近断层地震动模拟现状
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摘要
地震动是由3个物理过程(震源破裂过程、波传播过程、场地反应)组成的一种复杂系统的产物,地震动模拟均是围绕这3个物理过程的建模开展的。地震动模拟目前仍然是一门相对较新的科学,强震观测中不断发现的新情况、新问题及其深入研究进一步推动近断层地震学理论和实践的发展。减少建模中的不确定性,用基于观测物理学的统计特征逐渐取代基于现象的假设描述,以改善地震动模拟的精度。基于大量地震动模拟的研究文献和资料,归纳、评述了近断层地震动模拟方法的现状、3个物理过程的建模方法及其发展趋势。
The ground motion is the outcome of a complicated system that consists of three physical processes(i.e.,earthquake source rupture process,seismic wave propagation,and site response),and is simulated based on modeling the three physical processes.The ground motion simulation is a relative new discipline.New cases and problems discovered progressively in strong motion observation and lucubrated on them will further promote development of both theory and practice about near-fault seismology.The precision in ground motion simulation will be improved by both reducing uncertainties in models and substituting statistical characteristics based on observation physics for hypotheses based on some phenomena.The present situation of simulation methods of near-fault ground motion,methods of modeling three physical processes,and their trends are reviewed based on a lot of literatures and data on ground motion simulations.
The ground motion is the outcome of a complicated system that consists of three physical processes(i.e.,earthquake source rupture process,seismic wave propagation,and site response),and is simulated based on modeling the three physical processes.The ground motion simulation is a relative new discipline.New cases and problems discovered progressively in strong motion observation and lucubrated on them will further promote development of both theory and practice about near-fault seismology.The precision in ground motion simulation will be improved by both reducing uncertainties in models and substituting statistical characteristics based on observation physics for hypotheses based on some phenomena.The present situation of simulation methods of near-fault ground motion,methods of modeling three physical processes,and their trends are reviewed based on a lot of literatures and data on ground motion simulations.
引文
[1]Aki K,Richards P G.Quantitative Seismology:Theory and Meth-ods[M].New York:W HFreeman&Co Ltd,1980.
[2]Boore D M.Stochastic simulation of high-frequency ground mo-tions based on seismological models of the radiated spectra[J].Bulletin ofthe Seismological SocietyofAmerica,1983,73:1 865-1884.
[3]Boore D M.Simulation of ground motion using the stochastic meth-od[J].Pure and Applied Geophysics,2003,160:635-676.
[4]Hartzell S.Earthquake aftershocks as Green′s functions[J].Geo-physical Research Letters,1978,5:1-4.
[5]Irikura K.Semi-empirical estimation of strong ground motions dur-ing large earthquakes[J].Bulletin,Disaster Prevention ResearchInstitute,Kyoto:Kyoto University,Japan,1983,33:63-104.
[6]Beresnev I,Atkinson G.FINSIM:A FORTRAN program for sim-ulating stochastic acceleration time histories from finite faults[J].Seismological Research Letters,1998,69:27-32.
[7]Motazedian D,Atkinson G M.Stochastic Finite-Fault ModelingBased on a Dynamic Corner Frequency[J].Bulletin ofthe Seismo-logical Society ofAmerica,2005,95(3):995-1 010.
[8]Kamae K,Irikura K,Pitarka A.Atechnique for simulating strongground motion using hybrid green′s function[J].Bulletin oftheSeismological Society ofAmerica,1998,88(2):357-367.
[9]Hartzell S,Harmsen S,Frankel A,et al.Calculation of broadbandtime histories of ground motion:Comparison of methods and vali-dation using strong-ground motion from the 1994 northridge earth-quake[J].Bulletin ofthe Seismological Society ofAmerica,1999,89(6):1 484-1 504.
[10]Pitarka A,Somerville P,Fukushima Y,et al.Simulation ofnear-fault strong-ground motion using hybrid Green′s functions[J].Bulletin ofthe Seismological Society ofAmerica,2000,90:566-586.
