基于广义逆算法的层状弹性介质中瑞雷面波反演
|
摘要
层状介质中的瑞雷面波不同于纵波和横波,它具有明显的频散特性,正是这一特性使得它能够在勘探及检测领域得到广泛的应用和研究。利用瑞雷波信息反演层状介质的性质和状态,是地震勘探、岩土工程领域关注的研究课题。反演问题是地球物理学的核心问题,它主要指根据观测到的数据,借助于正问题的数学模型,来求解地下介质的几何分布或物性参数分布。本文通过介绍和比较现有的线性及非线性反演方法,提出将广义逆算法反演应用于面波反演中的思想,通过计算和分析证实了该方法是可行且有效的。
本文首先分别对各向同性介质、均匀半空间介质和层状介质进行了讨论,分析了瑞雷面波的频散特性。然后针对几种目前反演面波频散曲线常用的反演方法:最小二乘法、遗传算法、模拟退火法等,比较了这些方法的优缺点及反演的效果。引入一种线性反演方法——广义逆算法,采用标量传递算法对瑞雷波频散函数进行数值计算模拟得到频散曲线,作为反演的基础,再进行编程实现瑞雷波反演模拟,并与最小二乘法反演比较该方法具有收敛速度快且稳定的优点。最后采用τ-p变换法对面波提纯和常规Fourier变换来提取频散曲线,利用本文方法对衡邵高速公路的瞬态面波勘探的数据反演了路基地下速度结构,完整地实现了在实际勘探中面波反演的流程。
总的来说,瑞雷波的反演研究是面波勘探领域中很重要的研究课题,反演解释方法的选择影响到地下介质性质及参数的准确性,也就直接关系到面波勘探的精度。由于地下介质的复杂性,可进一步发展复杂地层介质的反演方法的研究。
Be different from the P wave and S wave in the layered medium, the Rayleigh surface wave (R wave) has the characteristic of frequency-dispersion, and is precisely this characteristic enables it to be able to the application of engineering geological exploration and engineering quality testing. It is a topic in the fields of the seismic exploration and geo-technical engineer to inverse the properties of the stratified in half space by using the Rayleigh waves. Inversion problem is the hard core in the geophysics, which is recurring to forward modeling and using the observational data to inverting the strata structure and the velocity parameter. Through the introduction and quite existing linear and the misalignment inversion method, this article proposes that the generalized counter algorithm inversion will apply in the surface wave inversion the thought.
This article first separately discusses the isotropic medium, the even half space medium and the stratified medium, and analyzes the Rayleigh surface wave's frequency dispersion characteristic. Then in view of several present inversion surface wave frequency dispersion curve commonly used inversion method: Least squares method (LSM), genetic algorithm (GA), simulation annealing (SA) and so on, compared with these method good and bad points and inversion effect. This paperintroduces one kind of linear inversion method------generalized counteralgorithm, used the scalar transmission algorithm to carry on the numerical calculus simulation to obtain the frequency dispersion curve., and carried on the programming to come true the Rayleigh surface wave inversion simulation. Compares with the least squares method inversion, this method has the convergence rate quick and the stable merit. The paper uses theτ-p transformation to purify surface wave depuration and the conventional Fourier transformation to pick up the frequency dispersion curve, does inversion about roadbed underground speed structure by the Heng-Shao highway's Transient surface wave exploration data, and actualizes the surface wave inversion flow completely in the actual exploration.
Generally speaking, the Rayleigh surface wave's inversion research is in the surface wave exploration domain the very important research subject. The inversion explained that the method choice affects the accuracy of the underground medium nature and the parameter, and also directly has a relationship with precision of surface wave exploration. As a result of the underground medium's complexity, we can develop the complex stratum medium inversion method research further.
