基于逆散射成像条件的最小二乘逆时偏移
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摘要
最小二乘逆时偏移(LSRTM)相对于常规逆时偏移(RTM)具有分辨率更高、振幅更准确、噪音更少等优势,可以对复杂的地质构造进行有效的成像.这种迭代更新反演成像方法十分依赖目标函数的梯度质量和计算效率.当地质模型中存在强反射界面或者记录中存在折射波时,基于常规互相关成像条件(CCC)的最小二乘逆时偏移梯度会包含很强的低频噪音,从而使反演的收敛速度和成像质量降低.为此,本文在最小二乘逆时偏移的梯度中引进了逆散射成像条件来压制这种低频噪音,并以此提出基于逆散射成像条件(ISC)的最小二乘逆时偏移方法.数值模拟结果表明,两者计算耗时基本一致,但逆散射成像条件能高效压制梯度中的低频噪音,从而使反演过程中收敛加速,成像质量得到显著提高.
Compared with the conventional reverse time migration(RTM),the least-squares reversetime migration(LSRTM)can effectively image complex geological structures with the advantages of higher resolution,higher fidelity and fewer artifacts.However,when sharp velocity interfaces exist in the model or when seismic records contain strong refraction signals,the gradient of the objective function calculated by using the conventional cross-correlation imaging condition can contain substantial low-frequency noise,leading to significant deterioration of the imaging quality.In this study,we propose an implementation of the least-squares reverse-time migration by incorporating the linear Born inverse scattering imaging condition.Numerical tests indicate that the proposed method can suppress the low-wavenumber imaging artifacts and therefore update the gradient more efficiently.It can accelerate the convergence of the objective function,and hence is more effective in improving the image quality.
Compared with the conventional reverse time migration(RTM),the least-squares reversetime migration(LSRTM)can effectively image complex geological structures with the advantages of higher resolution,higher fidelity and fewer artifacts.However,when sharp velocity interfaces exist in the model or when seismic records contain strong refraction signals,the gradient of the objective function calculated by using the conventional cross-correlation imaging condition can contain substantial low-frequency noise,leading to significant deterioration of the imaging quality.In this study,we propose an implementation of the least-squares reverse-time migration by incorporating the linear Born inverse scattering imaging condition.Numerical tests indicate that the proposed method can suppress the low-wavenumber imaging artifacts and therefore update the gradient more efficiently.It can accelerate the convergence of the objective function,and hence is more effective in improving the image quality.
引文
Baysal E,Kosloff D D,Sherwood J W C.1983.Reverse time migration.Geophysics,48(11):1514-1524,doi:10.1190/1.1441434.
Baysal E,Kosloff D D,Sherwood J W C.1984.A two-way nonreflecting wave equation.Geophysics,49(2):132-141,doi:10.1190/1.1441644.
Brandsberg-Dahl S,Chemingui N,Whitmore D,et al.2013.3DRTMangle gathers using an inverse scattering imaging condition.∥83rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,3958-3962,doi:10.1190/segam2013-1402.1.
Claerbout J F.1971.Toward a unified theory of reflector mapping.Geophysics,36(3):467-481,doi:10.1190/1.1440185.
Claerbout J F.1992.Earth Soundings Analysis:Processing Versus Inversion.London:Blackwell Scientific Publications,Inc.
Dai W,Fowler P,Schuster G T.2012.Multi-source least-squares reverse time migration.Geophysical Prospecting,60(4):681-695,doi:10.1111/j.1365-2478.2012.01092.x.
Dai W,Schuster G T.2013.Plane-wave least-squares reverse-time migration.Geophysics,78(4):S165-S177,doi:10.1190/geo2012-0377.1.
Du Q Z,Zhu Y T,Zhang M Q,et al.2013.A study on the strategy of low wavenumber noise suppression for prestack reverse-time depth migration.Chinese Journal of Geophysics(in Chinese),56(7):2391-2401,doi:10.6038/cjg20130725.
Fang X Z,Shi Y,Ke X,et al.2015.Investigation on high-accuracy pre-stack reverse-time migration for VTI medium.Progress in Geophysics(in Chinese),30(4):1677-1684,doi:10.6038/pg20150422.
Fletcher R P,Fowler P J,Kitchenside P,et al.2006.Suppressing unwanted internal reflections in prestack reverse-time migration.Geophysics,71(6):E79-E82,doi:10.1190/1.2356319.