[11]Somerville P G.Emerging art:Earthquake ground motion[C]∥Dakolas P,Yegian M,eds.Proceedings-Geotechnical EarthquakeEngineering and Soil Dynamics III,ASCE Speciality Conf.Spe-cial Pub.No.75,Seattle,WA,1998:1-38.
[12]Luo Qifeng,Hu Yuxian.An improved empirical Green functionmethod and synthesis of near-field acceleration in Lulong earth-quake[J].Journal ofEarthquake Engineering and EngineeringVibration,1990,10(3):1-12.[罗奇峰,胡聿贤.改进的经验格林函数法和卢龙近场加速度合成[J].地震工程与工程振动,1990,10(3):1-12.]
[13]Wang Guoxin.A study on attenuation of strong ground motion[D].Harbin:Institute of Engineering Mechanics,China Earth-quake Administration,2001.[王国新,强地震动衰减研究[D].哈尔滨:中国地震局工程力学研究所,2001.]
[14]Wald D J,Heaton T H,Hudnut K W.The slip history of the1994 Northridge,California,earthquake determined from strong-motion,teleseismic,GPS,and leveling[J].Bulletin ofthe Seis-mological Society ofAmerica,1996,86:S49-S70.
[15]Wang Haiyun.Finite fault source model for predicting near fieldstrong ground motion[D].Harbin:Institute of Engineering Me-chanics,China Earthquake Administration,2004.[王海云.近场强地震动预测的有限断层震源模型[D].哈尔滨:中国地震局工程力学研究所,2004.]
[16]Zhang Xiaozhi,Xie Lili,Wang Haiyun,et al.Illustrative exam-ple in simulating near-fault ground motion field by explicit finiteelement method[J].Journal ofEarthquake Engineering and En-gineering Vibration,2005,25(6):5-11.[张晓志,谢礼立,王海云,等.近断层强地面运动影响场显式有限元数值模拟的示意性算例[J].地震工程与工程震动,2005,25(6):5-11.]
[17]Zhang Xiaozhi,Xie Lili,Wang Haiyun,et al.Models and meth-ods for simulating near-fault ground motion field of a city by ex-plicit finite element method[J].Journal ofEarthquake Engineer-ing and Engineering Vibration,2006,26(6):11-16.[张晓志,谢礼立,王海云,等.某正倾滑断层引起的近断层强地面运动的有限元数值模拟[J].地震工程与工程震动,2006,26(6):11-16.]
[18]Pan Bo,Xu Jiandong,Haruko Sekigguchi,et al.Simulation ofthe near-fault strong ground motion in BEIJING region[J].Seis-mology and Geology,2006,28(4):623-634.[潘波,许建东,关口春子,等.北京地区近断层强地震动模拟[J].地震地质,2006,28(4):623-634.]
[19]Reid H F.The earthquake of southeastern Maine,March 21,1904[J].Bulletin ofthe Seismological Society ofAmerica,1911,1:44-47.
[20]O′Connell D R H,Ake J P.Earthquake ground motion estima-tion[C]∥Rodrigue C,Rovai E,eds.Earthquakes:Two-VolumeSet(Hazards and Disasters).New York:Routledge,2001:760.
[21]Miyake H,Iwata T,Irikura K.Source characterization for broad-band ground-motion simulation:Kinematic Heterogeneous sourcemodel and strong motion generation area[J].Bulletin ofthe Seis-mological Society ofAmerica,2003,93(6):2 531-2 545.
[22]Zeng Y,Anderson J,Yu G.A composite source model for com-puting realistic synthetic strong ground motions[J].GeophysicalResearth Letters,1994,21:725-728.
[23]Frankel A.Simulating strong motions of large earthquakes usingrecordings of small earthquakes:The Loma Prieta mainshock as atest case[J].Bulletin ofthe Seismological Society ofAmerica,1995,85:1 144-1 160.
