弹性各向同性介质一次散射波场高斯束Born正演
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摘要
本文提出了一种弹性波一次散射波场的正演方法——弹性波高斯束Born正演.该方法以线性散射理论为基础,通过Born近似建立起地下散射点处不同波型的反射率同弹性波主分量波场之间的数据映射关系,利用高斯束所包含的走时、振幅和极性信息进行不同波型的局部平面波的合成,进而通过逆倾斜叠加将所合成的局部平面波转化为时空域的多分量地震记录.该方法不但保持了射线类方法高效的优点,还具备了处理多次走时波场的能力,从而保证了复杂构造的波场模拟的精度.文中两个数值模型的应用效果表明,本文所提出的弹性波高斯束Born正演算法具有近似于波动方程有限差分法的波场模拟精度以及高得多的计算效率.
We present in this paper a Gaussian beam Born modeling method for simulating singlescattering waves in elastic isotropic medium.Based on the linearized single scattering theory,we first construct the linear data mapping between multi-mode subsurface reflectivities and principal components of elastic waves,then compose multi-mode local plane-waves using the traveltimes,amplitudes and polarizations of Gaussian beams,and finally obtain the simulated multi-component data by transforming the composed local plane-waves to time-space domain.The proposed method not only keeps high efficiency of ray-based methods,but also is capable of dealing with multiarrivals,and thus achieves accurate wavefield simulation in complex media.Trials on two synthetic models demonstrate that,compared with finite-difference modeling,this method can simulate the first order scattering waves in complex media with similar accuracy and much higher efficiency.
We present in this paper a Gaussian beam Born modeling method for simulating singlescattering waves in elastic isotropic medium.Based on the linearized single scattering theory,we first construct the linear data mapping between multi-mode subsurface reflectivities and principal components of elastic waves,then compose multi-mode local plane-waves using the traveltimes,amplitudes and polarizations of Gaussian beams,and finally obtain the simulated multi-component data by transforming the composed local plane-waves to time-space domain.The proposed method not only keeps high efficiency of ray-based methods,but also is capable of dealing with multiarrivals,and thus achieves accurate wavefield simulation in complex media.Trials on two synthetic models demonstrate that,compared with finite-difference modeling,this method can simulate the first order scattering waves in complex media with similar accuracy and much higher efficiency.
引文
Aki K,Richards P G.2002.Quantitative Seismology.2nd ed.Sausalito,CA:University Science Books.
Bai M,Chen X H,Wu J,et al.2016.Q-compensated migration by Gaussian beam summation method.Journal of Geophysics and Engineering,13(1):35-48.
Beylkin G,Burridge R.1990.Linearized inverse scattering problems in acoustics and elasticity.Wave Motion,12(1):15-52.
Cerveny V.1983.Synthetic body wave seismograms for laterally varying layered structures by the Gaussian beam method.Geophysical Journal International,73(2):389-426.
Cerveny V,Coppoli A D M.1992.Ray-Born synthetic seismograms for complex structures containing scatterers.Journal of Seismic Exploration,1:191-206.
Cerveny V.2005.Seismic Ray Theory.Cambridge,UK:Cambridge University Press.
Chapman C.2004.Fundamentals of Seismic Wave Propagation.Cambridge,UK:Cambridge University Press.
Gao Z H,Sun J G,Sun X,et al.2017.A fast algorithm for depth migration by the Gaussian beam summation method.Journal of Geophysics and Engineering,14(1):173-183.
Gibson R L Jr,Toks9z M N,Batini F.1993.Ray-Born modelling of fracture-zone reflections in the Larderello geothermal field.Geophysical Journal International,114(1):81-90.
Goertz A.2002.True-Amplitude Multicomponent Migration of Elastic Wavefields.Logos Verlag Berlin.
Gray S H,Bleistein N.2009.True-amplitude Gaussian-beam migration.Geophysics,74(2):S11-S23.
Hill N R.2001.Prestack Gaussian-beam depth migration.Geophysics,66(4):1240-1250.
Huang X G,Sun H,Sun J G.2016.Born modeling for heterogeneous media using the Gaussian beam summation based Green′s function.Journal of Applied Geophysics,131:191-201.
Jackson G M,Mason I M,Lee D.1991.Multicomponent commonreceiver gather migration of single-level walk-away seismic profiles.Geophysical Prospecting,39(8):1015-1029.
Lüth S,Buske R,Giese R,et al.2005.Fresnel volume migration of multicomponent data.Geophysics,70(6):S121-S129.
Minakov A,Keers H,Kolyukhin D,et al.2017.Acoustic waveform inversion for ocean turbulence.Journal of Physical Oceanography,47(6):1473-1491.
Moser T J.2012.Review of ray-Born forward modeling for migration and diffraction analysis.Studia Geophysica et Geodaetica,56(2):411-432.
Sachl L.2013.Validation of 3Dsynthetic seismograms based on the ray-Born approximation.Studia Geophysica et Geodaetica,57(1):84-102.
Schleicher J,Tygel M,Hubral P.2007.Seismic True-Amplitude Imaging.SEG Geophysical Developments Series No.12.SEG.
Stolt R H,Weglein A B.2012.Seismic Imaging and Inversion:Volume 1:Application of Linear Inverse Theory.Cambridge:Cambridge University Press.
Takahashi T.1995.Prestack migration using arrival angle information.Geophysics,60(1):154-163.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266.
Tengesdal H C B.2013.Ray-Born modelling and full waveform inversion[Master′s thesis].Bergen,Norway:The University of Bergen.
Yuan M L,Huang J P,Liao W Y,et al.2017.Least-squares
Gaussian beam migration.Journal of Geophysics and Engineering,14(1):184-196.