本文首先分别对各向同性介质、均匀半空间介质和层状介质进行了讨论,分析了瑞雷面波的频散特性。然后针对几种目前反演面波频散曲线常用的反演方法:最小二乘法、遗传算法、模拟退火法等,比较了这些方法的优缺点及反演的效果。引入一种线性反演方法——广义逆算法,采用标量传递算法对瑞雷波频散函数进行数值计算模拟得到频散曲线,作为反演的基础,再进行编程实现瑞雷波反演模拟,并与最小二乘法反演比较该方法具有收敛速度快且稳定的优点。最后采用τ-p变换法对面波提纯和常规Fourier变换来提取频散曲线,利用本文方法对衡邵高速公路的瞬态面波勘探的数据反演了路基地下速度结构,完整地实现了在实际勘探中面波反演的流程。
总的来说,瑞雷波的反演研究是面波勘探领域中很重要的研究课题,反演解释方法的选择影响到地下介质性质及参数的准确性,也就直接关系到面波勘探的精度。由于地下介质的复杂性,可进一步发展复杂地层介质的反演方法的研究。
Be different from the P wave and S wave in the layered medium, the Rayleigh surface wave (R wave) has the characteristic of frequency-dispersion, and is precisely this characteristic enables it to be able to the application of engineering geological exploration and engineering quality testing. It is a topic in the fields of the seismic exploration and geo-technical engineer to inverse the properties of the stratified in half space by using the Rayleigh waves. Inversion problem is the hard core in the geophysics, which is recurring to forward modeling and using the observational data to inverting the strata structure and the velocity parameter. Through the introduction and quite existing linear and the misalignment inversion method, this article proposes that the generalized counter algorithm inversion will apply in the surface wave inversion the thought.
This article first separately discusses the isotropic medium, the even half space medium and the stratified medium, and analyzes the Rayleigh surface wave's frequency dispersion characteristic. Then in view of several present inversion surface wave frequency dispersion curve commonly used inversion method: Least squares method (LSM), genetic algorithm (GA), simulation annealing (SA) and so on, compared with these method good and bad points and inversion effect. This paperintroduces one kind of linear inversion method------generalized counteralgorithm, used the scalar transmission algorithm to carry on the numerical calculus simulation to obtain the frequency dispersion curve., and carried on the programming to come true the Rayleigh surface wave inversion simulation. Compares with the least squares method inversion, this method has the convergence rate quick and the stable merit. The paper uses theτ-p transformation to purify surface wave depuration and the conventional Fourier transformation to pick up the frequency dispersion curve, does inversion about roadbed underground speed structure by the Heng-Shao highway's Transient surface wave exploration data, and actualizes the surface wave inversion flow completely in the actual exploration.
Generally speaking, the Rayleigh surface wave's inversion research is in the surface wave exploration domain the very important research subject. The inversion explained that the method choice affects the accuracy of the underground medium nature and the parameter, and also directly has a relationship with precision of surface wave exploration. As a result of the underground medium's complexity, we can develop the complex stratum medium inversion method research further.
引文
[1]D.G Harkerider & D.L.Anderson.Free oscillations of the earth,1,Toroidal oscillations.J.Geophs.Res.1960,65:675-693
[2]佐藤范。用GR-810激振系统进行勘探。日本VIC株式会社,1986
[3]杨成林。瑞雷波勘探法原理及应用。物探与化探,1989,13(6):465-468