[24]Herrero A,Bernard P.A kinematic self similar rupture processfor earthquakes[J].Bulletin ofthe Seismological SocietyofAmeri-ca,1994,84:1 216-1 228.
[25]Bernard P,Herrero A,Berge C.Modeling directivity of heteroge-neous earthquake rupture[J].Bulletin ofthe Seismological SocietyofAmerica,1996,86:1 149-1 160.
[26]Somerville P,Irikura K,Graves R,et al.Characterizing crustalearthquake slip models for the prediction of strong ground motion[J].Seismological Research Letters,1999,70:59-80.
[27]Mai P M,Beroza G C.Aspatial randomfield model to character-ize complexity in earthquake slip[J].Journal ofGeophysical Re-search,2002,107(B11):2 308.
[28]Hisada Y.Atheoretical omega-square model considering the spa-tial variation in slip and rupture velocity[J].Bulletin ofthe Seis-mological Society ofAmerica,2000,90:387-400.
[29]Hisada Y.Atheoretical omega-square model considering the spa-tial variation in slip and rupture velocity,part 2:Case for a twodimensional source model[J].Bulletin ofthe Seismological Socie-ty ofAmerica,2001,91:651-666.
[30]Gallovic F,Brokesove J.On strong ground motion synthesis withk-2slip distributions[J].Journal ofSeismology,2004,8(2):211-224.
[31]Wang Haiyun,Tao Xiaxin.Characterizing a shallow earthquakeasperity model for predicting near field strong ground motion[J].Journal ofHarbin institute oftechnology,2005,37(11):1 533-1 539.[王海云,陶夏新.近场强地震动预测中浅源地震的Asperity模型特征[J].哈尔滨工业大学学报,2005,37(11):1 533-1 539.]
[32]Silva W J,Lee K.WES RASCAL code for synthesizing earth-quake ground motions[C]∥State of the Art for Assessing Earth-quake Hazards in the United States,Report 24,US Army Engi-neers Waterway Experiment Station,Misc.1987:S-73-1.
[33]Schneider J F,Silva W J,Stark C L.Ground motion model forthe 1989 M6.9 Loma Prieta earthquake including effects ofsource,path,and site[J].Earthquake Spectra,1993,9(2):251-287.
[34]Hutchings L.Kinematic earthquake models and synthesizedground motion using empirical Green′s functions[J].Bulletin ofthe Seismological Society ofAmerica,1994,84:1 028-1 050.
[35]Heaton TH,Hall J F,Wald D J,et al.Response of high-riseand base-isolated buildings to a hypothetical Mw7.0 blind thrustearthquake[J].Science,1995,267:206-211.
[36]Jarpe S P,Kasameyer P W.Validation of a procedure for calcu-lating broadband strong-motion time histories with empiricalGreen′s functions[J].Bulletin ofthe Seismological Society ofA-merica,1996,86:1 116-1 129.
[37]O′Connell D R H.Synthesizing site-specific near-field groundmotinos from reverse faults:New perspectives on peak velocityhazards using broadband site responses[R].Earthquake Engi-neering Research Institude,Proceedings CDROMof the Sixth U.S.National Conference on Earthquake Engineering,1998.
[38]O′Connell D R H.Replication of apparent nonlinear seismic re-sponse with linear wave propagation models[J].Science,1999,283:2 045-2 050.
[39]Zeng Y,Anderson J.Evaluation of numerical procedures for sim-ulating near-fault long-period ground motions using the Zengmethod[R].Pacific Earthquake Engineering Research Center U-tilities Program Report 2000/01,2000.
[40]Day S M.Efficient simulation of constant Q using coarse-grainedmemory variables[J].Bulletin ofthe Seismological Society ofA-merica,1998,88:1 051-1 062.
[41]Boore D M,Joyner WB.Site amplifications for generic rock sites[J].Bulletin ofthe Seismological Society ofAmerica,1997,87(2):327-341.
