地震散射波的高精度数值模拟与振幅分析
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摘要
随着地震勘探要求和技术的不断提高,散射波地震勘探方法逐渐引起人们的重视,尤其在构造复杂地区的高精度勘探中,散射波理论具有广泛的应用前景.本文在讨论了现阶段几种散射波数值模拟方法的利弊后,设计了一种基于微扰论的FK域积分法,在散射场的二次震源和空间能量衰减处理两方面做了改进,其计算精度和效率均得到了提高.此外,采用该算法针对散射波动力学进行了正演模拟试算,从扰动介质空间分布和扰动量两个角度定量地分析了散射波振幅动力学方面的特征.在此基础上得到了五个经验常数,并给出了对应的计算公式和物理意义,通过这五个常数可以划分散射波不同形态的动力学特征.
The scattered wave seismic method is now well appreciated and developed with the advancement of technology and requirement of seismic survey.Particularly in high-precision prospecting of complicated structure area,it has broad application prospect.Different current numerical modeling of scattered wave has their advantages and disadvantages.This paper has designed a method of Integration in FK domain based on perturbation theory to solve scattered field,which could obtain scattered field by integration in FK domain after get the total wave field.It has improved the data source of scattered field and the processing of space energy.The computational accuracy and efficiency of scattered field have got better.In addition,based on the algorithm a forward modeling test is carried out for the dynamics of scattered field.The features of kinetics of scattered wave amplitude are analyzed quantitatively from the perspectives of space distribution of perturbing body and disturbance quantity.Based on this,it obtains five experiential constants and provides the corresponding formula and physical significance.Scattered wave could be classified into different dynamical characteristics by the constants.
The scattered wave seismic method is now well appreciated and developed with the advancement of technology and requirement of seismic survey.Particularly in high-precision prospecting of complicated structure area,it has broad application prospect.Different current numerical modeling of scattered wave has their advantages and disadvantages.This paper has designed a method of Integration in FK domain based on perturbation theory to solve scattered field,which could obtain scattered field by integration in FK domain after get the total wave field.It has improved the data source of scattered field and the processing of space energy.The computational accuracy and efficiency of scattered field have got better.In addition,based on the algorithm a forward modeling test is carried out for the dynamics of scattered field.The features of kinetics of scattered wave amplitude are analyzed quantitatively from the perspectives of space distribution of perturbing body and disturbance quantity.Based on this,it obtains five experiential constants and provides the corresponding formula and physical significance.Scattered wave could be classified into different dynamical characteristics by the constants.
引文
[1]尹军杰,刘学伟,李文慧.地震波散射理论及应用研究综述.地球物理学进展,2005,20(1):123-134.Yin J J,Liu X W,Li W H.The view of seismic wavescattering theory and its applications.Progress in Geophysics(in Chinese),2005,20(1):123-134.
[2]吴如山,[美]安艺敬一.地震波的散射与衰减.李裕澈,卢寿德等译.北京:地震出版社,1993.Wu R S,Aki K.Scattering and Attenuation of SeismicWaves(in Chinese).Translated by Li Y C,Lu S D,et al.Beijing:Seismological Press,1993.
[3]Hudson J A,Knopoff L.Predicting the overall properties ofcomposite materials with small-scale inclusions or cracks.Pure and Applied Geophysics,1989,131(4):551-576.
[4]Tournat V,Pagneux V,Lafarge D,et al.Multiplescattering of acoustic waves and porous absorbing media.Physical Review E,2004,70(2):1-10.
[5]van Wijk K,Komatitsch D,Scales J A,et al.Analysis ofstrong scattering at the micro-scale.J.Acoust.Soc.Am.,2004,115(3):1006-1011.
[6]贾豫葛,李小凡,张美根等.地震波散射研究的若干重要进展.地球物理学进展,2005,20(4):939-944.Jia Y G,Li X F,Zhang M G,et al.Some important progressin research upon seismic wave scattering.Progress inGeophysics(in Chinese),2005,20(4):939-944.
[7]高伟,王宁.基于背向散射脉冲传播时间统计特性的随机界面参数反演研究.地球物理学报,2008,51(1):260-265.Gao W,Wang L.Inversion of rough surface parametersbased on travel-time statistics of backscattered pulses.Chinese J.Geophys.(in Chinese),2008,51(1):260-265.
