基于高斯束的初至波菲涅尔体地震层析成像
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摘要
在中心射线路径作为唯一已知条件的前提下,利用动力学射线追踪可以方便地实现射线路径上格林函数的计算,但傍轴格林函数则难以计算。高斯束是动力学射线追踪的一个重要应用。在高频假设前提下,本文将高斯束作为源点产生的格林函数,进而实现菲涅尔体地震层析成像中核函数的快速计算,最后应用此方法进行菲涅尔体走时地震层析成像的理论模型试验。与波动方程菲涅尔体走时地震层析成像反演结果的对比表明,在高频假设前提下,基于动力学射线追踪进行菲涅尔体地震层析成像反演是可行的。
When only the center raypath is known,dynamic raytracing can be easily used to calculate the Green's function of the points on the raypath,but hard for those outside the raypath.Gaussian beam is one of the important applications of dynamic raytracing.Under high-frequency assumption,the Gaussian beam is treated as the Green's function in this paper,through which the sensitivity kernel in Fresnel volume tomography(FVT) can be calculated efficiently.Finally,FVT based on this method is performed on a synthetic data.The comparison of the FVT results with wave equation method indicates that under high-frequency assumption FVT realized by dynamic raytracing can be used in practice.
When only the center raypath is known,dynamic raytracing can be easily used to calculate the Green's function of the points on the raypath,but hard for those outside the raypath.Gaussian beam is one of the important applications of dynamic raytracing.Under high-frequency assumption,the Gaussian beam is treated as the Green's function in this paper,through which the sensitivity kernel in Fresnel volume tomography(FVT) can be calculated efficiently.Finally,FVT based on this method is performed on a synthetic data.The comparison of the FVT results with wave equation method indicates that under high-frequency assumption FVT realized by dynamic raytracing can be used in practice.
引文
[1]刘玉柱,董良国,李培明等.初至波菲涅尔体地震层析成像.地球物理学报,2009,52(9):2310～2320Liu Yuzhu,Dong Liangguo,Li Peiming et al.Fres-nel volume tomography based on the first arrival ofthe seismic wave.Chinese Journal Geophysics,2009,52(9):2310～2320
[2]Pratt R G.Frequency-domain elastic wave modeling byfinite differences:A tool for crosshole seismic imaging(short note).Geophysics,1990,55(5):626～632
[3]Pratt R G.Gauss-Newton and full Newton methodsin frequency-space seismic waveform inversion.Geo-physical Journal International,1998,133(2):341～362
[4]Pratt R G.Seismic waveform inversion in the fre-quency domain,Part 1:Theory and verification in aphysical scale model.Geophysics,1999,64(3):888～901
[5]Jo Churl-Hyun,Changsoo Shin,Jung Hee Suh.Anoptimal 9-point finite-difference frequency-space 2-Dscalar wave extrapolator.Geophysics,1996,61(2):529～537
[6]Shin Changsoo.A frequency-space 2-D scalar waveextrapolator using extended 25-point finite-differenceoperator.Geophysics,1998,63(1):289～296
[7]Weber M.Computation of body-wave seismograms inabsorbing 2-D media using the Gaussion beam meth-od:Comparison with exact methods.GeophysicalJournal International,1988,92(1):9～24
[8]Vidale J E,Heidi Houston.Rapid calculation of seismicamplitudes.Geophysics,1990,55(11):1504～1507
[9]ervenV.Seismic Ray Theory.Cambridge Univer-sity Press,2001
[10]Bishop T N,Bube K P,Cutler R T et al.Tomo-graphic determination of velocity and depth in lateralvarying media.Geophysics,1985,50(6):903～923
[11]Marquering H,Nolet G,Dahlen F A.Three-dimen-sional waveform sensitivity kernels.GeophysicalJournal International,1998,132(3):521～534
[12]Marquering H,Dahlen F A,Nolet G.Three-dimen-sional sensitivity kernels for finite-frequency travel-times:the banana-doughnut paradox.GeophysicalJournal International,1999,137(3):805～815
[13]Woodward M J.Wave-equation tomography.Geo-physics,1992,57(1):15～26
[14]Spetzler G,Snieder R.The effect of small-scale he-terogeneity on the arrival time of waves.GeophysicalJournal International,2001,145(3):786～796
[15]Spetzler G,Snieder R.The fresnel volume and trans-mitted waves.Geophysics,2004,69(3):653～663
[16]Dahlen F A,Hung S H,Nolet G.Fréchet kernelsfor finite-frequency traveltimes-I.Theory.Geophysi-cal Journal International,2000,141(1):157～174
[17]Dahlen F A.Finite-frequency sensitivity kernels forboundary topography perturbations.GeophysicalJournal International,2005,162(2):525～540
[18]Hung S H,Dahlen F A,Nolet G.Wavefront heal-ing:a banana-doughnut perspective.GeophysicalJournal International,2001,146(2):289～312
