基于能量密度的自解耦互相关成像条件
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摘要
基于能量密度构建的弹性波能量成像条件,可以准确提取弹性波场的能量信息,并可以有效压制背向散射.但是该成像条件得到的成像结果将所有弹性波场能量信息耦合在一起,难以区分纯波模式的能量信息.为此,我们从势能及动能两方面将能量场解耦,得到纯纵波(PP)、纯横波(SS)、转换波(C)能量场.根据能量守恒定律,基于Helmholtz原理对位移场的空间导数进行因式分解,将弹性势能自解耦得到纯纵波、纯横波及转换波势能;引入体应力构建得到P波及S波速度,将弹性动能分解为纯纵波、纯横波和转换波动能.从而,构建基于能量密度自解耦得到纯波能量互相关成像条件.数值实验表明自解耦成像条件可实现弹性波场能量的分解,并得到背向散射压制、振幅有效保持的PP波、SS波和C波成像结果.
Constructed by energy density,elastic wavefield imaging condition using the energy norm provides energy information of wave field accurately and suppresses back scattering.However,the elastic wavefield information is coupled as an entire part,making it impossible to differentiate varieties of energy information from pure wave.In this regard,we decouple energy density in the two aspects of potential energy and kinetic energy and obtain pure wave energy of PP wave and SS wave and converted wave.Following the law of conservation of energy and Helmholtz principle,we calculate the factorization of the spatial derivative of the displacement field and obtain potential energy of pure P-wave and pure shear wave and converted wave as a result of the decoupling of elastic wave.We also calculate the velocity of P-wave and S-wave by the construction of volume stress and require kinetic energy from the decoupling of pure P-wave and pure S-wave and pure converted wave.Numerical experiment indicates self-decoupled imaging condition realized the decoupling of elastic wave field energy,making it effective to image PP wave and SS wave and converted wave with the suppression of back scattering and the continuous preservation of amplitude,contributing to seismic processing and interpretation.
Constructed by energy density,elastic wavefield imaging condition using the energy norm provides energy information of wave field accurately and suppresses back scattering.However,the elastic wavefield information is coupled as an entire part,making it impossible to differentiate varieties of energy information from pure wave.In this regard,we decouple energy density in the two aspects of potential energy and kinetic energy and obtain pure wave energy of PP wave and SS wave and converted wave.Following the law of conservation of energy and Helmholtz principle,we calculate the factorization of the spatial derivative of the displacement field and obtain potential energy of pure P-wave and pure shear wave and converted wave as a result of the decoupling of elastic wave.We also calculate the velocity of P-wave and S-wave by the construction of volume stress and require kinetic energy from the decoupling of pure P-wave and pure S-wave and pure converted wave.Numerical experiment indicates self-decoupled imaging condition realized the decoupling of elastic wave field energy,making it effective to image PP wave and SS wave and converted wave with the suppression of back scattering and the continuous preservation of amplitude,contributing to seismic processing and interpretation.
引文
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Chang W F,McMechan G A.1986.Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,51(1):67-84.
Chang W F,McMechan G A.1994.3-D elastic prestack,reversetime depth migration.Geophysics,59(4):597-609.
Claerbout J F.1971.Toward a unified theory of reflector mapping.Geophysics,36(3):467-481.
Du Q Z,Zhu Y T,Ba J.2012.Polarity reversal correction for elastic reverse time migration.Geophysics,77(2):S31-S41.
Du Q Z,Gong X F,Zhang M Q,et al.2014.3DPS-wave imaging with elastic reverse-time migration.Geophysics,79(5):S173-S184
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Kaelin B,Guitton A.2006.Imaging condition for reverse time migration.∥76th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2594-2598.
Li Z C,Zhang H,Liu Q M,et al.2007.Numeric simulation of elastic wavefield separation by staggering grid high-order finitedifference algorithm.Oil Geophysical Prospecting(in Chinese),42(5):510-515.
Loewenthal R,Sancho J,Fersht A R.1991.Fluorescence spectrum of barnase:contributions of three tryptophan residues and a histidine-related pH dependence.Biochemistry,30(27):6775-6779.
Ma D T,Zhu G M.2003.Numerical modeling of P-wave and S-wave separation in elastic wavefield.Oil Geophysical Prospecting(in Chinese),38(5):482-486.
Nguyen B D,McMechan G A.2012.Excitation amplitude imaging condition for prestack reverse-time migration.Geophysics,78(1):S37-S46
Nguyen B D,McMechan G A.2014.Five ways to avoid storing source wavefield snapshots in 2Delastic prestack reverse time migration.Geophysics,80(1):S1-S18
Rocha D,Tanushev N,Sava P.2016.Isotropic elastic wavefield imaging using the energy norm.Geophysics,81(4):S207-S219.
Sun C Y,Li Z C.2011.Fundamentals of Seismic Wave Dynamics(in Chinese).Beijing:Petroleum Industry Press.
Sun R,McMechan G A.2001.Scalar reverse-time depth migration of prestack elastic seismic data.Geophysics,66(5):1519-1527.
Sun R,McMechan G A,Lee C S,et al.2006.Prestack scalar reverse-time depth migration of 3Delastic seismic data.Geophysics,71(5):S199-S207.
Xiao X,Leaney W S.2010.Local vertical seismic profiling(VSP)elastic reverse-time migration and migration resolution:Saltflank imaging with transmitted P-to-S waves.Geophysics,75(2):S35-S49.
Xu Z L.1990.Elasticity Mechanics(Book 1)(in Chinese).3rd ed.Beijing:Higher Education Press.