[8]Wu R S,Huang L J,Xie X B.Backscattered wavecalculation using the De wolf approximation and a phase-screen propagator:Expanded Abstracts of the TechnicalProgram.SEG′65th Annual Meeting,1995:1293-1296.
[9]李振春,王清振.地震波衰减机理及能量补偿研究综述.地球物理学进展,2007,22(4):1147-1152.Li Z C,Wang Q Z.A review of research on mechanism ofseismic attenuation and energy compensation.Progress inGeophysics(in Chinese),2007,22(4):1147-1152.
[10]刘洪,袁江华,勾永峰等.地震逆散射波场和算子的谱分解.地球物理学报,2007,50(1):240-247.Liu H,Yuan J H,Gou Y F,et al.Spectral factorization ofwavefield and operator in seismic inverse scattering.ChineseJ.Geophys.(in Chinese),2007,50(1):240-247.
[11]陶智勇.弹性波逆散射微扰论.地球物理学报,2005,48(4):918-923.Tao Z Y.Elastic wave inverse scattering perturbationtheory.Chinese J.Geophys.(in Chinese),2005,48(4):918-923.
[12]丁科,宋守根,谢忠球.逆散射理论的发展及应用前景.地球物理学进展,2005,20(3):661-666.Ding K,Song S G,Xie Z Q.Development and futureapplication of inverse scattering theory.Progress inGeophys.(in Chinese),2005,20(3):661-666.
[13]高伟,王宁.基于背向散射脉冲传播时间统计特性的随机界面参数反演研究.地球物理学报,2008,51(1):260-265.Gao W,Wang N.Inversion of rough surface parametersbased on travel-time statistics of backscattered pulses.Chinese J.Geophys.(in Chinese),2008,51(1):260-265.
[14]Wu R S,Aki K.Elastic wave scattering by a random mediumand the small scale inhomogeneities in the lithosphere.Journal of Geophysical Research,1985,90(B12):10261-10273.
[15]符力耘,杨慧珠,牟永光.非均匀介质散射问题的体积分方程数值解法.力学学报,1998,30(4):488-494.Fu L Y,Yang H J,Mu Y G.Volume integral equationmethod for scattering problems of inhomogeneous media.Journal of Theoretical and Applied Mechanics(in Chinese),1998,30(4):488-494.
[16]孙明,林君.金属矿地震散射波场的数值模拟研究.地质与勘探,2001,37(4):68-70.Sun M,Lin J.Study of seismic scattering wave fieldnumerical modelfor metallic ore exploration.Geology andProspecting(in Chinese),2001,37(4):68-70.
[17]田丽花.地震波散射场正演数值模拟.北京:中国地质大学(北京),2007.Tian L H.Seismic Wave Numerical Value Forward Modelingof the Scattered Field(in Chinese).Beijing:China Universityof Geosciences(Beijing),2007.
[18]秦雪霏.地震波多次散射波场属性分析.长春:吉林大学,2007.Qin X F.The Characters Analysis about the Multiply Scatterof Seismic Wave(in Chinese).Changchun:Jilin University,2007.
[19]郭继亮.随机介质散射波场数值模拟与特征分析.西安:长安大学,2009.Guo J L.The Numerical Simulation of Scattering in RandomMedia and the Analysis of the Wavefield(in Chinese).Xi′an:Chang′an University,2009.
[20]刘铁华.地震散射波理论与数值模拟.西安:长安大学,2010.Liu T H.The Theory and Numerical Simulation of Scattering(in Chinese).Xi′an:Chang′an University,2010.
[2]吴如山,[美]安艺敬一.地震波的散射与衰减.李裕澈,卢寿德等译.北京:地震出版社,1993.Wu R S,Aki K.Scattering and Attenuation of SeismicWaves(in Chinese).Translated by Li Y C,Lu S D,et al.Beijing:Seismological Press,1993.
[3]Hudson J A,Knopoff L.Predicting the overall properties ofcomposite materials with small-scale inclusions or cracks.Pure and Applied Geophysics,1989,131(4):551-576.
[4]Tournat V,Pagneux V,Lafarge D,et al.Multiplescattering of acoustic waves and porous absorbing media.Physical Review E,2004,70(2):1-10.
