摘要
浅层地表介质的剪切波速是工程抗震设计、场地地震危险性分析、场地地震效应研究等研究的重要基础。面波勘探方法是一种利用人工震源激发产生的Rayleigh（瑞雷）面波来反演地下介质弹性参数特别是剪切波速的现场原位测试方法，工作效率高且经济成本低。本文针对面波勘探中相对较新的多道面波分析方法（MASW）在地下介质剪切波速探测中的应用进行了研究，主要研究内容及取得的成果如下：
(1)利用传递矩阵法（Dunkin）计算了水平层位条件下的Rayleigh波相速度频散曲线，并总结了频散曲线在速度半波长域的分层特征。利用交错网格有限差分法模拟了水平层位及复杂层位条件下的Rayleigh波场，总结了复杂层位条件下的Rayleigh波场的特征以及频率深度域中的频散特征。
(2)对常用的提取频散曲线的方法（F-K法、-p变换法、相移法）进行了改进，使得改进后的三种方法具有基本相同的精度，增强了频率速度域中各阶模态的分辨能力。
(3)对常用的线性反演方法阻尼最小二乘法和非线性反演方法模拟退火法在瑞雷波频散曲线反演中的方法技术进行了综合分析，并提出了阻尼最小二乘与模拟退火联合反演介质剪切波速的新方法。新方法克服了阻尼最小二乘法容易陷入局部极值的缺陷，也提高了模拟退火法的反演效率。
(4)对Hayashi and Suzuki(2004)提出的利用多道面波分析方法构建地下二维剖面的CMP Cross-Correlation法进行了应用研究。结果显示，该方法只能够适用于水平层状介质或阶梯状水平层位条件下频散曲线的基阶模态，而频散曲线的高阶模态无法获得。同时，通过对倾斜层位模型的模拟结果进行处理，发现该方法不适用于倾斜层位条件下频散曲线的获取。
(5)利用本文改进的频散曲线提取方法以及阻尼最小二乘与模拟退火联合反演方法对成都盆地实测的面波记录进行了分析，得到了成都盆地的覆盖层厚度以及等效剪切波速(VS20)。根据Boore (2011)提出的平均剪切波速VS30与上层平均剪切波速VSz之间的对数线性关系回归了成都盆地VS30与上层平均剪切波速VSz之间关系。结果显示，成都盆地VS30与VSz之间的变化趋势与Boore (2011)利用KiK-net钻孔数据回归的关系曲线非常接近。这一结果对于成都盆地场地VS30的估计提供了可靠的依据，同时也为该地区地震动衰减关系建立中估计场地影响因素提供了可靠的数据基础。
The shear wave velocity of near surface materials and its effects onseismic wave propagation are of fundamental interest in many engineeringand research domains. Such as seismic-resistant design of buildings, seismichazard evaluation of a region, evaluating seismic site response. Surfacewave methods are sorts of shear wave velocity in situ test methods. Based onthe dispersive property of the Rayleigh wave, which means the Rayleighwaves with different frequencies will transmit with different phase velocities,these methods can be applied to obtain the shear wave velocities and otherelastic modules of the sub-materials using an artificial source to generate theRayleigh waves. Multi-channel Analysis of Surface Wave (MASW) method,which is one of the surface wave methods and is still in the front ofinteresting, is growing in many geophysical and geotechnical applicationsdue to its low cost and efficiency. In this paper, the utility details of theMASW method is discussed, and some process techniques and algorithmsetc, which comprised in the MASW method, are improved. The maincontents and results of this research are as follows:
(1) The Rayleigh wave dispersion curves for flat layered models arecalculated by means of the transfer matrix method (Dunkin,1965). Thedispersion curves’ characters in the phase-velocity and the half-wavelength domain for the flat layered models are summarized. Meanwhile,the Rayleigh wave fields for some flat layered models and complicatedmodels are simulated using the staggered grid finite difference method.The characters of the Rayleigh wave fields and their dispersion curvesare summarized too.
(2) Improvements are made for the three commonly used dispersion curveimaging methods, namely the F-K transform, the τ-p transform and thephase-shift methods. The results show that the three methods afterimproved can get the same resolution in imaging the Rayleigh wavedispersion curves. Besides, the improvements can help the three methodsto enhance the separating capability of different modes.