[42]Anderson J G,Hough S.Amodel for the shape of the fourier am-plitude spectrum of acceleration at high frequencies[J].Bulletinofthe Seismological Society ofAmerica,1984,74(5):1 969-1 993.
[43]Bonilla L F.Computation of linear and nonlinear response fornear field ground motion[D].Santa Barbara:University of Cali-fornia,2000.
[44]Graves R W,Pitarka A,Somerville P G.Ground motion amplifi-cation in the Santa Monica area:Effects of shallow basin edgestructure[J].Bulletin ofthe Seismological Society ofAmerica,1998,88:1 224-1 242.
[45]Kawase H.The cause of the damage belt in Kobe:“The basin-edge effect,”constructive interference of the direct S-wave withthe basin-induced diffracted/Rayleigh waves[J].SeismologicalResearch Letters,1996,67(5):25-34.
[46]Pitarka A,Irikura K,Iwata T,et al.Three-dimensional simula-tion of the near-fault ground motions for the 1995 Hyogo-Nanbu(Kobe),Japan,earthquake[J].Bulletin ofthe Seismological So-ciety ofAmerica,1998,88:428-440.
[47]Alex C M,Olsen K B.Lens-effect in Santa Monica?[J].Geo-physical Researth Letters,1998,25:3 441-3 444.
[48]Davis P M,Rubinstein J L,Liu K H,et al.Northridge earth-quake damage caused by geologic focusing of seismic waves[J].Science,2000,289:1 746-1 750.
[49]Schultz C A.Enhanced backscattering of seismic waves from ir-regular interfaces[D].Cambridge:Massachusetts Institue ofTechnology,1994.
[50]Bouchon M,Schultz C A,Toksoz M N.Effect of three-dimen-sional topography on seismic motion[J].Journal ofGeophysicalResearch,1996,101:5 835-5 846.
[51]Spudich P,Hellweg M,Lee WHK.Directional topographic siteresponse observed in aftershocks of the 1994 Northridge,Califor-nia,earthquake:Implications for main shock motions[J].Bulle-tin of the Seismological Society of America,1996,86:S193-S208.
[52]Stewart J P,Chiou S J,Bray J D,et al.Ground Motion Evalua-tion Procedures for Performance-Based Design[R].PEER Re-port 2001/09.Pacific Earthquake Engineering Research Center,College of Engineering,University of California,Berkeley,2001.
[53]Ashford S A,Sitar N,Lysmer J,et al.Topographic Effects onthe Seismic Response of Steep Slopes[J].Bulletin ofthe Seismo-logical Society ofAmerica,1997,87:701-709.
[54]Ashford S A,Sitar N.Analysis of topographic amplification of in-clined shear waves in a steep coastal bluff[J].Bulletin oftheSeismological Society ofAmerica,1997,87:692-700.
[55]Oreskes N,Shrader-Frechette K,Belitz K.Verification,valida-tion,and confirmation of numerical models in the Earth sciences[J].Science,1994,264:641-646.
[2]Boore D M.Stochastic simulation of high-frequency ground mo-tions based on seismological models of the radiated spectra[J].Bulletin ofthe Seismological SocietyofAmerica,1983,73:1 865-1884.
[3]Boore D M.Simulation of ground motion using the stochastic meth-od[J].Pure and Applied Geophysics,2003,160:635-676.
[4]Hartzell S.Earthquake aftershocks as Green′s functions[J].Geo-physical Research Letters,1978,5:1-4.
[5]Irikura K.Semi-empirical estimation of strong ground motions dur-ing large earthquakes[J].Bulletin,Disaster Prevention ResearchInstitute,Kyoto:Kyoto University,Japan,1983,33:63-104.
[6]Beresnev I,Atkinson G.FINSIM:A FORTRAN program for sim-ulating stochastic acceleration time histories from finite faults[J].Seismological Research Letters,1998,69:27-32.