[5]van Wijk K,Komatitsch D,Scales J A,et al.Analysis ofstrong scattering at the micro-scale.J.Acoust.Soc.Am.,2004,115(3):1006-1011.
[6]贾豫葛,李小凡,张美根等.地震波散射研究的若干重要进展.地球物理学进展,2005,20(4):939-944.Jia Y G,Li X F,Zhang M G,et al.Some important progressin research upon seismic wave scattering.Progress inGeophysics(in Chinese),2005,20(4):939-944.
[7]高伟,王宁.基于背向散射脉冲传播时间统计特性的随机界面参数反演研究.地球物理学报,2008,51(1):260-265.Gao W,Wang L.Inversion of rough surface parametersbased on travel-time statistics of backscattered pulses.Chinese J.Geophys.(in Chinese),2008,51(1):260-265.
[8]Wu R S,Huang L J,Xie X B.Backscattered wavecalculation using the De wolf approximation and a phase-screen propagator:Expanded Abstracts of the TechnicalProgram.SEG′65th Annual Meeting,1995:1293-1296.
[9]李振春,王清振.地震波衰减机理及能量补偿研究综述.地球物理学进展,2007,22(4):1147-1152.Li Z C,Wang Q Z.A review of research on mechanism ofseismic attenuation and energy compensation.Progress inGeophysics(in Chinese),2007,22(4):1147-1152.
[10]刘洪,袁江华,勾永峰等.地震逆散射波场和算子的谱分解.地球物理学报,2007,50(1):240-247.Liu H,Yuan J H,Gou Y F,et al.Spectral factorization ofwavefield and operator in seismic inverse scattering.ChineseJ.Geophys.(in Chinese),2007,50(1):240-247.
[11]陶智勇.弹性波逆散射微扰论.地球物理学报,2005,48(4):918-923.Tao Z Y.Elastic wave inverse scattering perturbationtheory.Chinese J.Geophys.(in Chinese),2005,48(4):918-923.
[12]丁科,宋守根,谢忠球.逆散射理论的发展及应用前景.地球物理学进展,2005,20(3):661-666.Ding K,Song S G,Xie Z Q.Development and futureapplication of inverse scattering theory.Progress inGeophys.(in Chinese),2005,20(3):661-666.
[13]高伟,王宁.基于背向散射脉冲传播时间统计特性的随机界面参数反演研究.地球物理学报,2008,51(1):260-265.Gao W,Wang N.Inversion of rough surface parametersbased on travel-time statistics of backscattered pulses.Chinese J.Geophys.(in Chinese),2008,51(1):260-265.
[14]Wu R S,Aki K.Elastic wave scattering by a random mediumand the small scale inhomogeneities in the lithosphere.Journal of Geophysical Research,1985,90(B12):10261-10273.
[15]符力耘,杨慧珠,牟永光.非均匀介质散射问题的体积分方程数值解法.力学学报,1998,30(4):488-494.Fu L Y,Yang H J,Mu Y G.Volume integral equationmethod for scattering problems of inhomogeneous media.Journal of Theoretical and Applied Mechanics(in Chinese),1998,30(4):488-494.
[16]孙明,林君.金属矿地震散射波场的数值模拟研究.地质与勘探,2001,37(4):68-70.Sun M,Lin J.Study of seismic scattering wave fieldnumerical modelfor metallic ore exploration.Geology andProspecting(in Chinese),2001,37(4):68-70.
[17]田丽花.地震波散射场正演数值模拟.北京:中国地质大学(北京),2007.Tian L H.Seismic Wave Numerical Value Forward Modelingof the Scattered Field(in Chinese).Beijing:China Universityof Geosciences(Beijing),2007.
[18]秦雪霏.地震波多次散射波场属性分析.长春:吉林大学,2007.Qin X F.The Characters Analysis about the Multiply Scatterof Seismic Wave(in Chinese).Changchun:Jilin University,2007.
[19]郭继亮.随机介质散射波场数值模拟与特征分析.西安:长安大学,2009.Guo J L.The Numerical Simulation of Scattering in RandomMedia and the Analysis of the Wavefield(in Chinese).Xi′an:Chang′an University,2009.
[20]刘铁华.地震散射波理论与数值模拟.西安:长安大学,2010.Liu T H.The Theory and Numerical Simulation of Scattering(in Chinese).Xi′an:Chang′an University,2010.
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