(3) The implementation details of the linearized inversion algorithm ofDamped Least Square (DLS) and the nonlinearized inversion algorithmof the Very Fast Simulated Annealing (VFSA) in surface wave disper-sion curve inversion considering high modes are analysed, and a hybridinversion algorithm of DLS with VFSA is proposed by this paper. Theproposed algorithm can not only overcome the defects of DLS that couldbe captured by local minimum, but also more efficiency than the VFSA algorithm.
(4) The CMP Cross-Correlation method (Hayashi and Suzuki,2004),which is used to construct two dimensional shear wave velocity profile,is verified using simulated wave field data. Results show that thismethod could only be used to approximate step flat layered model andcould not be used to approximate dipping layered model. In addition,using this method, only the fundamental mode of the Rayleigh wave’sdispersion curve can be obtained.
(5) Finally, the research results of this paper are applied to the in situ testedrecords from the two regions of Chengdu basin and that of Dujiangyanmunicipal area, the equivalent shear wave velocities (VS20) andoverburdens of the two regions are obtained. Using the time averageshear wave velocity (VS30) estimating relation lgVS30=f(lgVSz) proposedby Boore (2011) which was used to estimate the VS30by VSzwhen VS30isunavailable by seismic methods or borehole tests, the relation’scoefficients of the Chengdu basin was determined. The results show thatthe relation of Chengdu basin is similar to that obtained by Boore (2011)using KiK-net borehole data. This relation is reliable for one to evaluatethe time averaged shear wave velocity (VS30) among the Chengdu basinwhen test VS30directly is unavailable, and for one to estimate the siteeffects while establishing ground motion attenuation relationship for theChengdu basin.
引文
[1]崔建文.一种改进的全局优化算法及其在面波频散曲线反演中的应用[J].地球物理学报.2004,47(3):521-527.
[2]曹丹平.多尺度地震资料正反演方法研究[D].中国石油大学（华东）.2008.
[3]柴华友，韦昌富.刚度缓变介质中瑞利波特征[J].岩土力学.2009,30(9):2545-2551.
[4]陈艳艳.瑞雷波频散曲线提取及快速反演分析应用研究[D].哈尔滨工业大学.2010.
[5]陈祥，孙进忠.改进的等效半空间法及瑞雷波频散曲线反演[J].地球物理学报.2006,49(2):569-576.
[6]陈可洋，杨微，刘洪林，吴清岭.二阶弹性波动方程高精度交错网格波场分离数值模拟[J].物探与化探.2009,33(6):700-703.
[7]董国良，马在田，曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报.2000,43(6):856-864.
[8]邓乐翔.瑞雷波场正演模拟及频散曲线的提取[D].长安大学.2010.
[9]丁彦礼.层状介质多阶模态瑞利面波应用研究[D].桂林工学院.2006.
[10]丁彦礼，单娜琳.瑞利面波最大模频散曲线的反演解释方法[J].桂林工学院学报.2007,27(3):322-328.
[11]凡友华，陈晓非，刘雪峰等. Rayleigh波的频散方程高频近似分解和多模式激发数目.地球物理学报，2007,50(1):233-239.
[12]巩向博，韩立国，王恩利，杜立志.压制噪声的高分辨率Radon变换法[J].吉林大学学报(地球科学版).2009,39(1):152-157.
[13]高静怀，何洋洋，马逸尘.粘弹性与弹性介质中Rayleigh面波特性对比研究[J].地球物理学报.2012,55(1):207-218.
[14]黄自萍，张铭，吴文青等.弹性波数值模拟的区域分裂法[J].地球物理学报.2004,47(6):1094-1100.
[15]何耀锋，陈蔚天，陈晓非.利用广义反射-透射系数方法求解含低速层水平层状模型中面波频散曲线问题.地球物理学报，2006,49(4):1074-1081.
[16]侯兰杰，陈兴长，陈慧等.表面波法确定卵石土地基承载力模型研究[J].岩土力学.2008,29(9):2572-2576.