[7]Motazedian D,Atkinson G M.Stochastic Finite-Fault ModelingBased on a Dynamic Corner Frequency[J].Bulletin ofthe Seismo-logical Society ofAmerica,2005,95(3):995-1 010.
[8]Kamae K,Irikura K,Pitarka A.Atechnique for simulating strongground motion using hybrid green′s function[J].Bulletin oftheSeismological Society ofAmerica,1998,88(2):357-367.
[9]Hartzell S,Harmsen S,Frankel A,et al.Calculation of broadbandtime histories of ground motion:Comparison of methods and vali-dation using strong-ground motion from the 1994 northridge earth-quake[J].Bulletin ofthe Seismological Society ofAmerica,1999,89(6):1 484-1 504.
[10]Pitarka A,Somerville P,Fukushima Y,et al.Simulation ofnear-fault strong-ground motion using hybrid Green′s functions[J].Bulletin ofthe Seismological Society ofAmerica,2000,90:566-586.
[11]Somerville P G.Emerging art:Earthquake ground motion[C]∥Dakolas P,Yegian M,eds.Proceedings-Geotechnical EarthquakeEngineering and Soil Dynamics III,ASCE Speciality Conf.Spe-cial Pub.No.75,Seattle,WA,1998:1-38.
[12]Luo Qifeng,Hu Yuxian.An improved empirical Green functionmethod and synthesis of near-field acceleration in Lulong earth-quake[J].Journal ofEarthquake Engineering and EngineeringVibration,1990,10(3):1-12.[罗奇峰,胡聿贤.改进的经验格林函数法和卢龙近场加速度合成[J].地震工程与工程振动,1990,10(3):1-12.]
[13]Wang Guoxin.A study on attenuation of strong ground motion[D].Harbin:Institute of Engineering Mechanics,China Earth-quake Administration,2001.[王国新,强地震动衰减研究[D].哈尔滨:中国地震局工程力学研究所,2001.]
[14]Wald D J,Heaton T H,Hudnut K W.The slip history of the1994 Northridge,California,earthquake determined from strong-motion,teleseismic,GPS,and leveling[J].Bulletin ofthe Seis-mological Society ofAmerica,1996,86:S49-S70.
[15]Wang Haiyun.Finite fault source model for predicting near fieldstrong ground motion[D].Harbin:Institute of Engineering Me-chanics,China Earthquake Administration,2004.[王海云.近场强地震动预测的有限断层震源模型[D].哈尔滨:中国地震局工程力学研究所,2004.]
[16]Zhang Xiaozhi,Xie Lili,Wang Haiyun,et al.Illustrative exam-ple in simulating near-fault ground motion field by explicit finiteelement method[J].Journal ofEarthquake Engineering and En-gineering Vibration,2005,25(6):5-11.[张晓志,谢礼立,王海云,等.近断层强地面运动影响场显式有限元数值模拟的示意性算例[J].地震工程与工程震动,2005,25(6):5-11.]
[17]Zhang Xiaozhi,Xie Lili,Wang Haiyun,et al.Models and meth-ods for simulating near-fault ground motion field of a city by ex-plicit finite element method[J].Journal ofEarthquake Engineer-ing and Engineering Vibration,2006,26(6):11-16.[张晓志,谢礼立,王海云,等.某正倾滑断层引起的近断层强地面运动的有限元数值模拟[J].地震工程与工程震动,2006,26(6):11-16.]
[18]Pan Bo,Xu Jiandong,Haruko Sekigguchi,et al.Simulation ofthe near-fault strong ground motion in BEIJING region[J].Seis-mology and Geology,2006,28(4):623-634.[潘波,许建东,关口春子,等.北京地区近断层强地震动模拟[J].地震地质,2006,28(4):623-634.]
[19]Reid H F.The earthquake of southeastern Maine,March 21,1904[J].Bulletin ofthe Seismological Society ofAmerica,1911,1:44-47.