Yue Y B.2011.Study on Gaussian beam migration in complex medium[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum.
Yue Y B,Li Z C,Qian Z P,et al.2012.Amplitude-preserved Gaussian beam migration under complex topographic conditions.Chinese Journal of Geophysics(in Chinese),55(4):1376-1383,doi:10.6038/j.issn.0001-5733.2012.04.033.
Yue Y B,Qian Z P,Zhang X D,et al.2019.Gaussian beam based Born modeling method for single-scattering waves in acoustic medium.Chinese Journal of Geophysics(in Chinese),62(2):648-656,doi:10.6038/cjg2019M0367.
岳玉波.2011.复杂介质高斯束偏移成像方法研究[博士论文].青岛:中国石油大学.
岳玉波,李振春,钱忠平等.2012.复杂地表条件下保幅高斯束偏移.地球物理学报,55(4):1376-1383,doi:10.6038/j.issn.0001-5733.2012.04.033.
岳玉波,钱忠平,张旭东等.2019.声波介质一次散射波场高斯束Born正演.地球物理学报,62(2):648-656,doi:10.6038/cjg2019M0367.
Bai M,Chen X H,Wu J,et al.2016.Q-compensated migration by Gaussian beam summation method.Journal of Geophysics and Engineering,13(1):35-48.
Beylkin G,Burridge R.1990.Linearized inverse scattering problems in acoustics and elasticity.Wave Motion,12(1):15-52.
Cerveny V.1983.Synthetic body wave seismograms for laterally varying layered structures by the Gaussian beam method.Geophysical Journal International,73(2):389-426.
Cerveny V,Coppoli A D M.1992.Ray-Born synthetic seismograms for complex structures containing scatterers.Journal of Seismic Exploration,1:191-206.
Cerveny V.2005.Seismic Ray Theory.Cambridge,UK:Cambridge University Press.
Chapman C.2004.Fundamentals of Seismic Wave Propagation.Cambridge,UK:Cambridge University Press.
Gao Z H,Sun J G,Sun X,et al.2017.A fast algorithm for depth migration by the Gaussian beam summation method.Journal of Geophysics and Engineering,14(1):173-183.
Gibson R L Jr,Toks9z M N,Batini F.1993.Ray-Born modelling of fracture-zone reflections in the Larderello geothermal field.Geophysical Journal International,114(1):81-90.
Goertz A.2002.True-Amplitude Multicomponent Migration of Elastic Wavefields.Logos Verlag Berlin.
Gray S H,Bleistein N.2009.True-amplitude Gaussian-beam migration.Geophysics,74(2):S11-S23.
Hill N R.2001.Prestack Gaussian-beam depth migration.Geophysics,66(4):1240-1250.
Huang X G,Sun H,Sun J G.2016.Born modeling for heterogeneous media using the Gaussian beam summation based Green′s function.Journal of Applied Geophysics,131:191-201.
Jackson G M,Mason I M,Lee D.1991.Multicomponent commonreceiver gather migration of single-level walk-away seismic profiles.Geophysical Prospecting,39(8):1015-1029.
Lüth S,Buske R,Giese R,et al.2005.Fresnel volume migration of multicomponent data.Geophysics,70(6):S121-S129.
Minakov A,Keers H,Kolyukhin D,et al.2017.Acoustic waveform inversion for ocean turbulence.Journal of Physical Oceanography,47(6):1473-1491.
Moser T J.2012.Review of ray-Born forward modeling for migration and diffraction analysis.Studia Geophysica et Geodaetica,56(2):411-432.
Sachl L.2013.Validation of 3Dsynthetic seismograms based on the ray-Born approximation.Studia Geophysica et Geodaetica,57(1):84-102.
Schleicher J,Tygel M,Hubral P.2007.Seismic True-Amplitude Imaging.SEG Geophysical Developments Series No.12.SEG.
Stolt R H,Weglein A B.2012.Seismic Imaging and Inversion:Volume 1:Application of Linear Inverse Theory.Cambridge:Cambridge University Press.
Takahashi T.1995.Prestack migration using arrival angle information.Geophysics,60(1):154-163.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266.
Tengesdal H C B.2013.Ray-Born modelling and full waveform inversion[Master′s thesis].Bergen,Norway:The University of Bergen.
Yuan M L,Huang J P,Liao W Y,et al.2017.Least-squares
Gaussian beam migration.Journal of Geophysics and Engineering,14(1):184-196.
Yue Y B.2011.Study on Gaussian beam migration in complex medium[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum.
Yue Y B,Li Z C,Qian Z P,et al.2012.Amplitude-preserved Gaussian beam migration under complex topographic conditions.Chinese Journal of Geophysics(in Chinese),55(4):1376-1383,doi:10.6038/j.issn.0001-5733.2012.04.033.
Yue Y B,Qian Z P,Zhang X D,et al.2019.Gaussian beam based Born modeling method for single-scattering waves in acoustic medium.Chinese Journal of Geophysics(in Chinese),62(2):648-656,doi:10.6038/cjg2019M0367.
岳玉波.2011.复杂介质高斯束偏移成像方法研究[博士论文].青岛:中国石油大学.
岳玉波,李振春,钱忠平等.2012.复杂地表条件下保幅高斯束偏移.地球物理学报,55(4):1376-1383,doi:10.6038/j.issn.0001-5733.2012.04.033.
岳玉波,钱忠平,张旭东等.2019.声波介质一次散射波场高斯束Born正演.地球物理学报,62(2):648-656,doi:10.6038/cjg2019M0367.
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