[17]蒋婵君.瑞雷面波资料处理方法研究[D].中南大学.2009.
[18]孔令召，侯兴民，陈建立.基于时频分析方法提取瞬态瑞利波频散曲线[J].地震工程与工程震动.2008,28(6):8-13.
[19]卢建旗，李山有，谢志南等.基于瑞雷波法的成都盆地场地剪切波速结构的确定[J].地震工程与工程震动.2012,32(2):35-40.
[20]卢建旗，李山有，李伟.基于瑞雷波法的都江堰市区场地剪切波速结构[J].地震工程与工程震动.2012,32(6):1-9.
[21]卢建旗，马建国.多道面波勘探技术在水利工程中的应用[J].黑龙江水利科技.2005,33(1):19-20.
[22]卢成武.直流电测深反演算法的研究[D].西北大学.2005.
[23]李幼铭，束沛镒.层状介质中地震面波频散函数和体波广义反射系数的计算[J].地球物理学报.1982,25(2):130-139.
[24]李晶.面波在地震波场中的特性研究及其应用.成都理工大学，2006.
[25]李宾.瑞雷波场正演模拟及频散曲线的提取[D].中国石油大学(华东).2010.
[26]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[J].物探与化探.1996,20(1):28-33.
[27]刘雪峰，凡友华. Rayleigh波勘探中之字形频散曲线起跳点频率研究[J].地球物理学报.2011,54(8):2124-2135.
[28]刘雪峰，凡友华，陈晓非. Rayleigh波频散曲线交叉及多模式耦合作用研究[J].地球物理学报.2009,52(9):2302-2309.
[29]刘雪明，凡友华，翟佳羽等.四种典型地层的瑞雷波之字型频散曲线数值模拟研究[J].地球物理学报.2009,52(12):3042-3050.
[30]刘喜亮.基于波动方程的瑞利面波有限差分正演模拟[D].中南大学.2005.
[31]林建生，陈俊峰，林子健等.场地地震安全性评价中确定地震动参数方面若干问题的研究[J].世界地震工程.2006,22(4):150-159.
[32]梁青.多模式瑞雷波频散曲线反演研究[D].中国地质大学（武汉）.2007.
[33]梁志强.层状介质多模式面波频散曲线研究[D].长安大学.2006.
[34]鲁来玉.分层半空间瑞利波模式分析和介质参数反演[D].中南大学.2009.
[35]罗银河，夏江海，刘江平等.基阶与高阶瑞利波联合反演研究[J].地球物理学报.2008,51(1):242-249.
[36]马翠莲.基于广义逆算法的层状弹性介质中瑞雷面波反演[D].中南大学.2008.
[37]牟永光，裴正林.三维复杂介质地震数值模拟[M].北京：石油工业出版社.2005.1.
[38]牛滨华，孙春岩.半空间均匀各项同性单相固体弹性介质与地震波传播[M].北京：地质出版社.2005.12.
[39]牛滨华，孙春岩，张中杰等.多项式Radon变换[J].地球物理学报.2001,44(2):263-271.
[40]宁刚，熊章强，陈持逊.波动方程有限差分正演模拟误差来源分析[J].物探与化探.2008,32(2):203-206.
[41]聂建新，杨顶辉，巴晶.含泥质低孔渗各向异性粘弹性介质中的波频散和衰减研究[J].地球物理学报.2010,53(2):385-392.
[42]潘冬明，胡明顺，崔若飞等.基于拉东变换的瑞雷面波频散曲线分析与应用[J].地球物理学报.2010,53(11):2760-2766.
[43]秦臻，姚姚，张才，宋建勇.频率域速度谱中提取面波的多模频散曲线方法[J].人民长江.2009,40(11):57-59.
[44]祁生文，孙进忠，何华.瑞雷波勘探的研究现状及展望[J].地球物理学进展.2002,17(4):630-635.
[45]宋先海，肖柏勋，顾汉明，朱培民.反演瞬态瑞雷波频散曲线映射二维横波速度剖面[J].物探化探计算技术.2003,25(2):105-109.