[20]O′Connell D R H,Ake J P.Earthquake ground motion estima-tion[C]∥Rodrigue C,Rovai E,eds.Earthquakes:Two-VolumeSet(Hazards and Disasters).New York:Routledge,2001:760.
[21]Miyake H,Iwata T,Irikura K.Source characterization for broad-band ground-motion simulation:Kinematic Heterogeneous sourcemodel and strong motion generation area[J].Bulletin ofthe Seis-mological Society ofAmerica,2003,93(6):2 531-2 545.
[22]Zeng Y,Anderson J,Yu G.A composite source model for com-puting realistic synthetic strong ground motions[J].GeophysicalResearth Letters,1994,21:725-728.
[23]Frankel A.Simulating strong motions of large earthquakes usingrecordings of small earthquakes:The Loma Prieta mainshock as atest case[J].Bulletin ofthe Seismological Society ofAmerica,1995,85:1 144-1 160.
[24]Herrero A,Bernard P.A kinematic self similar rupture processfor earthquakes[J].Bulletin ofthe Seismological SocietyofAmeri-ca,1994,84:1 216-1 228.
[25]Bernard P,Herrero A,Berge C.Modeling directivity of heteroge-neous earthquake rupture[J].Bulletin ofthe Seismological SocietyofAmerica,1996,86:1 149-1 160.
[26]Somerville P,Irikura K,Graves R,et al.Characterizing crustalearthquake slip models for the prediction of strong ground motion[J].Seismological Research Letters,1999,70:59-80.
[27]Mai P M,Beroza G C.Aspatial randomfield model to character-ize complexity in earthquake slip[J].Journal ofGeophysical Re-search,2002,107(B11):2 308.
[28]Hisada Y.Atheoretical omega-square model considering the spa-tial variation in slip and rupture velocity[J].Bulletin ofthe Seis-mological Society ofAmerica,2000,90:387-400.
[29]Hisada Y.Atheoretical omega-square model considering the spa-tial variation in slip and rupture velocity,part 2:Case for a twodimensional source model[J].Bulletin ofthe Seismological Socie-ty ofAmerica,2001,91:651-666.
[30]Gallovic F,Brokesove J.On strong ground motion synthesis withk-2slip distributions[J].Journal ofSeismology,2004,8(2):211-224.
[31]Wang Haiyun,Tao Xiaxin.Characterizing a shallow earthquakeasperity model for predicting near field strong ground motion[J].Journal ofHarbin institute oftechnology,2005,37(11):1 533-1 539.[王海云,陶夏新.近场强地震动预测中浅源地震的Asperity模型特征[J].哈尔滨工业大学学报,2005,37(11):1 533-1 539.]
[32]Silva W J,Lee K.WES RASCAL code for synthesizing earth-quake ground motions[C]∥State of the Art for Assessing Earth-quake Hazards in the United States,Report 24,US Army Engi-neers Waterway Experiment Station,Misc.1987:S-73-1.
[33]Schneider J F,Silva W J,Stark C L.Ground motion model forthe 1989 M6.9 Loma Prieta earthquake including effects ofsource,path,and site[J].Earthquake Spectra,1993,9(2):251-287.
[34]Hutchings L.Kinematic earthquake models and synthesizedground motion using empirical Green′s functions[J].Bulletin ofthe Seismological Society ofAmerica,1994,84:1 028-1 050.
[35]Heaton TH,Hall J F,Wald D J,et al.Response of high-riseand base-isolated buildings to a hypothetical Mw7.0 blind thrustearthquake[J].Science,1995,267:206-211.
[36]Jarpe S P,Kasameyer P W.Validation of a procedure for calcu-lating broadband strong-motion time histories with empiricalGreen′s functions[J].Bulletin ofthe Seismological Society ofA-merica,1996,86:1 116-1 129.
