地震反演成像中的Hessian算子研究
详细信息 本馆镜像全文    |  推荐本文 | | 获取馆网全文
摘要
总结了牛顿类地震反演方法中Hessian算子的作用,对其在地震反演成像中的数学物理含义进行了分析.Hessian算子是误差泛函对模型参数的二阶导数,反映了误差泛函对模型变化的二次型特征.分析声波方程下的Hessian算子的格林函数表达形式,发现其表达了整个观测系统和子波频带等因素对地震数据空间到模型空间投影过程的影响.提出了两种分别适用于最小二乘偏移和全波形反演的Hessian算子简化格式.平面波Hessian算子应用于最小二乘偏移能够得到相对保真的成像结果,改善了地震偏移成像的精度.地下偏移距Hessian算子应用于全波形反演能够加快反演迭代的计算效率.最后,对Hessian算子在地震反演成像中的价值进行了讨论和评价.
In this paper,we summarize the influence of Hessian operator in seismic inversion methods and review the mathematical and physical meanings of the Hessian operator in the seismic inversion imaging.Hessian operator is the second derivation of the misfit function to the seismic model parameters.It can be seen by analyzing its Green's function formulation under the acoustic wave approximation that the Hessian reflects the effects of the seismic acquisition system and wavelet frequency band during the projection of information from the data spaces to the model spaces.We propose two pseudo-Hessian forms for the least-squares migration and the full waveform inversion separately.The application of plane-wave Hessian operator can lead to an amplitude-preserved migration result.The sub-offset Hessian can be used to the full waveform inversion to enhance the efficiency of inversion.At last,we discuss and evaluate the Hessian operator in seismic inversion imaging.
引文
[1]Claerbout J F.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
    [2]Tarantola A.Inversion of seismic reflection data in theacoustic approximation.Geophysics,1984,49(8):1259-1266.
    [3]任浩然,王华忠,黄光辉.地震波反演成像方法的理论分析与对比.岩性油气藏,2012,24(5):12-18.Ren H R,Wang H Z,Huang G H.Theoretical analysis andcomparison of seismic wave inversion and imaging methods.Lithologic Reservoirs(in Chinese),2012,24(5):12-18.
    [4]任浩然,王华忠,张立彬.沿射线路径的波动方程延拓吸收与衰减补偿方法.石油物探,2007,46(6):557-561.Ren H R,Wang H Z,Zhang L B.Compensation forabsorption and attenuation using wave equation continuationalong ray path.Geophysical Prospecting for Petroleum(inChinese),2007,46(6):557-561.
    [5]Etgen J,Gray S H,Zhang Y.An overview of depth imagingin exploration geophysics.Geophysics,2009,74(6):WCA5-WCA17.
    [6]Plessix R E,Mulder W A.Frequency-domain finite-difference amplitude-preserving migration.GeophysicsJournal International,2004,157(3):975-987.
    [7]Ren H R,Wu R S,Wang H Z.Wave equation least squareimaging using the local angular Hessian for amplitudecorrection.Geophysical Prospecting,2011,59(4):651-661.
    [8]Ribodetti A,Operto S,Agudelo W,et al.Joint ray+Bornleast-squares migration and simulated annealing optimizationfor target-oriented quantitative seismic imaging.Geophysics,2011,76(2):R23-R42.
    [9]Pratt G,Shin C,Hicks G J.Gauss-Newton and full Newtonmethods in frequency-space seismic waveform inversion.Geophysical Journal International,1998,133(2):341-362.
    [10]Hadamard J.An Essay on the Psychology of Invention in theMathematical Field.Princeton:Princeton University Press,1945.
    [11]陈生昌,曹景忠,马在田.稳定的Born近似叠前深度偏移方法.石油地球物理勘探,2001,36(3):291-296.Chen S C,Cao J Z,Ma Z T.Stable pre-stack depthmigration method with Born approximation.Oil GeophysicalProspecting(in Chinese),2001,36(3):291-296.
    [12]Lailly P.The seismic inverse problem as a sequence of beforestack migrations.//Bednar J B,ed.Conference on InverseScattering:Theory and Application.Philadelphia:Society forIndustrial and Applied Mathematics,1983:206-220.
    [13]Yu J,Hu J,Schuster G T,et al.Prestack migrationdeconvolution.Geophysics,2006,71(2):S53-S62.
    [14]Lecomte I.Resolution and illumination analyses in PSDM:Aray-based approach.The Leading Edge,2008,27(5):650-663.
    [15]Tang Y.Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian.Geophysics,2009,74(6):WCA95-WCA107.
    [16]Bagaini C,Spagnolini U.2-D continuation operators andtheir applications.Geophysics,1996,61(6):1846-1858.
    [17]Formel S.Theory of differential offset continuation.Geophysics,2003,68(2):718-732.
    [18]Stolt R H,Benson A K.Seismic Migration Theory andPractice:Theory and Practice.London:Geophysical Press,1986.
    [19]冯波,王华忠.三维偏移距平面波有限差分偏移叠前时间偏移.地球物理学报,2011,54(11):2916-2925.Feng B,Wang H Z.3Doffset plane-wave finite-differencepre-stack time migration.Chinese J.Geophys.(in Chinese),2011,54(11):2916-2925.
    [20]Sava P C,Fomel S.Angle-domain common-image gathers bywavefield continuation methods.Geophysics,2003,68(3):1065-1074.
    [21]刘守伟,王华忠,程玖兵等.时空移动成像条件及偏移速度分析.地球物理学报,2008,51(6):1883-1891.Liu S W,Wang H Z,Cheng J B,et al.Space-time-shiftimaging condition and migration velocity analysis.Chinese J.Geophys.(in Chinese),2008,51(6):1883-1891.

版权所有:© 2023 中国地质图书馆 中国地质调查局地学文献中心