Ke X,Shi Y,Wang W H.2018.An efficient wavefield simulation and reconstruction method for least-squares reverse time migration.Journal of Seismic Exploration,27:183-200.
Komatitsch D,Tromp J.2003.A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation.Geophysical Journal International,154(1):146-153,doi:10.1046/j.1365-246x.2003.01950.x.
Liu F Q,Zhang G Q,Morton S A,et al.2007.Reverse-time migration using one-way wavefield imaging condition.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2170-2174,doi:10.1190/1.2792917.
Liu F Q,Zhang G Q,Morton S A,et al.2011.An effective imaging condition for reverse-time migration using wavefield decomposition.Geophysics,76(1):S29-S39,doi:10.1190/1.3533914.
Loewenthal D,Stoffa P L,Faria E L.1987.Suppressing the unwanted reflections of the full wave equation.Geophysics,52(7):1007-1012,doi:10.1190/1.1442352.
Nemeth T,Wu C J,Schuster G T.1999.Least-squares migration of incomplete reflection data.Geophysics,64(1):208-221,doi:10.1190/1.1444517.
Op′t Root T J P M,Stolk C C,De Hoop M V.2012.Linearized inverse scattering based on seismic reverse time migration.Journal de Mathématiques Pures et Appliquées,98(2):211-238,doi:10.1016/j.matpur.2012.02.009.
Plessix R E.2006.A review of the adjoint-state method for computing the gradient of a functional with geophysical applications.Geophysical Journal International,167(2):495-503,doi:10.1111/j.1365-246x.2006.02978.x.
Schuster G T.1993.Least-squares cross-well migration.∥63rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,110-113,doi:10.1190/1.1822308.
Shi Y,Wang Y H.2016.Reverse time migration of 3D vertical seismic profile data.Geophysics,81(1):S31-S38,doi:10.1190/geo2015-0277.1.
Tarantola A.1984a.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266,doi:10.1190/1.1441754.
Tarantola A.1984b.Linearized inversion of seismic reflection data.Geophysical Prospecting,32(6):998-1015,doi:10.1111/j.1365-2478.1984.tb00751.x.
Wang B L,Gao J H,Chen W C,et al.2012.Efficient boundary storage strategies for seismic reverse time migration.Chinese Journal of Geophysics(in Chinese),55(7):2412-2421,doi:10.6038/j.issn.0001-5733.2012.07.025.
Wang Y F,Liang W Q,Nashed Z,et al.2014.Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method.Geophysics,79(5):T277-T285,doi:10.1190/geo2014-0078.1.
Wang Z K,Li J Y,Wang B F,et al.2017.Time-domain explicit finite-difference method based on the mixed-domain function approximation for acoustic wave equation.Geophysics,82(5):T237-T248,doi:10.1190/geo2017-0012.1.
Whitmore N D.1983.Iterative depth migration by backward time propagation.∥53rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,382-385,doi:10.1190/1.1893867.
Whitmore N D,Crawley S.2012.Applications of RTM inverse scattering imaging conditions.∥82nd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1-6,doi:10.1190/segam2012-0779.1.
Wong M,Ronen S,Biondi B.2011.Least-squares reverse time migration/inversion for ocean bottom data:A case study.∥81st Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2369-2373,doi:10.1190/1.3627684.
Wu D,Yao G,Cao J J,et al.2016.Least-squares RTM with L1norm regularisation.JournalofGeophysicsandEngineering,13(5):666-673,doi:10.1088/1742-2132/13/5/666.
Yang J Z,Liu Y Z,Dong L G.2016.Least-squares reverse time migration in the presence of density variations.Geophysics,81(6):S497-S509,doi:10.1190/geo2016-0075.1.
Yao G,Jakubowicz H.2016.Least-squares reverse-time migration in a matrix-based formulation.GeophysicsProspecting,64(3):611-621,doi:10.1111/1365-2478.12305.
Yao G,Wu D,Debens H A.2016.Adaptive finite difference for seismic wavefield modelling in acoustic media.Scientific Reports,6:30302,doi:10.1038/srep30302.
Yao G,Wu D.2017.Reflection full waveform inversion.Science China Earth Sciences,60(10):1783-1794,doi:10.1007/s11430-016-9091-9.
Yao G,Da Silva N V,Wu D.2017.Forward modelling formulas for least-squares reverse-time migration.Exploration Geophysics,doi:10.1071/EG16157.
