射线中心坐标系中傍轴单程波方程数值模拟与偏移成像
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摘要
目前地震波叠前深度偏移成像方法主要有基于波动方程高频近似解的积分类方法和基于微分波动方程有限差分解或混合域解法两大类。高斯束方法是介于两者之间的描述波传播与成像的方法,其存在问题是在描述射线中心坐标系中的波传播过程中引入的近似过多,除了高频近似外,垂直于射线路径任一点的平面内波场的振幅仅仅简单地用射线路径上该点振幅的高斯衰减获得,不能描述射线束内复杂波现象。为此,推导出射线中心坐标系下傍轴单程波方程,在射线束内利用傍轴单程波方程实现波场的传播,以精确描述局部波场。该方法不仅结合了射线的灵活性,还较好地描述局部射线束内波场。与简单射线理论和复杂波动理论相比,该方法在灵活性和精确性之间取折中,能更方便地解决复杂构造成像和层析速度估计问题。数值试验结果证明了该方法的正确性。
Prestack depth migration methods include two categories.One is kirchhoff method based on high-frequency approximate solution of wave equation,the other is differential method based on the finite difference solution or mixed-domain solution of wave equation.Gaussian beam method is between them and is used for wave propagation chracterization and imaging.The problem of Gaussian beam method is that too many approximations are introduced when characterizing the wave propagation in the ray-centered coordinates.In addition to high-frequency approximation,the amplitudes of wave field whose plane is perpendicular to any point of the ray path is merely derived from the amplitude Gauss attenuation of that point,which is too simple to characterize the complex wave phenomena.Therefore,we derived the one-way wave equation in ray-centered coordinates and used the equation to extrapolate wave field in ray beam to accurately characterize local wave field.The method preserves the flexibility of ray method and the accuracy of wave equation method to describe the wave field within certain ray beams.Compared with simple ray theory and complex wave equation theory,the method makes a compromise between the flexibility and accuracy.It can be used to complex subsurface structure imaging and tomography velocity estimation more conveniently.Numerical examples demonstrate the correctness of the method.
Prestack depth migration methods include two categories.One is kirchhoff method based on high-frequency approximate solution of wave equation,the other is differential method based on the finite difference solution or mixed-domain solution of wave equation.Gaussian beam method is between them and is used for wave propagation chracterization and imaging.The problem of Gaussian beam method is that too many approximations are introduced when characterizing the wave propagation in the ray-centered coordinates.In addition to high-frequency approximation,the amplitudes of wave field whose plane is perpendicular to any point of the ray path is merely derived from the amplitude Gauss attenuation of that point,which is too simple to characterize the complex wave phenomena.Therefore,we derived the one-way wave equation in ray-centered coordinates and used the equation to extrapolate wave field in ray beam to accurately characterize local wave field.The method preserves the flexibility of ray method and the accuracy of wave equation method to describe the wave field within certain ray beams.Compared with simple ray theory and complex wave equation theory,the method makes a compromise between the flexibility and accuracy.It can be used to complex subsurface structure imaging and tomography velocity estimation more conveniently.Numerical examples demonstrate the correctness of the method.
引文
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[11]郭朝斌,李振春,岳玉波,等.高斯束成像技术及其应用[J].石油物探,2011,50(1):38-44,58Guo C B,Li Z C,Yue Y B,et al.Gaussian beam mi-gration and its application[J].Geophysical Prospec-ting for Petroleum,2011,50(1):38-44,58
[12]岳玉波,李振春,钱忠平,等.复杂地表条件下保幅高斯束偏移[J].地球物理学报,2012,55(4):1376-1383Yue Y B,Li Z C,Qian Z P,et al.Amplitude-pre-served Gaussian beam migration under complex top-ographic conditions[J].Chinese Journal Geophysics,2012,55(4):1376-1383
[13]Brandsberg-Dahl S,Etgen J.Beam-wave migration[J].Expanded Abstracts of 65th EAGE Annual Con-ference,2003,977-980
[14]Claerbout J F.Toward a unified theory of reflectormapping[J].Geophysics,1971,36(3):467-481
[15]Sava P,Fomel S.Riemannian wavefield extrapolation[J].Geophysics,2005,70(3):T45-T56
[2]Cerveny V,Psencik I.Gaussian beams and paraxialray approximation in three-dimensional elastic inho-mogeneous media[J].Journal of Geophysics,1983,53(1):1-15
[3]Cerveny V.Gaussian beam synthetic seismograms[J].Journal of Geophysics,1985,58(1):44-72
[4]Popov M M.A new method of computation of wavefields using Gaussian beams[J].Wave Motion,1982,4(1):85-97
[5]Felsen L B.Complex-source-point solution of thefield equations and their relation to the propagationand scattering of Gaussian beams[J].SymposiaMatematica,1976,18(1):39-56
[6]Hill N R.Gaussian beam migration[J].Geophysics,1990,55(11):1416-1428
[7]Hill N R.Prestack Gaussian-beam depth migration[J].Geophysics,2001,66(4):1240-1250
[8]Gray S H.Gaussian beam migration of common-shotrecords[J].Geophysics,2005,70(4):S71-S77
[9]Gray S H,Bleistein N.True-amplitude Gaussian-beam migration[J].Geophysics,2009,74(2):S11-S23
[10]Zhu T,Gray S H,Wang D,et al.Prestack Gaussian-beam depth migration in anisotropic media[J].Geo-physics,2007,72(3):S133-S138
[11]郭朝斌,李振春,岳玉波,等.高斯束成像技术及其应用[J].石油物探,2011,50(1):38-44,58Guo C B,Li Z C,Yue Y B,et al.Gaussian beam mi-gration and its application[J].Geophysical Prospec-ting for Petroleum,2011,50(1):38-44,58
[12]岳玉波,李振春,钱忠平,等.复杂地表条件下保幅高斯束偏移[J].地球物理学报,2012,55(4):1376-1383Yue Y B,Li Z C,Qian Z P,et al.Amplitude-pre-served Gaussian beam migration under complex top-ographic conditions[J].Chinese Journal Geophysics,2012,55(4):1376-1383
[13]Brandsberg-Dahl S,Etgen J.Beam-wave migration[J].Expanded Abstracts of 65th EAGE Annual Con-ference,2003,977-980
[14]Claerbout J F.Toward a unified theory of reflectormapping[J].Geophysics,1971,36(3):467-481
[15]Sava P,Fomel S.Riemannian wavefield extrapolation[J].Geophysics,2005,70(3):T45-T56
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