[46]宋先海，肖柏勋，黄荣荣等.用等厚薄层自适应迭代阻尼最小二乘法反演瑞雷波频散曲线[J].物探与化探.2003,27(3):212-216.
[47]佘德平.波场传播规律的数值模拟及其应用[D].河海大学.2007.
[48]邵广周，李庆春.联合应用p变换法和相移法提取面波频散曲线[J].石油地球物理勘探.2010,45(6):836-840.
[49]师黎静.基于地脉动的近地表三维速度结构探测和建模成像[D].中国地震局工程力学研究所.2007.
[50]沈操，牛滨华，余钦范. Radon变换的MATLAB实现[J].物探化探计算技术.2000,
[51]石耀霖，金文.面波频散反演地球内部构造的遗传算法[J].地球物理学报.1995,38(2):189-198.
[52]唐圣松.二维起伏地表模型瑞雷波场正演研究[D].中南大学.2009.
[53]王周，李朝晖，龙桂华等.求解弹性波有限差分法中自由边界处理方法的对比[J].工程力学.2012,29(4):77-83.
[54]王维红，首皓，刘洪等.线性同轴波场分离的高分辨率p变换法[J].地球物理学进展.2006,21(1):74-78.
[55]吴晓丰.起伏地表条件下地震波数值模拟[D].同济大学海洋与地球科学学院.2006.
[56]肖柏勋，凡友华，刘家琦.我国瑞雷面波勘探方法研究现状分析[J].工程地球物理学进展.2000,7:17-24.
[57]谢志南.近场波动数值模拟的几点注记[D].中国地震局工程力学研究所.2006.
[58]熊章强，张大洲，秦臻等.瑞雷波数值模拟中的边界条件及模拟实例分析[J].中南大学学报(自然科学版).2008,39(4):824-830.
[59]杨天春，吴燕清，刘新华.对瑞利波频散曲线计算中高频数值溢出的处理.煤炭学报，2007,32(10):1041-1045.
[60]杨晶晶.弹性波方程的数值模拟[D].同济大学理学院.2005.
[61]喻畑，李小军.基于NGA模型的汶川地震区地震动衰减关系[J].岩土工程学报.2012,34(3):552-558.
[62]张碧星，鲁来玉，鲍光淑.瑞利波勘探中之字形频散曲线研究[J].地球物理学报.2002,45(2):245-274.
[63]张大洲，熊章强，顾汉明.高精度瑞雷波有限差分数值模拟及波场分析[J].地球物理学进展.2009,24(4):1313-1319.
[64]张齐，胡进军，姜治军，谢礼力. NGA模型概述及其在中国适用性的初步探讨[J].土木工程学报.2012,45增刊(2):42-46.
[65]张立.层状介质中瑞利面波波场特征分析和反演方法研究[D].西安交通大学.2009.
[66]张华.复杂地表条件下弹性波数值模拟方法研究[D].中国石油大学(华东).2008.
[67]周青云，何永峰，靳平等.利用多重滤波方法提取面波频散曲线[J].西北地震学报.2009,28(1):46-50.
[68]周怀来.多波波场正演模拟与波场特征分析研究[D].成都理工大学.2009.
[69]祝贺君，张伟，陈晓非.二维各向异性介质中地震波场的高阶同位网格有限差分模拟[J].地球物理学报.2009,52(6):1-11.
[70]赵伟.层状介质瑞利面波的波形模拟及其频散曲线分析[D].桂林工学院.2007.
[71]翟佳羽，赵园园，安酉.面波频散反演地下层状结构的蚁群算法[J].物探与化探.2010,34(4):476-481.
[72]詹麟，朱培民.用趋势面分析方法提高模拟退火反演的效率[J].地球科学中国地质大学学报.2001,26(5):538-540.
[73] Arben Pitarka.3D Elastic Finite-Difference Modeling of Seismic Motion Using Stag-gered Grids with Nonuniform Spacing [J]. Bulletin of the Seismological Society ofAmerica.1999,89(1):54-68.
[74] Arthur Frankel. How Can Seismic Hazard around the New Madrid Seismic Zone BeSimilar to That in California?[J]. Seismological Research Letters.2004,75(5):575-586.