[19]Zhang Z G,Shen Y,Zhao L.Finite-frequency sensi-tivity kernels for head waves.Geophysical JournalInternational,2007,171(2):847～856
[20]Liu Yuzhu,Dong Liangguo,Wang Yuwei et al.Sen-sitivity kernels for seismic Fresnel volume tomo-graphy.Geophysics,2009,74(5):U35～U46
[21]Popov M M,Psencik I.Computation of ray ampli-tudes in inhomogeneous media with cured interfaces.Studia Geoph et Geod,1978,22(3):v248～258
[22]ervenV,Soares J E P.Fresnel volume ray trac-ing.Geophysics,1992,57(7):902～915
[23]刘玉柱,董良国.初至波层析影响因素分析.石油地球物理勘探,2007,42(5):544～553Liu Yuzhu,Dong Liangguo.Analysis of the factorsof the first arrival tomography in the inversion of nearsurface velocity structure.OGP,2007,42(5):544～553
[24]刘玉柱,董良国,夏建军.初至波走时层析成像中的正则化方法.石油地球物理勘探,2007,42(6):682～685,698Liu Yuzhu,Dong Liangguo,Xia Jianjun.Regulariza-tion methods in first arrival tomography.OGP,2007,42(6):682～685,698
[2]Pratt R G.Frequency-domain elastic wave modeling byfinite differences:A tool for crosshole seismic imaging(short note).Geophysics,1990,55(5):626～632
[3]Pratt R G.Gauss-Newton and full Newton methodsin frequency-space seismic waveform inversion.Geo-physical Journal International,1998,133(2):341～362
[4]Pratt R G.Seismic waveform inversion in the fre-quency domain,Part 1:Theory and verification in aphysical scale model.Geophysics,1999,64(3):888～901
[5]Jo Churl-Hyun,Changsoo Shin,Jung Hee Suh.Anoptimal 9-point finite-difference frequency-space 2-Dscalar wave extrapolator.Geophysics,1996,61(2):529～537
[6]Shin Changsoo.A frequency-space 2-D scalar waveextrapolator using extended 25-point finite-differenceoperator.Geophysics,1998,63(1):289～296
[7]Weber M.Computation of body-wave seismograms inabsorbing 2-D media using the Gaussion beam meth-od:Comparison with exact methods.GeophysicalJournal International,1988,92(1):9～24
[8]Vidale J E,Heidi Houston.Rapid calculation of seismicamplitudes.Geophysics,1990,55(11):1504～1507
[9]ervenV.Seismic Ray Theory.Cambridge Univer-sity Press,2001
[10]Bishop T N,Bube K P,Cutler R T et al.Tomo-graphic determination of velocity and depth in lateralvarying media.Geophysics,1985,50(6):903～923
[11]Marquering H,Nolet G,Dahlen F A.Three-dimen-sional waveform sensitivity kernels.GeophysicalJournal International,1998,132(3):521～534
[12]Marquering H,Dahlen F A,Nolet G.Three-dimen-sional sensitivity kernels for finite-frequency travel-times:the banana-doughnut paradox.GeophysicalJournal International,1999,137(3):805～815
[13]Woodward M J.Wave-equation tomography.Geo-physics,1992,57(1):15～26
[14]Spetzler G,Snieder R.The effect of small-scale he-terogeneity on the arrival time of waves.GeophysicalJournal International,2001,145(3):786～796
[15]Spetzler G,Snieder R.The fresnel volume and trans-mitted waves.Geophysics,2004,69(3):653～663
[16]Dahlen F A,Hung S H,Nolet G.Fréchet kernelsfor finite-frequency traveltimes-I.Theory.Geophysi-cal Journal International,2000,141(1):157～174
[17]Dahlen F A.Finite-frequency sensitivity kernels forboundary topography perturbations.GeophysicalJournal International,2005,162(2):525～540
[18]Hung S H,Dahlen F A,Nolet G.Wavefront heal-ing:a banana-doughnut perspective.GeophysicalJournal International,2001,146(2):289～312
[19]Zhang Z G,Shen Y,Zhao L.Finite-frequency sensi-tivity kernels for head waves.Geophysical JournalInternational,2007,171(2):847～856
[20]Liu Yuzhu,Dong Liangguo,Wang Yuwei et al.Sen-sitivity kernels for seismic Fresnel volume tomo-graphy.Geophysics,2009,74(5):U35～U46
[21]Popov M M,Psencik I.Computation of ray ampli-tudes in inhomogeneous media with cured interfaces.Studia Geoph et Geod,1978,22(3):v248～258
[22]ervenV,Soares J E P.Fresnel volume ray trac-ing.Geophysics,1992,57(7):902～915
[23]刘玉柱,董良国.初至波层析影响因素分析.石油地球物理勘探,2007,42(5):544～553Liu Yuzhu,Dong Liangguo.Analysis of the factorsof the first arrival tomography in the inversion of nearsurface velocity structure.OGP,2007,42(5):544～553
[24]刘玉柱,董良国,夏建军.初至波走时层析成像中的正则化方法.石油地球物理勘探,2007,42(6):682～685,698Liu Yuzhu,Dong Liangguo,Xia Jianjun.Regulariza-tion methods in first arrival tomography.OGP,2007,42(6):682～685,698
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