基于一阶弹性波方程的能量互相关成像条件
|
摘要
基于地震波场能量构建的能量互相关成像条件,具有易实现、物理意义明确及背向散射压制效果明显等优势.但是,目前构建的能量互相关成像条件仅适用于二阶弹性波方程,难以直接应用于一阶弹性波方程.为此,本文针对一阶弹性波方程,基于能量守恒定理及能量密度,构建以速度-应力为参数的能量范数以表征弹性波场能量,将速度-应力能量范数拓展为能量内积以提取弹性波场反射能量.震源端与检波端的基矢量正方向保持一致的基础上,构建得到可有效压制背向散射的弹性波能量成像条件.数值模拟结果表明:该成像条件可以得到背向散射压制、振幅有效保持的能量成像结果.
The energy cross-correlation imaging condition,which takes the advantages of easy realization and suppressing the backscattering effectively,permits to generate images with definite physical meanings.However,such a condition designed by the second-order elastic wave equation cannot be used directly in the first-order elastic wave equation.To solve this problem,based on the energy conservation theorem and energy density,we construct an energy norm characterized by velocity-stress fields,representing the elastic wavefield energy.As for the source wavefield and the receive wavefield,we extend the velocity-stress energy norm to the energy inner product.Combined with the propagation direction of the forward and backward velocity-stress fields,the energy cross-correlation imaging condition is proposed to attenuate the backscattering.Numerical experiments indicate that this condition allow us to extract the results of reflected wavefield energy without extra computation and to suppress backscattering noise effectively.
The energy cross-correlation imaging condition,which takes the advantages of easy realization and suppressing the backscattering effectively,permits to generate images with definite physical meanings.However,such a condition designed by the second-order elastic wave equation cannot be used directly in the first-order elastic wave equation.To solve this problem,based on the energy conservation theorem and energy density,we construct an energy norm characterized by velocity-stress fields,representing the elastic wavefield energy.As for the source wavefield and the receive wavefield,we extend the velocity-stress energy norm to the energy inner product.Combined with the propagation direction of the forward and backward velocity-stress fields,the energy cross-correlation imaging condition is proposed to attenuate the backscattering.Numerical experiments indicate that this condition allow us to extract the results of reflected wavefield energy without extra computation and to suppress backscattering noise effectively.
引文
Baysal E,Kosloff D,Sherwood J W C.1983.Reverse time migration.Geophysics,48(11):1514-1524.
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.1987.Elastic reverse-time migration.Geophysical Prospecting,52(3):243-256.
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,Guo C F,Zhao Q,et al.2017.Vector-based elastic reverse time migration based on scalar imaging condition.Geophysics,82(2):S111-S127.
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.
Du S T.1996.Seismic Waves Dynamics Theory and Methods.Dongying:University of Petroleum Press.
Hu D S.1989.Elastic Wave Dynamics.Beijing:Geological Publishing House.
Levander A R.1988.Fourth-order finite-difference P-SV seismograms.Geophysics,53(11):1425-1436.
Liu F Q,Morton S A,Leveille J P,et al.2007.Reverse-time migration using one-way wavefield imaging condition.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2170-2174.
Loewenthal D,Stoffa P L,Faria E L.1987.Suppressing the unwanted reflections of the full wave equation.Geophysics,52(7):1007-1012.
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.
McMechan G A.1983.Migration by extrapolation of time-dependent boundary values.Geophysical Prospecting,31(3):413-420.
Nguyen B D,McMechan G A.2012.Excitation amplitude imaging condition for prestack reverse-time migration.Geophysics,78(1):S37-S46.
Rocha D,Tanushev N,Sava P.2016a.Acoustic wavefield imaging using the energy norm.Geophysics,81(4):S151-S163.
Rocha D,Tanushev N,Sava P.2016b.Isotropic elastic wavefield imaging using the energy norm.Geophysics,81(4):S207-S219.