[75] Barbara Romanowicz. Inversion of Surface Waves: A Review [J]. International Hand-book of Earthquake and Engineering Seismology.2002,81(A):149-173.
[76] Beatriz Benjumea, James A. Hunter, Susan E. Pullan, et al. VS30and FundamentalSite Period Estimates in Soft Sediments of the Ottawa Valley from Near-SurfaceGeophysical Measurements [J]. JEEG.2008,13(4):313-323.
[77] Brady R. Cox, A. M. ASCE, Andrew N. Beekman. Intrmethod Variability in ReMiDispersion Measurements and Vs Estimates at Shallow Bedrock Sites [J]. JOURNALOF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING.2011,137(4):354-362.
[78] Carlo G. Lai PhD and Glenn J. Rix PhD. Simultaneous Inversion of Rayleigh PhaseVelocity and Attenuation for Near-Surface Site Characterization [D].1998Georgiainstitute of technology school of civil and environmental engineering.
[79] C. Comina, S. Foti, D. Boiero, L. V. Socco. Reliability of VS,30Evaluation fromSurface-Wave Tests [J]. Journal of Geotechnical and Geoenvironmental Engineering.2011,137(6):579-586.
[80] C. J. Wills and K. B. Clahan. Developing a Map of Geologically Defined Site Cond-ition Categories for California [J]. Bulletin of the Seismological Society of America.2006,96(4A):1483-1501.
[81] C. J. Wills. Differences in Shear-Wave Velocity due to Measurement Methods: ACautionary Note [J]. Seismological Research Letters.1998,69(3):216-221.
[82] Choon B. Park, Richard D. Miller, Jianghai Xia. Multichannel analysis of surfacewaves [J]. Geophysics.1999,64(3):800-808.
[83] Choon Byong Park, Richard D. Miller and Julian Iwanov. Filtering surface waves [J].report.2009,39(1):152-157.
[84] Chun-Hung Lin and Chih-Ping Lin. Metamorphosing the SASW Method by2DWavefield Transformation [J]. Journal of Geotechnical and GeoenvironmentalEngineering.2012,138:1027-1032.
[85] Daniel R. H. O’Connell and James P. Tuner. Interferometric Multichannel Analysis ofSurface Waves(IMASW)[J]. Bulletin of the Seismological Society of America.2011,101(5):2122-2141.
[86] David M. Boore, Eric M. Thompson, and Hélo se Cadet. Regional Correlations ofVs30and Velocities Averaged Over Depths Less Than and Greater Than30Meters [J].Bulletin of the Seismological Society of America.2011,101(6):3046-3059.
[87] David M. Boore. Estimating VS30(or NEHRP Site Classes) from Shallow VelocityModels (Depths <30m)[J]. Bulletin of the Seismological Society of America.2004,94(2):591-597.
[88] David G. Harkrider, Don L. Anderson. Computation of surface wave dispersion formultilayered anisotropic media [J]. Bulletin of the Seilmological Society of America.1962,52(2):321-332.
[89] Donghong Pei, Hohn N. Louie, Satish K. Pullammanappallil. Improvements onComputation of Phase Velocities of Rayleigh Waves Based on the Generalized R/TCoefficient Method [J]. Bulletin of the Seilmological Society of America.2008,98(1):280-287.
[90] Dong-Joo Min, Changsoo Shin, Hai Soo Yoo. Free-Surface Boundary Condition inFinite-Difference Elastic Wave Modeling [J]. Bulletin of the Seismological Society ofAmerica.2004,94(1):237-250.
[91] Donald W. Marquardt. An Algorithm for Least-Squares Estimation of NonlinearParameters [J]. Journal of the Society for industrial and Applied Mathematics.1963,11(2):431-441.
[92] E.Gottsch mmer and K. B. Olsen. Accuracy of the Explicit Planar Free-SurfaceBoundary Condition Implemented in a Fourth-Order Staggered-Grid Velocity-StressFinite-Difference Scheme [J]. Bulletin of the Seismological Society of America.2001,91(3):617-623.