[37]O′Connell D R H.Synthesizing site-specific near-field groundmotinos from reverse faults:New perspectives on peak velocityhazards using broadband site responses[R].Earthquake Engi-neering Research Institude,Proceedings CDROMof the Sixth U.S.National Conference on Earthquake Engineering,1998.
[38]O′Connell D R H.Replication of apparent nonlinear seismic re-sponse with linear wave propagation models[J].Science,1999,283:2 045-2 050.
[39]Zeng Y,Anderson J.Evaluation of numerical procedures for sim-ulating near-fault long-period ground motions using the Zengmethod[R].Pacific Earthquake Engineering Research Center U-tilities Program Report 2000/01,2000.
[40]Day S M.Efficient simulation of constant Q using coarse-grainedmemory variables[J].Bulletin ofthe Seismological Society ofA-merica,1998,88:1 051-1 062.
[41]Boore D M,Joyner WB.Site amplifications for generic rock sites[J].Bulletin ofthe Seismological Society ofAmerica,1997,87(2):327-341.
[42]Anderson J G,Hough S.Amodel for the shape of the fourier am-plitude spectrum of acceleration at high frequencies[J].Bulletinofthe Seismological Society ofAmerica,1984,74(5):1 969-1 993.
[43]Bonilla L F.Computation of linear and nonlinear response fornear field ground motion[D].Santa Barbara:University of Cali-fornia,2000.
[44]Graves R W,Pitarka A,Somerville P G.Ground motion amplifi-cation in the Santa Monica area:Effects of shallow basin edgestructure[J].Bulletin ofthe Seismological Society ofAmerica,1998,88:1 224-1 242.
[45]Kawase H.The cause of the damage belt in Kobe:“The basin-edge effect,”constructive interference of the direct S-wave withthe basin-induced diffracted/Rayleigh waves[J].SeismologicalResearch Letters,1996,67(5):25-34.
[46]Pitarka A,Irikura K,Iwata T,et al.Three-dimensional simula-tion of the near-fault ground motions for the 1995 Hyogo-Nanbu(Kobe),Japan,earthquake[J].Bulletin ofthe Seismological So-ciety ofAmerica,1998,88:428-440.
[47]Alex C M,Olsen K B.Lens-effect in Santa Monica?[J].Geo-physical Researth Letters,1998,25:3 441-3 444.
[48]Davis P M,Rubinstein J L,Liu K H,et al.Northridge earth-quake damage caused by geologic focusing of seismic waves[J].Science,2000,289:1 746-1 750.
[49]Schultz C A.Enhanced backscattering of seismic waves from ir-regular interfaces[D].Cambridge:Massachusetts Institue ofTechnology,1994.
[50]Bouchon M,Schultz C A,Toksoz M N.Effect of three-dimen-sional topography on seismic motion[J].Journal ofGeophysicalResearch,1996,101:5 835-5 846.
[51]Spudich P,Hellweg M,Lee WHK.Directional topographic siteresponse observed in aftershocks of the 1994 Northridge,Califor-nia,earthquake:Implications for main shock motions[J].Bulle-tin of the Seismological Society of America,1996,86:S193-S208.
[52]Stewart J P,Chiou S J,Bray J D,et al.Ground Motion Evalua-tion Procedures for Performance-Based Design[R].PEER Re-port 2001/09.Pacific Earthquake Engineering Research Center,College of Engineering,University of California,Berkeley,2001.
[53]Ashford S A,Sitar N,Lysmer J,et al.Topographic Effects onthe Seismic Response of Steep Slopes[J].Bulletin ofthe Seismo-logical Society ofAmerica,1997,87:701-709.
[54]Ashford S A,Sitar N.Analysis of topographic amplification of in-clined shear waves in a steep coastal bluff[J].Bulletin oftheSeismological Society ofAmerica,1997,87:692-700.
[55]Oreskes N,Shrader-Frechette K,Belitz K.Verification,valida-tion,and confirmation of numerical models in the Earth sciences[J].Science,1994,264:641-646.
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