声波介质一次散射波场高斯束Born正演
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摘要
Born正演是一种常用的地震波场正演模拟方法,也是线性化地震反演的理论基础.在实际应用时,Born正演通常结合常规的地震射线方法进行实现.为了克服常规地震射线方法的弊端,并且保证地震波场的模拟精度和计算效率,本文提出了一种基于高斯束的一阶散射波场Born正演方法.该方法分为两个环节:首先,我们利用高斯束的走时和振幅信息将地下散射点处的反射率映射为地表束中心位置处的局部平面波;然后,我们利用逆倾斜叠加将局部平面波转化为接收点处的时空域散射波场.在具体的实施过程中,我们提出一种以wavelet-bank方式实现的局部平面波合成方法,同现有的算法相比,可以在保持计算精度的同时,大大减少计算时间;此外,我们还利用最速下降法优化了高斯束的迭代循环过程,进一步提高了Born正演的计算效率.两个模型的应用效果证明,本文所提出的高斯束Born正演方法可以精确、高效的实现声波介质一次散射波场的正演模拟,为三维大规模地震波场的正演问题提供了一种切实可行的实现方案.
Born approximation is a commonly used simulation method for seismic reflection waves as well as the theoretical basis of linearized seismic inversion.It is usually implemented with the conventional zeroth-order ray method.In order to overcome the shortcomings of the ray method and ensure the accuracy and efficiency of the simulation processing,we present here a Gaussian beam based Born modeling method for single-scattering waves.First,we map the subsurface reflectivity to local plane-waves at the sparsely sampled beam center locations using the calculated Gaussian beams.Then,we transform the local plane-waves to the simulated scattering wavefields using inverse slant stacking.In the actual implementations,we present a wavelet-bank approach to calculate the local plane-waves in time domain,which significantly reduce computational costcompared with the existing methods.Meanwhile,we use steepest-descent method to reduce the computational loops over Gaussian beams so as to further ensure the efficiency.Trials on two synthetic models demonstrate that our proposed method can accurately and efficiently simulate the first order reflection waves in complex media and provides a feasible way to deal with the large scale,3 Dseismic forward and inverse problems.
Born approximation is a commonly used simulation method for seismic reflection waves as well as the theoretical basis of linearized seismic inversion.It is usually implemented with the conventional zeroth-order ray method.In order to overcome the shortcomings of the ray method and ensure the accuracy and efficiency of the simulation processing,we present here a Gaussian beam based Born modeling method for single-scattering waves.First,we map the subsurface reflectivity to local plane-waves at the sparsely sampled beam center locations using the calculated Gaussian beams.Then,we transform the local plane-waves to the simulated scattering wavefields using inverse slant stacking.In the actual implementations,we present a wavelet-bank approach to calculate the local plane-waves in time domain,which significantly reduce computational costcompared with the existing methods.Meanwhile,we use steepest-descent method to reduce the computational loops over Gaussian beams so as to further ensure the efficiency.Trials on two synthetic models demonstrate that our proposed method can accurately and efficiently simulate the first order reflection waves in complex media and provides a feasible way to deal with the large scale,3 Dseismic forward and inverse problems.
引文
Beydoun W B,Mendes M.1989.Elastic ray-Born L2-migration/inversion.Geophysical Journal International,97(1):151-160.
Beylkin G,Burridege R.1990.Linearized inverse scattering problems in acoustics and elasticity.Wave Motion,12(1):15-52.
Bleistein N.1987.On the imaging of reflectors in the earth.Geophysics,52(7):931-942.
Bleistein N,Cohen J K,Stockwell J W Jr.2001.Mathematics of Multidimensional Seismic Imaging,Migration,and Inversion.New York:Springer.
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.2005.Seismic Ray Theory.Cambridge,UK:Cambridge University Press.
Chapman C.2004.Fundamentals of Seismic Wave Propagation.Cambridge,UK:Cambridge University Press.
Cohen J K,Hagin F G,Bleistein N.1986.Three-dimensional Born inversion with an arbitrary reference.Geophysics,51(8):1552-1558.
Gray S H.2005.Gaussian beam migration of common-shot records.Geophysics,70(4):S71-S77.
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.
Hudson J A,Heritage J R.1981.The use of the Born approximation in seismic scattering problems.Geophysical Journal International,66(1):221-240.
Jaramillo H H,Bleistein N.1999.The link of Kirchhoff migration
and demigration to Kirchhoff and Born modeling.Geophysics,64(6):1793-1805.
Li H,Feng B,Wang H Z.2012.A new wave field modeling method by using Gaussian Packets.Geophysical Prospecting for Petroleum(in Chinese),51(4):327-337.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266.
Tessmer E.2000.Seismic finite-difference modeling with spatially varying time steps.Geophysics,65(4):1290-1293.
Virieux J,Calandra H,Plessix R.2011.A review of the spectral,pseudo-spectral,finite-difference and finite-element modelling techniques for geophysical imaging.Geophysical Prospecting,59(5):794-813.
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.
李辉,冯波,王华忠.2012.波场模拟的高斯波包叠加方法.石油物探,51(4):327-337.
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.
Beylkin G,Burridege R.1990.Linearized inverse scattering problems in acoustics and elasticity.Wave Motion,12(1):15-52.
Bleistein N.1987.On the imaging of reflectors in the earth.Geophysics,52(7):931-942.
Bleistein N,Cohen J K,Stockwell J W Jr.2001.Mathematics of Multidimensional Seismic Imaging,Migration,and Inversion.New York:Springer.
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.2005.Seismic Ray Theory.Cambridge,UK:Cambridge University Press.
Chapman C.2004.Fundamentals of Seismic Wave Propagation.Cambridge,UK:Cambridge University Press.
Cohen J K,Hagin F G,Bleistein N.1986.Three-dimensional Born inversion with an arbitrary reference.Geophysics,51(8):1552-1558.
Gray S H.2005.Gaussian beam migration of common-shot records.Geophysics,70(4):S71-S77.
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.
Hudson J A,Heritage J R.1981.The use of the Born approximation in seismic scattering problems.Geophysical Journal International,66(1):221-240.
Jaramillo H H,Bleistein N.1999.The link of Kirchhoff migration
and demigration to Kirchhoff and Born modeling.Geophysics,64(6):1793-1805.
Li H,Feng B,Wang H Z.2012.A new wave field modeling method by using Gaussian Packets.Geophysical Prospecting for Petroleum(in Chinese),51(4):327-337.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266.
Tessmer E.2000.Seismic finite-difference modeling with spatially varying time steps.Geophysics,65(4):1290-1293.
Virieux J,Calandra H,Plessix R.2011.A review of the spectral,pseudo-spectral,finite-difference and finite-element modelling techniques for geophysical imaging.Geophysical Prospecting,59(5):794-813.
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.
李辉,冯波,王华忠.2012.波场模拟的高斯波包叠加方法.石油物探,51(4):327-337.
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.
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