二维弹性随机介质中的波场特征
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摘要
本文通过波动方程交错网格有限差分正演 ,模拟了地震波在二维弹性随机介质中的传播及其自激自收时间记录 ;在层状随机介质模型中将声波和弹性波的波场作了比较 ,结果显示两者的差别很大。为研究二维弹性随机介质模型中的波场特征 ,我们将理论记录剖面分成三个不同的时间区段 ,并在三个不同的时间区段上分别计算剖面的横向中心频率、纵向中心频率、波场能量相对值三个统计特征量。这样 ,对应每一个弹性随机介质模型 ,由计算得到 9个不同的波场特征量。通过研究介质模型发生变化时对应的波场特征量的变化特点 ,最终得出了随机介质的自相关长度、粗糙度等模型特征与记录剖面的扰动频率及能量等波场特征密切相关的结论 :在随机介质中 ,波场的统计特征量强烈地依赖于介质的统计特性 ,如自相关长度和粗糙度等 ;随机介质模型对应的地震记录存在有散射波及地震波尾等复杂波场特征。
Through the staggered-grid finite-difference f- orward modeling of wave equation,the paper modeled the propagation of seismic wave in 2-D elastic random medium and self-excited and self-received time-records;comparison of acoustic wave with elastic wave is made in layered random medium model,which showed that both have big difference.In order to study the wavefield characters in 2-D elastic random medium model,we divided the theoretical records into three different time segments and computed three statistical characterististic values of section separately in three different time segments:laterally central frequency,vertically central frequency and relative value of wavefield energy.Then,corresponding to each elastic random medium model,9 different wavefield-characterized values are obtained by computation.Finally,through studying the changed characters corresponding to characteristic values of wawefield when medium models are changed;the conclusion that closely related the model characters (self-correlation length and roughness of random medium etc.) to wavefield characters (disturbed frequency and energy of recorded section etc.): the statistic characteristic values of wavefield strongly rely on statistic characters of medium,such as correlation length and roughness etc.;the seismic records corresponding to random medium models are characterized by complex wavefield such as scattered wave and seismic wave tail.
Through the staggered-grid finite-difference f- orward modeling of wave equation,the paper modeled the propagation of seismic wave in 2-D elastic random medium and self-excited and self-received time-records;comparison of acoustic wave with elastic wave is made in layered random medium model,which showed that both have big difference.In order to study the wavefield characters in 2-D elastic random medium model,we divided the theoretical records into three different time segments and computed three statistical characterististic values of section separately in three different time segments:laterally central frequency,vertically central frequency and relative value of wavefield energy.Then,corresponding to each elastic random medium model,9 different wavefield-characterized values are obtained by computation.Finally,through studying the changed characters corresponding to characteristic values of wawefield when medium models are changed;the conclusion that closely related the model characters (self-correlation length and roughness of random medium etc.) to wavefield characters (disturbed frequency and energy of recorded section etc.): the statistic characteristic values of wavefield strongly rely on statistic characters of medium,such as correlation length and roughness etc.;the seismic records corresponding to random medium models are characterized by complex wavefield such as scattered wave and seismic wave tail.
引文
[1] KornM.Seism ic wave in random media.Journal ofAppliedGeophysics,1993,29:247～269
[2] IkelleL et al.2-D random media with ellipsoidalautocorrelation function.Geophysics,1993,58(9):1359～1372
[3] 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
[4] 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,2001,36(5):546～552
[5] BirchF.The velocity of compressional waves in rocksto10 kb.J GeophysRes,1961,66:2199～2224
[6] VirieuxJ.SH- wave propagation in heterogeneousmedia:Velocity- stress finite difference method.Geophysics,1984,49(11):1933～1957
[7] VirieuxJ.P-SV wave propagation in heterogeneousmedia:Velocity stress finite difference method.Geophysics,1986,51:889～901
[8] IgelH et al.Accuracy of staggered3-D finite- dif-ference grids for anisotropic wave propagation.ExpandedAbstracts of the62 ndSEG Mtg,1992,1244～1246
[9] L evanderA.Fourth- order finite differenceP-SVseismograms.Geophysics,1988,53:1425～1436
[10] 董良国等.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
[11] 董良国等.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
[12] 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
[13] CerjanC et al.A nonreflecting boundary conditionfor discrete acoustic wave and elastic- wave equation.Geophysics,1985,50:705～708
[14] RothM andKornM.Single- scattering theory versusnumerical modeling in two- dim ensional randommedia.GeophysJ Int,1993,112:124～140
[15] MatsunamiK.L aboratory tests of excitation andattenuation of coda waves using2-D models ofscattering m edia.PhysEarth planetInter,1991,67:36～4
[2] IkelleL et al.2-D random media with ellipsoidalautocorrelation function.Geophysics,1993,58(9):1359～1372
[3] 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
[4] 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,2001,36(5):546～552
[5] BirchF.The velocity of compressional waves in rocksto10 kb.J GeophysRes,1961,66:2199～2224
[6] VirieuxJ.SH- wave propagation in heterogeneousmedia:Velocity- stress finite difference method.Geophysics,1984,49(11):1933～1957
[7] VirieuxJ.P-SV wave propagation in heterogeneousmedia:Velocity stress finite difference method.Geophysics,1986,51:889～901
[8] IgelH et al.Accuracy of staggered3-D finite- dif-ference grids for anisotropic wave propagation.ExpandedAbstracts of the62 ndSEG Mtg,1992,1244～1246
[9] L evanderA.Fourth- order finite differenceP-SVseismograms.Geophysics,1988,53:1425～1436
[10] 董良国等.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
[11] 董良国等.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
[12] 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
[13] CerjanC et al.A nonreflecting boundary conditionfor discrete acoustic wave and elastic- wave equation.Geophysics,1985,50:705～708
[14] RothM andKornM.Single- scattering theory versusnumerical modeling in two- dim ensional randommedia.GeophysJ Int,1993,112:124～140
[15] MatsunamiK.L aboratory tests of excitation andattenuation of coda waves using2-D models ofscattering m edia.PhysEarth planetInter,1991,67:36～4
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