.The CREWESProject Research Report.Calgary:The University of Calgary,2:112-115.
Thomsen L.1986.Weak elastic anisotropy.Geophysics,51(10):1954-1966.
Veire H H,LandrM.2006.Simultaneous inversion of PP and PSseismic data.Geophysics,71(3):R1-R10.
Wang M C.2007.Method and application of multiwave prestack joint inversion lithologic parameters in VTI media[Master′s thesis](in Chinese).Chengdu:Chengdu University of Technology.
Wang Y,Dong L G.2015.Multi-parameter full waveform inversion for acoustic VTI media using the truncated Newton method.Chinese Journal of Geophysics(in Chinese),58(8):2873-2885,doi:10.6038/cjg20150821.
Xun H,Dong M Y,Mou Y G.1997.Wave field simulation using reflectivity method and body-wave radiation patterns in anisotropic media.Oil Geophysical Prospecting(in Chinese),32(5):605-614.
Zhang G Z,Du B Y,Li H S,et al.2014.The method of joint prestack inversion of PP and P-SV waves in shale gas reservoirs.Chinese Journal of Geophysics(in Chinese),57(12):4141-4149,doi:10.6038/cjg20141225.
Zhong Z,Li L M,Shi Y H.2011.Pre-stack AVA lithologic parameters inversion and its precision.Geophysical Prospecting for Petroleum(in Chinese),50(3):225-233.
杜炳毅,杨午阳,王恩利等.2016.基于Russell近似的纵横波联合反演方法研究.地球物理学报,59(8):3016-3024,doi:10.6038/cjg20160824.
侯栋甲,刘洋,胡国庆等.2014a.基于贝叶斯理论的叠前多波联合反演弹性模量方法.地球物理学报,57(4):1251-1264,doi:10.6038/cjg20140422.
侯栋甲,刘洋,任志明等.2014b.基于贝叶斯理论的VTI介质多波叠前联合反演.石油物探,53(3):294-303.
李勤,李庆春,张林.2014.VTI介质多波各向异性参数分析.石油地球物理勘探,49(3):503-507.
刘玉柱,王光银,董良国等.2014.VTI介质多参数联合走时层析成像方法.地球物理学报,57(10):3402-3410,doi:10.6038/cjg20141026.
刘玉柱,王光银,杨积忠等.2015.基于Born敏感核函数的VTI介质多参数全波形反演.地球物理学报,58(4):1305-1316,doi:10.6038/cjg20150418.
王明春.2007.VTI介质多波叠前联合反演岩性参数方法及应用[硕士论文].成都:成都理工大学.
王义,董良国.2015.基于截断牛顿法的VTI介质声波多参数全波形反演.地球物理学报,58(8):2873-2885,doi:10.6038/cjg20150821.
寻浩,董敏煜,牟永光.1997.各向异性介质中反射率法波场模拟及体波辐射图案.石油地球物理勘探,32(5):605-614.
张广智,杜炳毅,李海山等.2014.页岩气储层纵横波叠前联合反演方法.地球物理学报:57(12):4141-4149,doi:10.6038/cjg20141225.
钟峙,李录明,史运华.2011.叠前AVA岩性参数反演方法及精度分析.石油物探,50(3):225-233.
Banik N C.1987.An effective anisotropy parameter in transversely isotropic media.Geophysics,52(12):1654-1664.
Daley P F,Hron F.1977.Reflection and transmission coefficients for transversely isotropic media.Bulletin of the Seismological Society of America,67(3):661-675.
Deb K,Agrawal R B.1995.Simulated binary crossover for continuous search space.Complex Systems,9(3):115-148.
Deb K,Agrawal S.1999.A niched-penalty approach for constraint handling in genetic algorithms.∥Artificial Neural Nets and Genetic Algorithms.Vienna:Springer,235-243.
Deb K,Pratap A,Agarwal S,et al.2002.A fast and elitist multiobjective genetic algorithm:NSGA-II.IEEE Transactions on Evolutionary Computation,6(2):182-197.
Du B Y,Yang W Y,Wang E L,et al.2016.Joint pre-stack inversion of multiple waves based on Russell approximation.Chinese Journal of Geophysics(in Chinese),59(8):3016-3024,doi:10.6038/cjg20160824.
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.
Fryer G J,Frazer L N.1984.Seismic waves in stratified anisotropic media.Geophysical Journal of the Royal Astronomical Society,78(3):691-710.
Goldberg D E.1989.Genetic Algorithms in Search,Optimization,and Machine Learning.Boston:Addison-Wesley Professional.
Graebner M.1992.Plane-wave reflection and transmission coefficients for a transversely isotropic solid.Geophysics,57(11):1512-1519.
Heyburn R,Fox B.2010.Multi-objective analysis of body and surface waves from the Market Rasen(UK)earthquake.Geophysical Journal International,181(1):532-544.
Hou D J,Liu Y,Hu G Q,et al.2014a.Prestack multiwave joint inversion for elastic moduli based on Bayesian theory.Chinese Journal of Geophysics(in Chinese),57(4):1251-1264,doi:10.6038/cjg20140422.
Hou D J,Liu Y,Ren Z M,et al.2014b.Multi-wave prestack joint inversion in VTI media based on Bayesian theory.Geophysical Prospecting for Petroleum(in Chinese),53(3):294-303.
Kennett B L N.1983.Seismic Wave Propagation in Stratified Media.Cambridge:Cambridge University Press.