Rocha D,Tanushev N,Sava P.2017.Anisotropic elastic wavefield imaging using the energy norm.Geophysics,82(3):S225-S234.
Sava P.2007.Stereographic imaging condition for wave-equation migration.Geophysics,72(6):A87-A91.
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.
Tanushev N M,Engquist B,Tsai R.2009.Gaussian beam decomposition of high frequency wave fields.Journal of Computational Physics,228(23):8856-8871.
Whitmore N D.1983.Iterative depth migration by backward time propagation.∥53rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,382-385.
Xu Z L.2006.Elasticity.Beijing:Higher Education Press.
Zhang X Y,Du Q Z,Zhang S K.2018.The self-decoupled crosscorrelation imaging condition based on energy density.Chinese Journal of Geophysics(in Chinese),61(12):4965-4975,doi:10.6038/cjg2018L0687.
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.
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.
杜世通.1996.地震波动力学.东营:石油大学出版社.
胡德绥.1989.弹性波动力学.北京:地质出版社.
徐芝纶.2006.弹性力学.4版.北京:高等教育出版社.
张晓语,杜启振,张树奎.2018.基于能量密度的自解耦互相关成像条件.地球物理学报,61(12):4965-4975,doi:10.6038/cjg2018L0687.
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.1987.Elastic reverse-time migration.Geophysical Prospecting,52(3):243-256.
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,Guo C F,Zhao Q,et al.2017.Vector-based elastic reverse time migration based on scalar imaging condition.Geophysics,82(2):S111-S127.
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.
Du S T.1996.Seismic Waves Dynamics Theory and Methods.Dongying:University of Petroleum Press.
Hu D S.1989.Elastic Wave Dynamics.Beijing:Geological Publishing House.
Levander A R.1988.Fourth-order finite-difference P-SV seismograms.Geophysics,53(11):1425-1436.
Liu F Q,Morton S A,Leveille J P,et al.2007.Reverse-time migration using one-way wavefield imaging condition.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2170-2174.
Loewenthal D,Stoffa P L,Faria E L.1987.Suppressing the unwanted reflections of the full wave equation.Geophysics,52(7):1007-1012.
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.
McMechan G A.1983.Migration by extrapolation of time-dependent boundary values.Geophysical Prospecting,31(3):413-420.
Nguyen B D,McMechan G A.2012.Excitation amplitude imaging condition for prestack reverse-time migration.Geophysics,78(1):S37-S46.
Rocha D,Tanushev N,Sava P.2016a.Acoustic wavefield imaging using the energy norm.Geophysics,81(4):S151-S163.
Rocha D,Tanushev N,Sava P.2016b.Isotropic elastic wavefield imaging using the energy norm.Geophysics,81(4):S207-S219.
Rocha D,Tanushev N,Sava P.2017.Anisotropic elastic wavefield imaging using the energy norm.Geophysics,82(3):S225-S234.
Sava P.2007.Stereographic imaging condition for wave-equation migration.Geophysics,72(6):A87-A91.
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.
Tanushev N M,Engquist B,Tsai R.2009.Gaussian beam decomposition of high frequency wave fields.Journal of Computational Physics,228(23):8856-8871.
Whitmore N D.1983.Iterative depth migration by backward time propagation.∥53rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,382-385.
Xu Z L.2006.Elasticity.Beijing:Higher Education Press.
Zhang X Y,Du Q Z,Zhang S K.2018.The self-decoupled crosscorrelation imaging condition based on energy density.Chinese Journal of Geophysics(in Chinese),61(12):4965-4975,doi:10.6038/cjg2018L0687.
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.
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.
杜世通.1996.地震波动力学.东营:石油大学出版社.
胡德绥.1989.弹性波动力学.北京:地质出版社.
徐芝纶.2006.弹性力学.4版.北京:高等教育出版社.
张晓语,杜启振,张树奎.2018.基于能量密度的自解耦互相关成像条件.地球物理学报,61(12):4965-4975,doi:10.6038/cjg2018L0687.
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.