[93] Frank WUTTKE, Hans-Gottfried SCHMIDT, Tom SCHANZ. Geotechnical SiteInvestigation of Subsurfaces by Surface Waves Considering Higher Modes[J].13thWorld Conference on earthquake Engineering.2004.
[94] Francesco Mulargia, Silvia Castellaro. Experimental Uncertainty on the Vs(z) Profileand Seismic Soil Classification [J]. Seismological Research Letters.2009,80(6):985-988.
[95] Fred Schwab. Surface Wave Dispersion Computations: Knopoff’s Method [J]. Bulletinof the Seilmological Society of America.1970,60(5):1491-1520.
[96] Fred Schwab and Leon Knopoff. Surface-Wave Dispersion Computations [J]. Bulletinof the Seilmological Society of America.1970,60(2):321-344.
[97] G. Dal Moro, M. Pipan. Joint Inversion of Surface Wave Dispersion Curves andReflection Travel Times via Multi-objective Evolutionary Algorithms [J]. Journal ofApplied Geophysics.2007,61:56-81.
[98] G-Akis Tselentis and George Delis. Rapid assessment of S-wave profiles from theinversion of multichannel surface wave dispersion data [J]. ANNALI DI GEOFISICA.1998,41,N,1:1-15.
[99] Giancarlo Dal Moro, Michele Pipan, Paolo Gabrielli. Rayleigh wave dispersion curveinversion via genetic algorithms and Marginal Posterior Probability Densityestimation [J]. Journal of Applied Geophysics.2007,61:39-55.
[100] Gail M. Atkinson, David M. Boore. Empirical Ground-Motion Relations forSubduction-Zone Earthquakes and Their Application to Cascadia and Other Regions[J]. Bulletin of the Seismological Society of America.2003,93(4):1703-1729.
[101] Ganpan Ke, Hefeng Dong, Age Kristensen and Mark Thompson. Modified Thomson-Haskell Matrix Methods for Surface-Wave Dispersion-Curve Calculation and TheirAccelerated Root-Searching Schemes [J]. Bulletin of the Seilmological Society ofAmerica.2011,101(4):1692-1703.
[102] Gail M. Atkinson, David M. Boore. Earthquake Ground-Motion Prediction Equationsfor Eastern North America [J]. Bulletin of the Seismological Society of America.2006,96(6):2181-2205.
[103] Hiroaki Yamanaka and Hiroshi Ishida. Application of Genetic Algorithms to anInversion of Surface-Wave Dispersion Data [J]. Bulletin of the Seismological Societyof America.1996,86(2):436-444.
[104] His-Ping Liu, David M. Boore, William B. Joyner et al. Comparison of PhaseVelocities from Array Measurements of Rayleigh Waves Associated with Microtremorand Results Calculated from Borehole Shear-Wave Velocity Profiles [J]. Bulletin ofthe Seismological Society of America.2000,90(3):666-678.
[105] Hélo se Cadet and Anne-Marie Duval. A Shear Wave Velocity Study Based on theKik-net Borehole Data: A Short Note [J]. Seismological Research Letters.2009,80(3):440-445.
[106] HE Yao-Feng, CHEN Wei-Tian, CHEN Xiao-Fei. Normal Modes Computation byGeneralized Reflection-Transmission Coefficients Method in Planar Layered HalfSpace [J]. Chinese Journal of Geophysics.2006,49(4):965-973.
[107] James B. Scott, Tiana Rasmussen, Barbara Luke, Wanda J. Taylor, et al.. ShallowShear Velocity and Seismic Microzonation of the Urban Las Vegas, Nevada, Basin [J].Bulletin of the Seismological Society of America.2006,96(3):1068-1077.
[108] J. A. Perez-Ruiz, F. Luzon, A. Garcia-Jerez. Simulation of an Irregular Free Surfacewith a Displacement Finite-Difference Scheme [J]. Bulletin of the SeismologicalSociety of America.2005,95(6):2216-2231.
[109] John G. Anderson, Yajie Lee, Yuehua Zeng, Steven Day. Control of Strong Motion bythe Upper30Meters [J]. Bulletin of the Seismological Society of America.1996,86(6):1749-1759.