Kozlovskaya E,Vecsey L,PlomerováJ,et al.2007.Joint inversion of multiple data types with the use of multiobjective optimization:Problem formulation and application to the seismic anisotropy investigations.Geophysical Journal International,171(2):761-779.
Li Q,Li Q C,Zhang L.2014.Anisotropic parameter analysis of multi-component data in VTI media.Oil Geophysical Prospecting(in Chinese),49(3):503-507.
Li T,Mallick S.2015.Multicomponent,multi-azimuth pre-stack seismic waveform inversion for azimuthally anisotropic media using aparallel and computationally efficient non-dominated sorting genetic algorithm.Geophysical Journal International,200(2):1134-1152.
Liu Y Z,Wang G Y,Dong L G,et al.2014.Joint inversion of VTIparameters using nonlinear traveltime tomography.Chinese Journal of Geophysics(in Chinese),57(10):3402-3410,doi:10.6038/cjg20141026.
Liu Y Z,Wang G Y,Yang J Z,et al.2015.Multi-parameter fullwaveform inversion for VTI media based on Born sensitivity kernels.Chinese Journal of Geophysics(in Chinese),58(4):1305-1316,doi:10.6038/cjg20150418.
Mallick S,Frazer L N.1987.Practical aspects of reflectivity modeling.Geophysics,52(10):1355-1364.
Ostrander W J.1984.Plane-wave reflection coefficients for gas sands at non-normal angles of incidence.Geophysics,49(10):1637-1648.
Padhi A,Mallick S.2013.Accurate estimation of density from the inversion of multicomponent pre-stack seismic waveform data using a nondominated sorting genetic algorithm.The Leading Edge,32(1):94-98.
Padhi A,Mallick S.2014.Multicomponent pre-stack seismic waveform inversion in transversely isotropic media using a non-dominated sorting genetic algorithm.Geophysical Journal International,196(3):1600-1618.
Rüger A.1997.P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry.Geophysics,62(3):713-722.
Rüger A.1998.Variation of P-wave reflectivity with offset and azimuth in anisotropic media.Geophysics,63(3):935-947.
Singh V P,Duquet B,Léger M,et al.2008.Automatic wave-equation migration velocity inversion using multiobjective evolutionary algorithms.Geophysics,73(5):VE61-VE73.
Stewart R R.1990.Joint P and P-SV inversion.The CREWESProject Research Report.Calgary:The University of Calgary,2:112-115.
Thomsen L.1986.Weak elastic anisotropy.Geophysics,51(10):1954-1966.
Veire H H,LandrM.2006.Simultaneous inversion of PP and PSseismic data.Geophysics,71(3):R1-R10.
Wang M C.2007.Method and application of multiwave prestack joint inversion lithologic parameters in VTI media[Master′s thesis](in Chinese).Chengdu:Chengdu University of Technology.
Wang Y,Dong L G.2015.Multi-parameter full waveform inversion for acoustic VTI media using the truncated Newton method.Chinese Journal of Geophysics(in Chinese),58(8):2873-2885,doi:10.6038/cjg20150821.
Xun H,Dong M Y,Mou Y G.1997.Wave field simulation using reflectivity method and body-wave radiation patterns in anisotropic media.Oil Geophysical Prospecting(in Chinese),32(5):605-614.
Zhang G Z,Du B Y,Li H S,et al.2014.The method of joint prestack inversion of PP and P-SV waves in shale gas reservoirs.Chinese Journal of Geophysics(in Chinese),57(12):4141-4149,doi:10.6038/cjg20141225.
Zhong Z,Li L M,Shi Y H.2011.Pre-stack AVA lithologic parameters inversion and its precision.Geophysical Prospecting for Petroleum(in Chinese),50(3):225-233.
杜炳毅,杨午阳,王恩利等.2016.基于Russell近似的纵横波联合反演方法研究.地球物理学报,59(8):3016-3024,doi:10.6038/cjg20160824.
侯栋甲,刘洋,胡国庆等.2014a.基于贝叶斯理论的叠前多波联合反演弹性模量方法.地球物理学报,57(4):1251-1264,doi:10.6038/cjg20140422.
侯栋甲,刘洋,任志明等.2014b.基于贝叶斯理论的VTI介质多波叠前联合反演.石油物探,53(3):294-303.
李勤,李庆春,张林.2014.VTI介质多波各向异性参数分析.石油地球物理勘探,49(3):503-507.
刘玉柱,王光银,董良国等.2014.VTI介质多参数联合走时层析成像方法.地球物理学报,57(10):3402-3410,doi:10.6038/cjg20141026.
刘玉柱,王光银,杨积忠等.2015.基于Born敏感核函数的VTI介质多参数全波形反演.地球物理学报,58(4):1305-1316,doi:10.6038/cjg20150418.
王明春.2007.VTI介质多波叠前联合反演岩性参数方法及应用[硕士论文].成都:成都理工大学.
王义,董良国.2015.基于截断牛顿法的VTI介质声波多参数全波形反演.地球物理学报,58(8):2873-2885,doi:10.6038/cjg20150821.
寻浩,董敏煜,牟永光.1997.各向异性介质中反射率法波场模拟及体波辐射图案.石油地球物理勘探,32(5):605-614.
张广智,杜炳毅,李海山等.2014.页岩气储层纵横波叠前联合反演方法.地球物理学报:57(12):4141-4149,doi:10.6038/cjg20141225.
钟峙,李录明,史运华.2011.叠前AVA岩性参数反演方法及精度分析.石油物探,50(3):225-233.
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