模拟的近断裂地震动场的空间相关性
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摘要
随着经济建设的发展,国内外都建造了许多大型空间结构。大跨度空间结构的地震动输入,需要考虑非一致的多点输入。目前一些研究者建议的多点输入地震动合成方法,需要根据密集台阵记录统计得到的相干函数,难于用于缺乏密集台阵观测记录的工程场地。另外,近场地震动受震源影响更为复杂,在近断层场地的多点输入合成方法中,应该考虑近断裂效应等重要的工程特性。
作者导师领导的课题组发展了一套估计近场地震动的新方法,即用有限断层表征震源,用随机方法合成高频地震动,用简化的数值格林函数方法计算低频地震动,将两部分地震动分别滤波后在时域中叠加。
本文在系统介绍方法的主要步骤的基础上,采用这套方法计算得到的马衔山北缘断裂中东段设定7.0级地震引起的兰州市及周边地区的地震动场数据,借助相干函数方法计算、分析了地震动场中表达的空间相关性。依次计算了选定点对间高频地震动、低频地震动和合成的宽频带地震动的相干系数,分析其随频率和距离变化的规律,并与现有的根据密集台阵观测数据统计的规律进行对比。结果表明,所用地震动场数据在低频段内相干系数达到0.9以上,显示了很强的相关性;在高频段相干性较差,有明显的振荡。另外,相干系数随距离的增大而减小,在低频段尤为明显。这两点结论与许多根据密集台阵观测数据统计分析的结论相符合。
本文结果验证了作者导师课题组发展的近场地震动估计方法能够表达近场地震动的空间相关性,可以用于大跨度空间结构的多点地震动输入。
With the development of economy, more and more extended structures appeared. Multiple-support excitation should be taken into account in the seismic analysis of this kind of structures. All the methods of Multiple-support excitation synthesis proposed so far need a coherence function based on records from dense seismic arrays, which made them unavailable for areas where earthquake records are insufficient. In addition, ground motion in the near-field is more complex than that in the far-field due to the effect of the source. The important engineering features of near-field ground motion, such as the directivity effect, should be considered in the multiple-support excitation synthesis in the near-fault field.
A new method was developed by the team lead by the author’s supervisor. In this method, the source is characterized by finite fault model, ground motions of short and long period range are simulated by the stochastic synthesis method and the numerical Green’s function method respectively, then two parts of ground motions are superposed in time domain after filtering.
The key procedure to apply the new method was introduced. Then, Near-source strong ground motion field in Lanzhou city and its vicinity caused by M7.0 earthquake from the middle-eastern segment of the northern margin of Maxianshan fault was simulated by the new method and used to analyze the spatial correlation. Coherence coefficients of high- and low-frequency and superposed ground motion for the specified station pairs were computed in turn to analyze the dependence of coherence coefficient on distance and on frequency. Results show that: 1. The coherence coefficient of the analyzed ground motion field is beyond 0.9 in the frequency range of lower than 1 Hz, which indicates a very good correlation, whereas that in the frequency range of higher than 1 Hz is lower than 0.7 which could be interpreted by the randomness of high-frequency ground motion;2. The coherence coefficients of high- and low-frequency and superposed ground motion all decrease as distance increases. These conclusions are consistent with those drawn from the statistical analysis of array records, which proves that simulation method by our team can characterize the spatial correlation and is available to the multiple-support excitation synthesis of extended structures.
作者导师领导的课题组发展了一套估计近场地震动的新方法,即用有限断层表征震源,用随机方法合成高频地震动,用简化的数值格林函数方法计算低频地震动,将两部分地震动分别滤波后在时域中叠加。
本文在系统介绍方法的主要步骤的基础上,采用这套方法计算得到的马衔山北缘断裂中东段设定7.0级地震引起的兰州市及周边地区的地震动场数据,借助相干函数方法计算、分析了地震动场中表达的空间相关性。依次计算了选定点对间高频地震动、低频地震动和合成的宽频带地震动的相干系数,分析其随频率和距离变化的规律,并与现有的根据密集台阵观测数据统计的规律进行对比。结果表明,所用地震动场数据在低频段内相干系数达到0.9以上,显示了很强的相关性;在高频段相干性较差,有明显的振荡。另外,相干系数随距离的增大而减小,在低频段尤为明显。这两点结论与许多根据密集台阵观测数据统计分析的结论相符合。
本文结果验证了作者导师课题组发展的近场地震动估计方法能够表达近场地震动的空间相关性,可以用于大跨度空间结构的多点地震动输入。
With the development of economy, more and more extended structures appeared. Multiple-support excitation should be taken into account in the seismic analysis of this kind of structures. All the methods of Multiple-support excitation synthesis proposed so far need a coherence function based on records from dense seismic arrays, which made them unavailable for areas where earthquake records are insufficient. In addition, ground motion in the near-field is more complex than that in the far-field due to the effect of the source. The important engineering features of near-field ground motion, such as the directivity effect, should be considered in the multiple-support excitation synthesis in the near-fault field.