[4]J.S.Heisey,K.H.Stoke and A.H.Meyer.Muduli of pavement systems from spectral analysis of sueface waves.Transfortation Research Record,No852,D.C.Washighton,1982
[5]S.Nazarian & K.H.Stokoe.In situ determination of elastic moduli of pavement systems by spectral-of-surface-waves method.Research Report 437-2,Austin,Center for Transportation,The University of Texas,1986
[6]裴江云,吴永刚,刘英杰。近地表低速带反演。长春地址学院学报。1994,24(3):317-320
[7]G.J.Rix and E.A.Leipski.Accuracy and Resolution of Surface Wave Inversion.Geotechnical Special Publication.1991,11:17-32
[8]J.H.Xia,R.D.MILLER & P.N Burton.Shear-wave velocity models from Rayleigh-wave dispersion in the broaker Aegean area.Geophys.J.Int.,v125.1996,p679-695
[9]R.W.Meier & G J.Rix.Initial study of surface wave inversion using artificial neural networks.Geotechnical Testing Journal,v16(4),1993,p574-581
[10]H.Yamanaka & H.Isbida.Application of genetic algorithms to an inversion of surface-wave dispersion data.Bull.Seism.Soc.Am,v86(2),1996,p436-444
[11]崔建文。利用面波资料反演波速剖面的全局优化方法。中国地震局工程力学研究所工学博士学位论文。1998:42-62
[12]肖伯勋,张碧星,杨文杰。瑞雷波勘探中“之”字型频散曲线的形成机理及反演研究。地球物理学报,v4,2000
[13]I.Ihara,H,Koguchi,Vchida.Inversion of dual mode surface waves to determine elastic constants Symposiu,1997.11,p545-548
[14]V.Ganji,N.Gucunski & S.Nazarian.Automated inversion procedure for spectral analysis of surface waves.J.Geot.Geoenv.Eng,v124(8),1998,p757-770
[15]喻明,兰从庆。利用地震面波进行前曾地下介质三维层析成像。物探与化探,v18(6),1994,p440-443
[16]朱良保。区域面波群速度反演的球谐函数法。地球物理学报。v40(4),1997,p503-511
[17]Z.Wang,J.Tromp & G.Ekstrom.Global & regional Surface-wave inversion:A spherical-spline parameterization.Geophysical Research Lettlers,v25(25),1998,p207-210
[18]A.Hering,R.Misiek,A.Gyulai.Joint inversion algorithm to process geoelectric and surface wave seismic data,Part I:Basic ideas.Geophysical Prospecting,v43(2),1995,p135-156
[19]H.Marquering & R.Snieder.Shear-wave velocity structure beneath Europe,the northeastern Atlantic and westen Asia from waveform inversions including surface-wave mode coupling.Geophys.J.Int.,v127(2),1996,p283-288
[20]肖柏勋.高模式瑞雷面波及其正反演研究.中南大学博士学位论文,2000年11月
[21]李学军.瞬态瑞雷波探测技术及其应用研究.石油地球物理勘探,1998年12月,33(增刊2):100-110
[22]刘云祯,王振东。瞬态表面波法的数据采集处理系统及其应用实例。物探与化探,1996,20(1):28-33
[23]崔占荣,张世洪,张俊喻。瞬态瑞雷波勘探中一些问题讨论。物探与化探,1997,v19(5):369-376
[24]包军强,张学强,刘江干,周鸿秋。浅层多波的分离、识别与提取。物探与化探,1998,22(5):336-376
[25]李锦飞。TRES-Ⅰ型多分量瑞雷波勘探仪的研究及应用,物探与化探,1998,22(2):129-133
[26]时福荣。互相关分析计算瑞雷波传播速度的原理和方法。物探化探计算基数,1990,12(4):357-360
[27]任青文。表面波谱分析法及其在工程中的应用。河海科技进展。1994,14(2):7-13
[28]陈云敏,吴世明,曾国熙。表面波谱分析测试技术。第三届全国土动力学 学术会议,上海。1990,(5):389-394
[29]张碧星,鲁来玉。用频率-波数法分析瑞雷波频散曲线。工程地球物理学报。2005,v2(4):245-248
[30]朱晓明,薛家俊,刘喜武等。时频分析在地震数据处理中的应用[J]。内蒙古石油化工,2007,33(8):96-99
[31]陈淑珍,刘怀林.基于τ-p变换的频散曲线及其算法实现[J].武汉大学学报(自然科学版),2000,46(1):123-126.
[32]孙云莲,刘敦敏。时-频分析与小波变换及其应用[J]。武汉大学学报(工学版),2003,36(2):103-106
[33]Garbor D.Theory of Communication[J].IEE(London),1964,93(3):429-457
[34]李建平.小波分析与信号处理-理论、应用及软件实现[M].重庆出版社,1997
[35]凡友华,刘家琦。层状介质中瑞雷面波的频散研究。哈尔滨工业大学学报。2001,No4
[36]柳辉。解非线性方程的牛顿迭代法及其应用[J]。重庆工学院学报,2007,21(15):95-98
[37]何华.频散曲线拟合瑞雷波勘探方法及其实现[D].北京:中国地质大学(北京),2000.
[38]赵东,王光杰,王兴泰,等.用遗传算法进行瑞利波反演[J].物探与化探,1995,19(3):178-185.
[39]胡家富,段永康,胡毅力,等.利用Rayleigh波反演浅土层的剪切波速度结构[J].地球物理学报,1999,42(3):393-400.