[110] Jea-won Chung, J. David Rogers. Seismic Site Classifications for the St. Louis UrbanArea [J]. Bulletin of the Seismological Society of America.2012,102(3):980-990.
[111] John W. Dunkin. Computation of modal solutions in layered, elastic media at highfrequencies [J]. Bulletin of the Seilmological Society of America.1965,55(2):335-358.
[112] Jianghai Xia, Richard D. Miller, Choon B. Park and Julian Iwanov. Construction of2-D Vertical Shear-wave Velocity field by the Multichannel Analysis of Surface WaveTechnique[J]. Preceedings of the Symposium on the Application of Geophysics toEngineering and Environmental Problems. EEGS2000:1197-1206.
[113] Jianghai Xia, Richard D. Miller and Choon B Park. Estimation of near-surfaceshear-wave velocity by inversion of Rayleigh waves [J]. Geophysics.1999,64(3):691-700.
[114] Kenneth W. Campbell, M.EERI, and Yousef Bozorgnia, M.EERI. NGA GroundMotion Model for the Geometric Mean Horizontal Component of PGA, PGV, PGDand5%Damped Linear Elastic Response Spectra for Periods Ranging from0.01to10s [J]. Earthquake Spectra.2008,24(1):139-171.
[115] Keiji Nagai, Adam O’Neill, Yoshinori Sanada et al.. Genetic Algorithm Inversion ofRayleigh Wave Dispersion from CMPCC Gather over a Shallow Fault Model [J].JEEG.2005,10(3):275-286.
[116] Koichi Hayashi, Haruhiko Suzuki. CMP cross-correlation analysis of multi-channelsurface wave data [J]. Exploration Geophysics.2004,35:7-13.
[117] Lucia Nardone, Rosalba Maresca. Shallow Velocity Structure and Site Effects at Mt.Vesuvius, Italy, from HVSR and Array Measurements of Ambient Vibrations [J].Bulletin of the Seismological Society of America.2011,101(4):1465-1477.
[118] Longzhu Chen, Jinying Zhu, Xishui Yan, Chunyun Song. On arrangement of sourceand receivers in SASWtesting [J]. Siol Dynamics and Earthquake Engineering.2004,24:389-396.
[119] Ludovic Bodet, Kasper wan Wijk, Adnand Bitri et al.. Surface-wave inversionlimitations from laser-Doppler physical modeling [J]. Journal of Environmental&Engineering Geophysics.2005,10(2):151-162.
[120] Maria Rosaria Gallipoli and Marco Mucciarelli. Comparison of Site Classificationfrom VS30, VS10, and HVSR in Italy [J]. Bulletin of the Seismological Society ofAmerica.2009,99(1):340-351.
[121] Mahdavi M., Siahkoohi H.R.. Multi-channel analysis of surface waves using CommonMidpoint Cross Correlation method [J]. JSUT.2010,35(3):1-6.
[122] Meredith Nettles and Adam M. Dziewonski. Effect of Higher-Mode Interference onMeasurements and Models of Fundamental-Mode Surface-Wave Dispersion [J].Bulletin of the Seilmological Society of America.2011,101(5):2270-2280.
[123] N. A. Haskell. The Dispersion of Surface Waves on Multilayered Media [J]. Bulletinof the Seilmological Society of America.1953,43:17-34.
[124] Paolo Bazzurro, C. Allin Cornell. Ground-Motion Amplification in Nonlinear SoilSites with Uncertain Properties [J]. Bulletin of the Seismological Society of America.2004,94(6):2090-2109.
[125] PEI Zheng-lin(裴正林), WANG Shang-xu(王尚旭). A staggered-grid high-orderfinite-difference modeling for elastic wave field in arbitrary tilt anisotropic media [J].ACTA SEISMOLOGICA SINICA.2005,18(4):471-482.
[126] Pierre Gehl, Lius Fabian Bonilla, and John Douglas. Accounting for Site Charact-erization Uncertanties When Developing Ground-Motion Prediction Equations [J].Bulletin of the Seismological Society of America.2011,101(3):1101-1108.
