带限局部平面波传播算子与偏移方法
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摘要
地震信号的带限特点限制了高频近似下的射线类算子在地震波模拟和偏移中的应用。本文基于射线理论构建带限信号局部平面波传播算子,兼顾射线类方法具有时空局部性和实现灵活高效的特点,有效进行带限地震波场的模拟和偏移。即分析传统高频射线在速度界面的传播特征,利用带限信号频带与菲涅耳带的关系,构建带限斯奈尔定律进行中心射线传播;在局部平面波假设下,基于带限中心射线做旁轴近似展开,构建带限局部平面波传播算子;在此基础上发展基于该算子的带限射线束偏移方法。数值实验结果表明,带限射线束较传统基于高频近似的射线束具有更强穿透能力,改善射线阴影区照明,从而提高复杂构造区成像质量。
The seismic signal is a kind of band-limited signal,and it limits the application of ray-based operators to seismic wave propagation and migration under the infinite high-frequency approximation.With the framework of conventional ray theory,this paper proposes a band-limited local plane wave propagator.Characterized by local space linearity and implementation flexibility,the propagator can effectively perform band-limited seismic wavefield propagation and migration.Based on the propagation characteristics of high-frequency rays between intervals,the band-limited Snells law is obtained for the central ray propagation with the relationship between the first Fresnel zone and the frequency band of signals.Then,the band-limited local plane wave propagator can be built with paraxial approximation under the local plane wave as-sumption.Finally a band-limited beam migration method is developed.Numerical experiments demonstrate that the band-limited beams have better illumination in ray-shadow areas and are beneficial to improve the imaging resolution in complex structures.
The seismic signal is a kind of band-limited signal,and it limits the application of ray-based operators to seismic wave propagation and migration under the infinite high-frequency approximation.With the framework of conventional ray theory,this paper proposes a band-limited local plane wave propagator.Characterized by local space linearity and implementation flexibility,the propagator can effectively perform band-limited seismic wavefield propagation and migration.Based on the propagation characteristics of high-frequency rays between intervals,the band-limited Snells law is obtained for the central ray propagation with the relationship between the first Fresnel zone and the frequency band of signals.Then,the band-limited local plane wave propagator can be built with paraxial approximation under the local plane wave as-sumption.Finally a band-limited beam migration method is developed.Numerical experiments demonstrate that the band-limited beams have better illumination in ray-shadow areas and are beneficial to improve the imaging resolution in complex structures.
引文
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[2]Woodward M J.Wave-equation tomography.Geophysics,1992,57(1):15-26.
[3]Biondi B.Solving the frequency dependent eikonal equation.SEG Technical Program Expanded Abstracts,1992,11:1315-1319.
[4]Hogan C M,Margrave G F.Ray-tracing and eikonal solutions for low-frequency wavefields.CREWES Research Report,2007.
[5]Foreman T.A Frequency Dependent Ray Theory[D].The University of Texas at Austin,1987.
[6]Protasov M,Gadylshin K.Exact frequency dependent rays on the basis of Helmholtz solver.SEG Technical Program Expanded Abstracts,2015,34:3739-3743.
[7]Lomax A.The wavelength-smoothing method for approximating broad-band wave propagation through complicated velocity structures.Geophysical Journal International,1994,117(2):313-334.
[8]Lomax A,Snieder R.Estimation of finite-frequency waveforms through wavelength-dependent averaging of velocity.Geophysical Journal International,1996,126(2):369-381.
[9]Protasov M I,Yarman C E,Nichols D et al.Frequencydependent ray-tracing through rugose interfaces.SEG Technical Program Expanded Abstracts,2011,30:2992-2996.
[10]Protasov M I,Osypov K S.Frequency dependent ray tracing for irregular boundaries.Seismic Technology,2014,11(3):1-11.
[11]Yarman C E,Cheng X,Osypov K et al.Band-limited ray tracing.Geophysical Prospecting,2013,61(6):1194-1205.
[12]ˇCervenV,Popov M M,Psencik I.Computation of wave fields in inhomogeneous media—Gaussian beam approach.Geophysical Journal International,1982,70(1):109-128.
[13]Hill N R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[14]Hill N R.Prestack Gaussian-beam depth migration.Geophysics,2001,66(4):1240-1250.