[40]陈祥,孙进忠 改进的等效半空间法及瑞雷波频散曲线反演.地球物理学报,2006,49(2):569 576
[41]曹小林,洪学海,曹俊兴.面波波形反演中的模拟退火法[J].成都理工学院学报,2000,27(3):296-301.
[42]刘争平。人工神经网络在测井-地震资料联合反演中的应用研究。哈尔滨工业大学博士学位论文。1997:29-37
[43]凡友华,刘家琦,韩波。瑞雷面波反演的人工神经网络方法。声学学报。
[44]姚姚。地球物理反演基本理论与应用方法[M]。中国地质大学出版社,2002。
[45]李平,许厚泽,卢造勋等。面波频散反演的数值模拟[J]。地壳形变与地震,2000,20(1):23-30
[46]陈祥.瑞雷波频散曲线拟合分析及其应用[硕士论文].北京:中国地质大学(北京)。2004
[47]Abo-Zena.A dispersion function computation for unlimited frequency values[J].Geophys.J.R.astr.Soc,1979,4(55):388-405.
[48]祁生文,孙进忠。何华.瑞雷波勘探的研究现状及展望.地球物理学进展,2002,17(4):630-635
[49]何华.频散曲线拟合瑞雷波勘探方法及其实现[D].北京:中国地质大学(北京),2000
[2]佐藤范。用GR-810激振系统进行勘探。日本VIC株式会社,1986
[3]杨成林。瑞雷波勘探法原理及应用。物探与化探,1989,13(6):465-468
[4]J.S.Heisey,K.H.Stoke and A.H.Meyer.Muduli of pavement systems from spectral analysis of sueface waves.Transfortation Research Record,No852,D.C.Washighton,1982
[5]S.Nazarian & K.H.Stokoe.In situ determination of elastic moduli of pavement systems by spectral-of-surface-waves method.Research Report 437-2,Austin,Center for Transportation,The University of Texas,1986
[6]裴江云,吴永刚,刘英杰。近地表低速带反演。长春地址学院学报。1994,24(3):317-320
[7]G.J.Rix and E.A.Leipski.Accuracy and Resolution of Surface Wave Inversion.Geotechnical Special Publication.1991,11:17-32
[8]J.H.Xia,R.D.MILLER & P.N Burton.Shear-wave velocity models from Rayleigh-wave dispersion in the broaker Aegean area.Geophys.J.Int.,v125.1996,p679-695
[9]R.W.Meier & G J.Rix.Initial study of surface wave inversion using artificial neural networks.Geotechnical Testing Journal,v16(4),1993,p574-581
[10]H.Yamanaka & H.Isbida.Application of genetic algorithms to an inversion of surface-wave dispersion data.Bull.Seism.Soc.Am,v86(2),1996,p436-444
[11]崔建文。利用面波资料反演波速剖面的全局优化方法。中国地震局工程力学研究所工学博士学位论文。1998:42-62
[12]肖伯勋,张碧星,杨文杰。瑞雷波勘探中“之”字型频散曲线的形成机理及反演研究。地球物理学报,v4,2000
[13]I.Ihara,H,Koguchi,Vchida.Inversion of dual mode surface waves to determine elastic constants Symposiu,1997.11,p545-548
[14]V.Ganji,N.Gucunski & S.Nazarian.Automated inversion procedure for spectral analysis of surface waves.J.Geot.Geoenv.Eng,v124(8),1998,p757-770
[15]喻明,兰从庆。利用地震面波进行前曾地下介质三维层析成像。物探与化探,v18(6),1994,p440-443
[16]朱良保。区域面波群速度反演的球谐函数法。地球物理学报。v40(4),1997,p503-511