Yan J,Sava P.2008.Isotropic angle-domain elastic reverse-time migration.Geophysics,73(6):S229-S239.
Yoon K,Shin C,Suh S,et al.2003.3Dreverse-time migration using the acoustic wave equation:An experience with the SEG/EAGE data set.The Leading Edge,22(1):38-41.
Yoon K,Marfurt K J.2006.Reverse-time migration using the Poynting vector.Exploration Geophysics,37(1):102-107.
Zhang Y,Zhang H Z,Zhang G Q.2011.A stable TTI reverse time migration and its implementation.Geophysics,76(3):WA3-WA11.
Zhang Z,Liu Y S,Xu T,et al.2013.A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation.Chinese Journal of Geophysics(in Chinese),56(10):3523-3533,doi:10.6038/cjg20131027.
李振春,张华,刘庆敏等.2007.弹性波交错网格高阶有限差分法波场分离数值模拟.石油地球物理勘探,42(5):510-515.
马德堂,朱光明.2003.弹性波波场P波和S波分解的数值模拟.石油地球物理勘探,38(5):482-486.
孙成禹,李振春.2011.地震波动力学基础.北京:石油工业出版社.
徐芝纶.1990.弹性力学-上册.3版.北京:高等教育出版社.
张智,刘有山,徐涛等.2013.弹性波逆时偏移中的稳定激发振幅成像条件.地球物理学报,56(10):3523-3533,doi:10.6038/cjg20131027.
Chang W F,McMechan G A.1986.Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,51(1):67-84.
Chang W F,McMechan G A.1994.3-D elastic prestack,reversetime depth migration.Geophysics,59(4):597-609.
Claerbout J F.1971.Toward a unified theory of reflector mapping.Geophysics,36(3):467-481.
Du Q Z,Zhu Y T,Ba J.2012.Polarity reversal correction for elastic reverse time migration.Geophysics,77(2):S31-S41.
Du Q Z,Gong X F,Zhang M Q,et al.2014.3DPS-wave imaging with elastic reverse-time migration.Geophysics,79(5):S173-S184
Du Q Z,Guo C F,Zhao Q,et al.2017.Vector-based elastic reverse time migration based on scalar imaging condition.Geophysics,82(2):S111-S127
Kaelin B,Guitton A.2006.Imaging condition for reverse time migration.∥76th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2594-2598.
Li Z C,Zhang H,Liu Q M,et al.2007.Numeric simulation of elastic wavefield separation by staggering grid high-order finitedifference algorithm.Oil Geophysical Prospecting(in Chinese),42(5):510-515.
Loewenthal R,Sancho J,Fersht A R.1991.Fluorescence spectrum of barnase:contributions of three tryptophan residues and a histidine-related pH dependence.Biochemistry,30(27):6775-6779.
Ma D T,Zhu G M.2003.Numerical modeling of P-wave and S-wave separation in elastic wavefield.Oil Geophysical Prospecting(in Chinese),38(5):482-486.
Nguyen B D,McMechan G A.2012.Excitation amplitude imaging condition for prestack reverse-time migration.Geophysics,78(1):S37-S46
Nguyen B D,McMechan G A.2014.Five ways to avoid storing source wavefield snapshots in 2Delastic prestack reverse time migration.Geophysics,80(1):S1-S18
Rocha D,Tanushev N,Sava P.2016.Isotropic elastic wavefield imaging using the energy norm.Geophysics,81(4):S207-S219.
Sun C Y,Li Z C.2011.Fundamentals of Seismic Wave Dynamics(in Chinese).Beijing:Petroleum Industry Press.
Sun R,McMechan G A.2001.Scalar reverse-time depth migration of prestack elastic seismic data.Geophysics,66(5):1519-1527.
Sun R,McMechan G A,Lee C S,et al.2006.Prestack scalar reverse-time depth migration of 3Delastic seismic data.Geophysics,71(5):S199-S207.
Xiao X,Leaney W S.2010.Local vertical seismic profiling(VSP)elastic reverse-time migration and migration resolution:Saltflank imaging with transmitted P-to-S waves.Geophysics,75(2):S35-S49.
Xu Z L.1990.Elasticity Mechanics(Book 1)(in Chinese).3rd ed.Beijing:Higher Education Press.
Yan J,Sava P.2008.Isotropic angle-domain elastic reverse-time migration.Geophysics,73(6):S229-S239.
Yoon K,Shin C,Suh S,et al.2003.3Dreverse-time migration using the acoustic wave equation:An experience with the SEG/EAGE data set.The Leading Edge,22(1):38-41.
Yoon K,Marfurt K J.2006.Reverse-time migration using the Poynting vector.Exploration Geophysics,37(1):102-107.
Zhang Y,Zhang H Z,Zhang G Q.2011.A stable TTI reverse time migration and its implementation.Geophysics,76(3):WA3-WA11.
Zhang Z,Liu Y S,Xu T,et al.2013.A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation.Chinese Journal of Geophysics(in Chinese),56(10):3523-3533,doi:10.6038/cjg20131027.
李振春,张华,刘庆敏等.2007.弹性波交错网格高阶有限差分法波场分离数值模拟.石油地球物理勘探,42(5):510-515.
马德堂,朱光明.2003.弹性波波场P波和S波分解的数值模拟.石油地球物理勘探,38(5):482-486.
孙成禹,李振春.2011.地震波动力学基础.北京:石油工业出版社.
徐芝纶.1990.弹性力学-上册.3版.北京:高等教育出版社.
张智,刘有山,徐涛等.2013.弹性波逆时偏移中的稳定激发振幅成像条件.地球物理学报,56(10):3523-3533,doi:10.6038/cjg20131027.