[15]Hale D.Migration by the Kirchhoff,slant stack,and Gaussian beam methods.CWP Annual Project Review Meeting,Colorado,1992.
[16]Gray S H.Gaussian beam migration of common-shot records.Geophysics,2005,70(1):953-959.
[17]邓飞,刘超颖,赵波等.高斯射线束正演与偏移.石油地球物理勘探,2009,44(3):265-269.Deng Fei,Liu Chaoying,Zhao Bo et al.Gaussian beams forward simulation and migration.OGP,2009,44(3):265-269.
[18]李振春,岳玉波,郭朝斌等.高斯波束共角度保幅深度偏移.石油地球物理勘探,2010,43(3):360-365.Li Zhenchun,Yue Yubo,Guo Chaobin et al.Gaussian beam common angle preserved-amplitude migration.OGP,2010,45(3):360-365.
[19]Zhu T,Gray S H,Wang D.Prestack Gaussian-beam depth migration in anisotropic media.Geophysics,2007,72(3):S133-S138.
[20]韩建光,王赟,张晓波等.VTI介质高斯束叠前深度偏移.石油地球物理勘探,2015,50(2):267-273.Han Jianguang,Wang Yun,Zhang Xiaobo et al.Gaussian beam prestack depth migration in VTI media.OGP,2015,50(2):267-273.
[21]刘强,张敏,李振春等.各向异性介质共炮域高斯束偏移.石油地球物理勘探,2016,51(5):930-937.Liu Qiang,Zhang Min,Li Zhenchun et al.Commonshot domain Gaussian beam migration in anisotropic media.OGP,51(5):930-937.
[22]代福材,黄建平,李振春等.角度域黏声介质高斯束叠前深度偏移方法.石油地球物理勘探,2017,52(2):283-293.Dai Fucai,Huang Jianping,Li Zhenchun et al.Angle domain prestack Gaussian beam migration for viscoacoustic media.OGP,2017,52(2):283-293.
[23]Hu C S,Stoffa P L.Slowness-driven Gaussian-beam prestack depth migration for low-fold seismic data.Geophysics,2009,74(6):WCA35-WCA45.
[24]Liu J,Palacharla G.Multiarrival Kirchhoff beam migration.Geophysics,2011,76(5):WB109-WB118.
[25]Bube K P,Washbourne J K.Wave tracing:Ray tracing for the propagation of band-limited signals:Part 1—Theory.Geophysics,2008,73(5):VE377-VE384.
[26]Washbourne J K,Bube K P,Carillo P et al.Wave tracing:Ray tracing for the propagation of band-limited signals:Part 2—Applications.Geophysics,2008,73(5):VE385-VE393.
[27]Gray S H,Xie Y,Notfors C et al.Taking apart beam migration.The Leading Edge,2009,28(9):1098-1108.
[28]Elad M.Sparse and Redundant Representations:from Theory to Applications in Signal and Image Processing.Springer Science&Business Media,2010.
[29]Liu S Y,Gu H and Feng B.Characteristic wave imaging in TTI media via compressed sensing.SEG Technical Program Expanded Abstracts,2016,35:4424-4429.
[30]Schneider W A.Integral formulation for migration in two and three dimensions.Geophysics,1978,43(1):49-76.
[31]Popov M M,Semtchenok N M,Popov P M et al.Depth migration by the Gaussian beam summation method.Geophysics,2010,75(2):S81-S93.
[2]Woodward M J.Wave-equation tomography.Geophysics,1992,57(1):15-26.
[3]Biondi B.Solving the frequency dependent eikonal equation.SEG Technical Program Expanded Abstracts,1992,11:1315-1319.
[4]Hogan C M,Margrave G F.Ray-tracing and eikonal solutions for low-frequency wavefields.CREWES Research Report,2007.
[5]Foreman T.A Frequency Dependent Ray Theory[D].The University of Texas at Austin,1987.
[6]Protasov M,Gadylshin K.Exact frequency dependent rays on the basis of Helmholtz solver.SEG Technical Program Expanded Abstracts,2015,34:3739-3743.
[7]Lomax A.The wavelength-smoothing method for approximating broad-band wave propagation through complicated velocity structures.Geophysical Journal International,1994,117(2):313-334.
[8]Lomax A,Snieder R.Estimation of finite-frequency waveforms through wavelength-dependent averaging of velocity.Geophysical Journal International,1996,126(2):369-381.