Yoon K,Marfurt K J,Starr W.2004.Challenges in reverse-time migration.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1057-1060,doi:10.1190/1.1851068.
Yoon K,Marfurt K J.2006.Reverse-time migration using the Poynting vector.Exploration Geophysics,37(1):102-107,doi:10.1071/eg06102.
Zhang J H,Yao Z X.2013.Optimized finite-difference operator for broadband seismic wave modeling.Geophysics,78(1):A13-A18,doi:10.1190/geo2012-0277.1.
Zhang Y,Sun J.2009.Practical issues in reverse time migration:True amplitude gathers,noise removal and harmonic source encoding.First Break,27(1):53-59,doi:10.3997/1365-2397.2009002.
杜启振,朱钇同,张明强等.2013.叠前逆时深度偏移低频噪声压制策略研究.地球物理学报,56(7):2391-2401,doi:10.6038/cjg20130725.
方修政,石颖,柯璇等.2015.VTI介质高精度叠前逆时偏移方法研究.地球物理学进展,30(4):1677-1684,doi:10.6038/pg20150422.
王保利,高静怀,陈文超等.2012.地震叠前逆时偏移的有效边界存储策略.地球物理学报,55(7):2412-2421,doi:10.6038/j.issn.0001-5733.2012.07.025.
Baysal E,Kosloff D D,Sherwood J W C.1984.A two-way nonreflecting wave equation.Geophysics,49(2):132-141,doi:10.1190/1.1441644.
Brandsberg-Dahl S,Chemingui N,Whitmore D,et al.2013.3DRTMangle gathers using an inverse scattering imaging condition.∥83rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,3958-3962,doi:10.1190/segam2013-1402.1.
Claerbout J F.1971.Toward a unified theory of reflector mapping.Geophysics,36(3):467-481,doi:10.1190/1.1440185.
Claerbout J F.1992.Earth Soundings Analysis:Processing Versus Inversion.London:Blackwell Scientific Publications,Inc.
Dai W,Fowler P,Schuster G T.2012.Multi-source least-squares reverse time migration.Geophysical Prospecting,60(4):681-695,doi:10.1111/j.1365-2478.2012.01092.x.
Dai W,Schuster G T.2013.Plane-wave least-squares reverse-time migration.Geophysics,78(4):S165-S177,doi:10.1190/geo2012-0377.1.
Du Q Z,Zhu Y T,Zhang M Q,et al.2013.A study on the strategy of low wavenumber noise suppression for prestack reverse-time depth migration.Chinese Journal of Geophysics(in Chinese),56(7):2391-2401,doi:10.6038/cjg20130725.
Fang X Z,Shi Y,Ke X,et al.2015.Investigation on high-accuracy pre-stack reverse-time migration for VTI medium.Progress in Geophysics(in Chinese),30(4):1677-1684,doi:10.6038/pg20150422.
Fletcher R P,Fowler P J,Kitchenside P,et al.2006.Suppressing unwanted internal reflections in prestack reverse-time migration.Geophysics,71(6):E79-E82,doi:10.1190/1.2356319.
Ke X,Shi Y,Wang W H.2018.An efficient wavefield simulation and reconstruction method for least-squares reverse time migration.Journal of Seismic Exploration,27:183-200.
Komatitsch D,Tromp J.2003.A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation.Geophysical Journal International,154(1):146-153,doi:10.1046/j.1365-246x.2003.01950.x.
Liu F Q,Zhang G Q,Morton S A,et al.2007.Reverse-time migration using one-way wavefield imaging condition.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2170-2174,doi:10.1190/1.2792917.
Liu F Q,Zhang G Q,Morton S A,et al.2011.An effective imaging condition for reverse-time migration using wavefield decomposition.Geophysics,76(1):S29-S39,doi:10.1190/1.3533914.
Loewenthal D,Stoffa P L,Faria E L.1987.Suppressing the unwanted reflections of the full wave equation.Geophysics,52(7):1007-1012,doi:10.1190/1.1442352.
Nemeth T,Wu C J,Schuster G T.1999.Least-squares migration of incomplete reflection data.Geophysics,64(1):208-221,doi:10.1190/1.1444517.
Op′t Root T J P M,Stolk C C,De Hoop M V.2012.Linearized inverse scattering based on seismic reverse time migration.Journal de Mathématiques Pures et Appliquées,98(2):211-238,doi:10.1016/j.matpur.2012.02.009.
