二维黏弹性随机介质中的波场特征
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摘要
在高分辨率地震数据中常常作为“噪声”处理的不相干扰动,其实部分是源于介质在小尺度上的非均匀性。随机介质模型及其相关理论,使人们有可能在统计的意义下反演出介质在小尺度上的非均匀特征(如空间自相关函数、平均异常尺度、标准差等)。本文通过波动方程的交错网格有限差分正演,模拟了地震波在二维黏弹性随机介质中的传播及其自激自收时间记录。研究了黏弹性随机介质中的波场特征以及黏弹性随机介质中的最大振幅波至旅行时、振幅衰减等特征,并得出了若干结论。通过正演模拟表明黏弹性随机介质模型对应的地震记录中有散射波、振幅衰减、旅行时扰动、地震波尾等复杂的波场特征;波的散射形式强烈依赖于介质的统计特性,如自相关函数、方差和吸收系数等;介质的自相关长度的变化对波前振幅的影响很小。
University of Geologic Science,Wuhan City,Hubei Province,430074,China Abstract:Non coherent disturbances are often treated as “noise”in high resolution seismic data,which actually partially resulted from inhomogeneity of medium in a small scale,that made one can make inversion of inhomogeneity of medium in small scale in statistical meaning (for instance,spatial autocorrelation function,average anomalous scale and standard deviation etc. ).By using staggered finite difference grads forward modeling for wave equation,the paper modeled seismic propagation in 2 D viscoelastic random medium and self shooting and self receiving records;studied characteristics of wavefield,arrival travel time in maximum amplitude and amplitude attenuation in viscoelastic random medium and gained some conclusions.It is showed by forward modeling that the complex characteristics of wavefield such as scattering wave,amplitude attenuation,traveltime disturbance and seismic tails etc. existed in seismic records associated with viscoelastic random medium model;the scattering form of wave strongly depends on statistical characters of medium such as autocorrelation,variance and absorption coefficient;the variation of autocorrelation length in medium has a little influence on amplitude of wavefront.
University of Geologic Science,Wuhan City,Hubei Province,430074,China Abstract:Non coherent disturbances are often treated as “noise”in high resolution seismic data,which actually partially resulted from inhomogeneity of medium in a small scale,that made one can make inversion of inhomogeneity of medium in small scale in statistical meaning (for instance,spatial autocorrelation function,average anomalous scale and standard deviation etc. ).By using staggered finite difference grads forward modeling for wave equation,the paper modeled seismic propagation in 2 D viscoelastic random medium and self shooting and self receiving records;studied characteristics of wavefield,arrival travel time in maximum amplitude and amplitude attenuation in viscoelastic random medium and gained some conclusions.It is showed by forward modeling that the complex characteristics of wavefield such as scattering wave,amplitude attenuation,traveltime disturbance and seismic tails etc. existed in seismic records associated with viscoelastic random medium model;the scattering form of wave strongly depends on statistical characters of medium such as autocorrelation,variance and absorption coefficient;the variation of autocorrelation length in medium has a little influence on amplitude of wavefront.
引文
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[10]侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究.地球物理学报,1995,38(2):243～251
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[14]姚姚,奚先.随机介质模型正演及其地震波场分析.石油物探,2002(1):31～36
[15]CerjanC,KosloffD,KosloffR andReshefM.Anonreflecting boundary condition for discreteacoustic wave and elastic- wave equation.Geophysics,1985,50:705～708
[16]RothM andKornM.Single- scattering theory versusnumerical modeling in two- dim ensional randommedia.GeophysJ Int,1993,112:124～140
[17]Matsunam iK.L aboratory tests of excitation andattenuation of coda waves using2-D m odels ofscattering m edia.PhysEarth planetInter,1991,67:36～47
[2]IkelleL ,YungS andDaubeF.2-D random m ediawith ellipsoidal autocorrelation function.Geophysics,1993,58(9):1359～1372
[3]MadariagaR.Dynamics of an expanding circular fau-lt.BSSA,1976,66(3):639～666
[4]VirieuxJ.SH- wave propagation in heterogeneous m e-dia:Velocity- stress finite difference m ethod.Geophysics,1984,49(11):1933～1957
[5]VirieuxJ.P-SV wave propagation in heterogeneousm edia:Velocity stress finite difference m ethod.Geophysics,1986,51:889～901
[6]IgelH,RiolletB andMoraP.Accuracy of staggered3-D finite- difference grids for anisotropic wavepropagation.ExpandedAbstracts of the62 ndSEGMtg.1992,1244～1246
[7]L evanderA.Fourth- order finite differenceP-SVseism ogram s.Geophysics,1988,53:1425～1436
[8]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报2000,43(6):856～864
[9]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411～419
[10]侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究.地球物理学报,1995,38(2):243～251
[11]BirchF.The velocity of compressional waves in rocksto10 kb.J Geophys.1961,66:2199～2224
[12]奚先,姚姚.随机介质模型的模拟与混合型随机介质.地球科学—中国地质大学学报,2002,27(1):67～71
[13]奚先,姚姚.二维随机介质及波动方程正演模拟.石油地球物理勘探,2001(5):546～552
[14]姚姚,奚先.随机介质模型正演及其地震波场分析.石油物探,2002(1):31～36
[15]CerjanC,KosloffD,KosloffR andReshefM.Anonreflecting boundary condition for discreteacoustic wave and elastic- wave equation.Geophysics,1985,50:705～708
[16]RothM andKornM.Single- scattering theory versusnumerical modeling in two- dim ensional randommedia.GeophysJ Int,1993,112:124～140
[17]Matsunam iK.L aboratory tests of excitation andattenuation of coda waves using2-D m odels ofscattering m edia.PhysEarth planetInter,1991,67:36～47
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