立体层析反演方法理论分析与应用测试
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摘要
立体层析反演方法是针对传统反射层析数据拾取困难这一问题提出的。该方法重新定义了层析反演的数据分量和模型分量,使得数据的提取不再需要沿着连续的层位进行;除地震波走时之外,炮、检点位置与炮、检点处射线的局部传播方向也被用来约束速度模型,且将模型分量映射到数据分量这一正过程只需要进行初值射线追踪。这些特点都增强了反演的稳定性。根据立体层析反演方法的特点,简化了立体层析反演的数据分量与模型分量,从而减小了反演的规模。考虑到射线扰动理论在射线中心坐标系下实现更简捷,Fréchet导数的计算在该坐标系下进行。通过3个二维理论模型数据反演实验,对简化后的方法进行了测试。实验一在理想无噪声数据中进行,验证了简化后方法的有3效性;实验二在含噪声数据中进行,进一步测试了方法的稳定性以及对噪声的适应能力;实验三以拾取的运动学属性作为反演的数据输入,为下一步将简化方法应用于实际数据反演奠定了基础。
Stereotomography is initially proposed to cope with difficulties associated with a highly interpretive picking in traditional reflection tomography.This method redefines data and model components in tomographic inversion,making the procedure of tracking events along continuous reflection layer unnecessary.In addition to two-way traveltime of seismic waves,the source and receiver positions combined with the local propagation directions of rays in source and receiver points are used to constrain the velocity field.Furthermore,the forward modeling can be completed only by a simple initial value ray tracing to map model component to data component.All this features enhance the robustness of inversion process.This paper simplifies data and model components of stereotomography to reduce the scale of inversion calculation.Considering the compact form of ray perturbation theory in ray centered coordinate,Fréchet derivatives of data to model are computed in this coordinate.Three 2D numerical models tests are presented to validate the proposed algorithm.The first one is demonstrated with ideally noisy free data directly calculated with ray tracing,which verified the validity of the presented simplified method.The second test is conducted with noisy data to certify the robustness and the adaptability to noise of the presented inversion processing.The third test adopts the picked kinematic properties as input data of the inversion,which sets the foundation for practical application of the presented method next step.
Stereotomography is initially proposed to cope with difficulties associated with a highly interpretive picking in traditional reflection tomography.This method redefines data and model components in tomographic inversion,making the procedure of tracking events along continuous reflection layer unnecessary.In addition to two-way traveltime of seismic waves,the source and receiver positions combined with the local propagation directions of rays in source and receiver points are used to constrain the velocity field.Furthermore,the forward modeling can be completed only by a simple initial value ray tracing to map model component to data component.All this features enhance the robustness of inversion process.This paper simplifies data and model components of stereotomography to reduce the scale of inversion calculation.Considering the compact form of ray perturbation theory in ray centered coordinate,Fréchet derivatives of data to model are computed in this coordinate.Three 2D numerical models tests are presented to validate the proposed algorithm.The first one is demonstrated with ideally noisy free data directly calculated with ray tracing,which verified the validity of the presented simplified method.The second test is conducted with noisy data to certify the robustness and the adaptability to noise of the presented inversion processing.The third test adopts the picked kinematic properties as input data of the inversion,which sets the foundation for practical application of the presented method next step.
引文
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[2]Liu Z.An analytical approach to migration velocityanalysis[J].Geophysics,1997,62(4):1238-1249
[3]Jeannot J P,Faye J P.Prestack migration velocities fromfocusing depth analysis[J].Expanded Abstracts of 56thAnnual Internat SEG Mtg,1986,438-440
[4]macKay S,Abma R.Imaging and velocity estimationwith depth-focusing analysis[J].Geophysics,1992,57(12):1608-1622
[5]Bishop T,Bube K,Cutler R,et al.Tomographic de-termination of velocity and depth in laterally varyingmedia[J].Geophysics,1985,50(6):903-923
[6]Farra V,Madariaga R.Seismic waveform modelingin heterogeneous media by ray perturbation theory[J].Journal of Geophysical Research,1987,92(B3):2697-2712
[7]Farra V,Madariaga R.Non-linear reflection tomography[J].Geophysical Journal,1988,95(1):135-147
[8]Yang K,Wang H Z,Ma Z T.An output imagingscheme of the common reflection surface stack[J].Journal of Seismic Exploration,2005,14(3):131-150
[9]杨锴.共反射面元叠加———从输入道观点到输出道观点[D].上海:同济大学,2003Yang K.Common reflection surface stack—from in-put imaging scheme to output imaging scheme[D].Shanghai:TongJi University,2003
[10]Riabinkin L A.Fundamentals of resolving power ofcontrolled directional reception(CDR)of seismicwaves[J].Expanded Abstracts of 61st Annual Inter-nat SEG Mtg,1991,36-60
[11]Sword C.Tomographic determination of interval ve-locities from picked reflection seismic data[J].Ex-panded Abstracts of 56th Annual Internat SEG Mtg,1986,657-660
[12]Duveneck E.Velocity model estimation with data-derived wavefront attributes[J].Geophysics,2004,65(1):265-274
[13]Billette F,Lambare G.Velocity macro-model estima-tion from seismic reflection data by stereotomogra-phy[J].Geophysical Journal International,1998,135:671-690
[14]Billette F,Le Bégat S,Podvin P,et al.Practical as-pects and applications of 2Dstereotomography[J].Geophysics,2003,68(3):1008-1021
[15]Lambare G.Stereotomography[J].Geophysics,2008,73(5):VE25-VE34
[16]de Boor C.A practical guide to splines[M].NewYork:Springer-Verlag,1978:1-390
[17]Bleistein N.Mathematical methods for wave phenomena[M].New York:Academic Press,Inc,1984:1-341
[18]陈忠,朱建伟等.数值计算方法[M].北京:石油工业出版社,2001:257-261Chen Z,Zhu J W.Numerical calculation methods[M].Beijing:Petroleum Industry Press,2001:257-261
[19]Vogel C R.Computational methods for inverse prob-lems[M].Philadelphia:Frontiers in Applied Mathe-matics,2002:1-8
[20]Costa J C,da Silva F J C,Gomes E N S,et al.Regu-larization in slope tomography[J].Geophysics,2008,73(5):VE39-VE47
[21]Spakman W.Iterative strategies of non-linear traveltime tomography using global earthquake data[C]//Iyer H M,Kirahara K.Seismic tomography:theoryand practice.London:Chapman&Hall,1993:190-226
[22]Shaw P R,Orcutt J A.Waveform inversion of seis-mic refraction data and application to young Pacificcrust[J].Geophysical Journal of the Royal Astro-nomical Society,1985,82:375-414
[23]Paige C C,Saunders M A.LSQR:an algorithm forsparse linear equations and sparse least squares[J].ACM Transaction on Mathematical Software,1982,8(1):43-71
[24]Gilbert F,Backus G.Propagator matrices in elasticwave and vibration problems[J].Geophysics,1996,31(2):326-332
[25]Cerveny V.Seismic ray theory[M].New York:Cambridge University Press,2001:99-400
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