Plessix R E.2006.A review of the adjoint-state method for computing the gradient of a functional with geophysical applications.Geophysical Journal International,167(2):495-503,doi:10.1111/j.1365-246x.2006.02978.x.
Schuster G T.1993.Least-squares cross-well migration.∥63rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,110-113,doi:10.1190/1.1822308.
Shi Y,Wang Y H.2016.Reverse time migration of 3D vertical seismic profile data.Geophysics,81(1):S31-S38,doi:10.1190/geo2015-0277.1.
Tarantola A.1984a.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266,doi:10.1190/1.1441754.
Tarantola A.1984b.Linearized inversion of seismic reflection data.Geophysical Prospecting,32(6):998-1015,doi:10.1111/j.1365-2478.1984.tb00751.x.
Wang B L,Gao J H,Chen W C,et al.2012.Efficient boundary storage strategies for seismic reverse time migration.Chinese Journal of Geophysics(in Chinese),55(7):2412-2421,doi:10.6038/j.issn.0001-5733.2012.07.025.
Wang Y F,Liang W Q,Nashed Z,et al.2014.Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method.Geophysics,79(5):T277-T285,doi:10.1190/geo2014-0078.1.
Wang Z K,Li J Y,Wang B F,et al.2017.Time-domain explicit finite-difference method based on the mixed-domain function approximation for acoustic wave equation.Geophysics,82(5):T237-T248,doi:10.1190/geo2017-0012.1.
Whitmore N D.1983.Iterative depth migration by backward time propagation.∥53rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,382-385,doi:10.1190/1.1893867.
Whitmore N D,Crawley S.2012.Applications of RTM inverse scattering imaging conditions.∥82nd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1-6,doi:10.1190/segam2012-0779.1.
Wong M,Ronen S,Biondi B.2011.Least-squares reverse time migration/inversion for ocean bottom data:A case study.∥81st Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2369-2373,doi:10.1190/1.3627684.
Wu D,Yao G,Cao J J,et al.2016.Least-squares RTM with L1norm regularisation.JournalofGeophysicsandEngineering,13(5):666-673,doi:10.1088/1742-2132/13/5/666.
Yang J Z,Liu Y Z,Dong L G.2016.Least-squares reverse time migration in the presence of density variations.Geophysics,81(6):S497-S509,doi:10.1190/geo2016-0075.1.
Yao G,Jakubowicz H.2016.Least-squares reverse-time migration in a matrix-based formulation.GeophysicsProspecting,64(3):611-621,doi:10.1111/1365-2478.12305.
Yao G,Wu D,Debens H A.2016.Adaptive finite difference for seismic wavefield modelling in acoustic media.Scientific Reports,6:30302,doi:10.1038/srep30302.
Yao G,Wu D.2017.Reflection full waveform inversion.Science China Earth Sciences,60(10):1783-1794,doi:10.1007/s11430-016-9091-9.
Yao G,Da Silva N V,Wu D.2017.Forward modelling formulas for least-squares reverse-time migration.Exploration Geophysics,doi:10.1071/EG16157.
Yoon K,Marfurt K J,Starr W.2004.Challenges in reverse-time migration.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1057-1060,doi:10.1190/1.1851068.
Yoon K,Marfurt K J.2006.Reverse-time migration using the Poynting vector.Exploration Geophysics,37(1):102-107,doi:10.1071/eg06102.
Zhang J H,Yao Z X.2013.Optimized finite-difference operator for broadband seismic wave modeling.Geophysics,78(1):A13-A18,doi:10.1190/geo2012-0277.1.
Zhang Y,Sun J.2009.Practical issues in reverse time migration:True amplitude gathers,noise removal and harmonic source encoding.First Break,27(1):53-59,doi:10.3997/1365-2397.2009002.
杜启振,朱钇同,张明强等.2013.叠前逆时深度偏移低频噪声压制策略研究.地球物理学报,56(7):2391-2401,doi:10.6038/cjg20130725.
方修政,石颖,柯璇等.2015.VTI介质高精度叠前逆时偏移方法研究.地球物理学进展,30(4):1677-1684,doi:10.6038/pg20150422.
王保利,高静怀,陈文超等.2012.地震叠前逆时偏移的有效边界存储策略.地球物理学报,55(7):2412-2421,doi:10.6038/j.issn.0001-5733.2012.07.025.