[9]Protasov M I,Yarman C E,Nichols D et al.Frequencydependent ray-tracing through rugose interfaces.SEG Technical Program Expanded Abstracts,2011,30:2992-2996.
[10]Protasov M I,Osypov K S.Frequency dependent ray tracing for irregular boundaries.Seismic Technology,2014,11(3):1-11.
[11]Yarman C E,Cheng X,Osypov K et al.Band-limited ray tracing.Geophysical Prospecting,2013,61(6):1194-1205.
[12]ˇCervenV,Popov M M,Psencik I.Computation of wave fields in inhomogeneous media—Gaussian beam approach.Geophysical Journal International,1982,70(1):109-128.
[13]Hill N R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[14]Hill N R.Prestack Gaussian-beam depth migration.Geophysics,2001,66(4):1240-1250.
[15]Hale D.Migration by the Kirchhoff,slant stack,and Gaussian beam methods.CWP Annual Project Review Meeting,Colorado,1992.
[16]Gray S H.Gaussian beam migration of common-shot records.Geophysics,2005,70(1):953-959.
[17]邓飞,刘超颖,赵波等.高斯射线束正演与偏移.石油地球物理勘探,2009,44(3):265-269.Deng Fei,Liu Chaoying,Zhao Bo et al.Gaussian beams forward simulation and migration.OGP,2009,44(3):265-269.
[18]李振春,岳玉波,郭朝斌等.高斯波束共角度保幅深度偏移.石油地球物理勘探,2010,43(3):360-365.Li Zhenchun,Yue Yubo,Guo Chaobin et al.Gaussian beam common angle preserved-amplitude migration.OGP,2010,45(3):360-365.
[19]Zhu T,Gray S H,Wang D.Prestack Gaussian-beam depth migration in anisotropic media.Geophysics,2007,72(3):S133-S138.
[20]韩建光,王赟,张晓波等.VTI介质高斯束叠前深度偏移.石油地球物理勘探,2015,50(2):267-273.Han Jianguang,Wang Yun,Zhang Xiaobo et al.Gaussian beam prestack depth migration in VTI media.OGP,2015,50(2):267-273.
[21]刘强,张敏,李振春等.各向异性介质共炮域高斯束偏移.石油地球物理勘探,2016,51(5):930-937.Liu Qiang,Zhang Min,Li Zhenchun et al.Commonshot domain Gaussian beam migration in anisotropic media.OGP,51(5):930-937.
[22]代福材,黄建平,李振春等.角度域黏声介质高斯束叠前深度偏移方法.石油地球物理勘探,2017,52(2):283-293.Dai Fucai,Huang Jianping,Li Zhenchun et al.Angle domain prestack Gaussian beam migration for viscoacoustic media.OGP,2017,52(2):283-293.
[23]Hu C S,Stoffa P L.Slowness-driven Gaussian-beam prestack depth migration for low-fold seismic data.Geophysics,2009,74(6):WCA35-WCA45.
[24]Liu J,Palacharla G.Multiarrival Kirchhoff beam migration.Geophysics,2011,76(5):WB109-WB118.
[25]Bube K P,Washbourne J K.Wave tracing:Ray tracing for the propagation of band-limited signals:Part 1—Theory.Geophysics,2008,73(5):VE377-VE384.
[26]Washbourne J K,Bube K P,Carillo P et al.Wave tracing:Ray tracing for the propagation of band-limited signals:Part 2—Applications.Geophysics,2008,73(5):VE385-VE393.
[27]Gray S H,Xie Y,Notfors C et al.Taking apart beam migration.The Leading Edge,2009,28(9):1098-1108.
[28]Elad M.Sparse and Redundant Representations:from Theory to Applications in Signal and Image Processing.Springer Science&Business Media,2010.
[29]Liu S Y,Gu H and Feng B.Characteristic wave imaging in TTI media via compressed sensing.SEG Technical Program Expanded Abstracts,2016,35:4424-4429.
[30]Schneider W A.Integral formulation for migration in two and three dimensions.Geophysics,1978,43(1):49-76.
[31]Popov M M,Semtchenok N M,Popov P M et al.Depth migration by the Gaussian beam summation method.Geophysics,2010,75(2):S81-S93.