[127] Rune Mittet. Free-surface boundary condition for elastic staggered-grid modelingschemes [J]. Geophysics.2002,67(5):1616-1623.
[128] Robb Eric S. Moss. Quantifying Measurement Uncertainty of Thirty-Meter Shear-Wave Velocity [J]. Bulletin of the Seismological Society of America.2008,98(3):1399-1411.
[129] Silvia Castellaro, Francesco Mulargia. VS30Estimates Using Constrained H/VMeasurements [J]. Bulletin of the Seismological Society of America.2009,99(2A):761-773.
[130] Seyed Mohammad Ali Zomorodian. Shear wave velocity of soils by the spectralanalysis of surface waves(SASW) method [D].1996PhD Carleton university and theUniversity of Ottawa.
[131] S. Parolai, P. Bormann, C. Milkereit. New Relationships between Vs, Thickness ofSediments and Resonance Frequency Calculated by the H/V Ratio of Seismic Noisefor the Cologne Area (Germany)[J]. Bulletin of the Seismological Society of America.2002,92(6):2521-2527.
[132] Stephen Hartzell, L. F. Bonilla, Robert A. Williams. Prediction of Nonlinear SoilEffects [J]. Bulletin of the Seismological Society of America.2004,94(5):1609-1629.
[133] Trevor I. Allen, David J. Wald. On the Use of High-Resolution Topographic Data as aProxy for Seismic Site Conditions (VS30)[J]. Bulletin of the Seismological Society ofAmerica.2009,99(2A):935-943.
[134] Takeshi Tsuji, Tor Arne Johansen, Bent Ole Ruud et al. Surface-wave analysis foridentifying unfrozen zones in subglacial sediments [J]. Geophysics.2012,77(3):EN17-EN27.
[135] T. Akhlaghi. Application of Algebraic Inverse Method to Surface Wave Testing ofPavements Using Free Plate Solution [J]. Preceedings of the InternationalMultiConference of Engineers and Computer Scientists.2008, Vol (2) IMECS2008:19-21.
[136] T. H. Watson. A note on fast computation of Rayleigh wave dispersion in themultilayered elastic half-space [J]. Bulletin of the Seilmological Society of America.1970,60(1):161-166.
[137] Tianyun Liu. Efficient Reformulation of the Thomson-Haskell Method for Comput-ation of Surface Waves in Layered Half-Space [J]. Bulletin of the SeilmologicalSociety of America.2010,100(5A):2310-2316.
[138] Weston A. Thelen, Matthew Clark, Christopher T. Lopez, Chris Loughner, et al. ATransect of200Shallow Shear-Velocity Profiles across the Los Angeles Basin [J].Bulletin of the Seismological Society of America.2006,96(3):1055-1067.
[139] Wen Ruizhi, Ren Yefei, Shi Dacheng. Improved HVSR site classification method forfree-field strong motion stations validated with Wenchuan aftershock recordings [J].Earthquake Engineering and Engineering Vibration.2011,10(3):325-337.
[140] Xiaofei Chen. A Systematic and Efficient Method of Computing Normal Modes forMultilayered Half-Space [J]. Geophysical Journal.1993,115(2):391-409.
[141] Xia Fan, Dong Liangguo, Ma Zaitian. The Numerical Modeling of3-D Elastic WaveEquation Using a High-Order Staggered-Grid Finite Difference Scheme [J]. AppliedGeophysics.2004,1(1):38-41.
[142] Yoojoong Choi, M.EERI, and Jonathan P. Stewart, M.EERI. Nonlinear Site Amp-lification as Function of30m Shear Wave Velocity [J]. Earthquake Spectra.2005,21(1):1-30.
[143] Zhou Yanguo, Chen Yunmin and Ling Daosheng. Shear wave velocity-basedliquefaction evaluation in the great Wenchuan earthquake: a preliminary case study [J].Earthquake Engineering and Engineering Vibration.2009,8(2):231-239.
[144] Zacharie Duputel, Michel Cara, Luis Rivera et al. Improving the analysis andinversion of multimode Rayleigh-wave dispersion by using group-delay timeinformation observed on arrays of high-frequency sensors [J]. Geophysics.2010,75(2): R13-R20.