[17]Z.Wang,J.Tromp & G.Ekstrom.Global & regional Surface-wave inversion:A spherical-spline parameterization.Geophysical Research Lettlers,v25(25),1998,p207-210
[18]A.Hering,R.Misiek,A.Gyulai.Joint inversion algorithm to process geoelectric and surface wave seismic data,Part I:Basic ideas.Geophysical Prospecting,v43(2),1995,p135-156
[19]H.Marquering & R.Snieder.Shear-wave velocity structure beneath Europe,the northeastern Atlantic and westen Asia from waveform inversions including surface-wave mode coupling.Geophys.J.Int.,v127(2),1996,p283-288
[20]肖柏勋.高模式瑞雷面波及其正反演研究.中南大学博士学位论文,2000年11月
[21]李学军.瞬态瑞雷波探测技术及其应用研究.石油地球物理勘探,1998年12月,33(增刊2):100-110
[22]刘云祯,王振东。瞬态表面波法的数据采集处理系统及其应用实例。物探与化探,1996,20(1):28-33
[23]崔占荣,张世洪,张俊喻。瞬态瑞雷波勘探中一些问题讨论。物探与化探,1997,v19(5):369-376
[24]包军强,张学强,刘江干,周鸿秋。浅层多波的分离、识别与提取。物探与化探,1998,22(5):336-376
[25]李锦飞。TRES-Ⅰ型多分量瑞雷波勘探仪的研究及应用,物探与化探,1998,22(2):129-133
[26]时福荣。互相关分析计算瑞雷波传播速度的原理和方法。物探化探计算基数,1990,12(4):357-360
[27]任青文。表面波谱分析法及其在工程中的应用。河海科技进展。1994,14(2):7-13
[28]陈云敏,吴世明,曾国熙。表面波谱分析测试技术。第三届全国土动力学 学术会议,上海。1990,(5):389-394
[29]张碧星,鲁来玉。用频率-波数法分析瑞雷波频散曲线。工程地球物理学报。2005,v2(4):245-248
[30]朱晓明,薛家俊,刘喜武等。时频分析在地震数据处理中的应用[J]。内蒙古石油化工,2007,33(8):96-99
[31]陈淑珍,刘怀林.基于τ-p变换的频散曲线及其算法实现[J].武汉大学学报(自然科学版),2000,46(1):123-126.
[32]孙云莲,刘敦敏。时-频分析与小波变换及其应用[J]。武汉大学学报(工学版),2003,36(2):103-106
[33]Garbor D.Theory of Communication[J].IEE(London),1964,93(3):429-457
[34]李建平.小波分析与信号处理-理论、应用及软件实现[M].重庆出版社,1997
[35]凡友华,刘家琦。层状介质中瑞雷面波的频散研究。哈尔滨工业大学学报。2001,No4
[36]柳辉。解非线性方程的牛顿迭代法及其应用[J]。重庆工学院学报,2007,21(15):95-98
[37]何华.频散曲线拟合瑞雷波勘探方法及其实现[D].北京:中国地质大学(北京),2000.
[38]赵东,王光杰,王兴泰,等.用遗传算法进行瑞利波反演[J].物探与化探,1995,19(3):178-185.
[39]胡家富,段永康,胡毅力,等.利用Rayleigh波反演浅土层的剪切波速度结构[J].地球物理学报,1999,42(3):393-400.
[40]陈祥,孙进忠 改进的等效半空间法及瑞雷波频散曲线反演.地球物理学报,2006,49(2):569 576
[41]曹小林,洪学海,曹俊兴.面波波形反演中的模拟退火法[J].成都理工学院学报,2000,27(3):296-301.
[42]刘争平。人工神经网络在测井-地震资料联合反演中的应用研究。哈尔滨工业大学博士学位论文。1997:29-37
[43]凡友华,刘家琦,韩波。瑞雷面波反演的人工神经网络方法。声学学报。
[44]姚姚。地球物理反演基本理论与应用方法[M]。中国地质大学出版社,2002。
[45]李平,许厚泽,卢造勋等。面波频散反演的数值模拟[J]。地壳形变与地震,2000,20(1):23-30
[46]陈祥.瑞雷波频散曲线拟合分析及其应用[硕士论文].北京:中国地质大学(北京)。2004
[47]Abo-Zena.A dispersion function computation for unlimited frequency values[J].Geophys.J.R.astr.Soc,1979,4(55):388-405.
[48]祁生文,孙进忠。何华.瑞雷波勘探的研究现状及展望.地球物理学进展,2002,17(4):630-635
[49]何华.频散曲线拟合瑞雷波勘探方法及其实现[D].北京:中国地质大学(北京),2000