A new method was developed by the team lead by the author’s supervisor. In this method, the source is characterized by finite fault model, ground motions of short and long period range are simulated by the stochastic synthesis method and the numerical Green’s function method respectively, then two parts of ground motions are superposed in time domain after filtering.
The key procedure to apply the new method was introduced. Then, Near-source strong ground motion field in Lanzhou city and its vicinity caused by M7.0 earthquake from the middle-eastern segment of the northern margin of Maxianshan fault was simulated by the new method and used to analyze the spatial correlation. Coherence coefficients of high- and low-frequency and superposed ground motion for the specified station pairs were computed in turn to analyze the dependence of coherence coefficient on distance and on frequency. Results show that: 1. The coherence coefficient of the analyzed ground motion field is beyond 0.9 in the frequency range of lower than 1 Hz, which indicates a very good correlation, whereas that in the frequency range of higher than 1 Hz is lower than 0.7 which could be interpreted by the randomness of high-frequency ground motion;2. The coherence coefficients of high- and low-frequency and superposed ground motion all decrease as distance increases. These conclusions are consistent with those drawn from the statistical analysis of array records, which proves that simulation method by our team can characterize the spatial correlation and is available to the multiple-support excitation synthesis of extended structures.
引文
[1]陈原.非一致激励条件下工程场地地震动相干函数的数值模拟——Ⅱ分析方法的应用[J].地震工程与工程振动,2006,26(1):36-42.
[2]陈原,李杰.一致激励条件下非线性工程场地地震动相干函数分析[J].防灾减灾工程学报,2006,26(4):369-376.
[3]陈原,李杰.考虑岩土介质随机特性的工程场地地震动相干函数研究[J].世界地震工程,2007,23(3):1-6.
[4]丁海平,刘启方,金星,袁一凡.基岩地震动的一个相干函数模型-走滑断层情形[J].地震学报,2004,26(1):62-67.
[5]冯启民,胡聿贤.空间相关地面运动的数学模型[J].地震工程与工程振动,1981,1(2):1-8.
[6]冯启民.地震动随机理论[J].世界地震工程.1986, 11(3):11-16.
[7]金星,廖振鹏.地震动随机场的物理模拟[J].地震工程与工程振动,1994,14(3):11-19.
[8]李小军,赵风新,胡聿贤.空间相关地震动场模拟的研究[J].地震学报,1997,19(2):212-215.
[9]金星,陈超,张明宇.震源对地震动空间相关性影响的定量研究[J].地震工程与工程振动,2000,20(1):1-10.
[10]金星,陈超,张明宇.单侧破裂震源对地震动空间相关性影响的远场分析[J].地震学报,2000,22(5):509-516.
[11]金星,陈超,张明宇.双侧破裂震源对地震动空间相关性影响的远场分析[J].自然灾害学报,2001,10(1):51-58.
[12]金星,刘启方.断层附近强地震动半经验合成方法的研究[J].地震工程与工程震动. 2002,22(4):22-27.
[13]李杰,廖松涛.工程场地地震动相干函数的数值模拟[J].地震工程与工程振动,2003,23(2):12-17.
[14]李杰.非一致激励条件下工程场地地震动相干函数的数值模拟——Ⅰ分析原理和方法[J].地震工程与工程振动,2006,26(1):30-35.
[15]廖振鹏著.工程波动理论导论(第二版)[M].科学出版社,2002.
[16]刘先明,叶继红,李爱群.空间相关多点地震动合成的简化方法[J].工程抗震,2003,(3):30-36.
[17]刘启方.断层附近强地面运动的初步研究[D].中国地震局工程力研究所. 2001.
[18]倪永军.考虑时间-空间变化的人工随机场模拟[J].地震学报,2002,24(4):407-412.
[19]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.
[20]屈铁军,王前信.空间相关的多点地震动合成基本公式[J].地震工程与工程振动,1998,18(1):8-15.
[21]孙平善.断层对地震动影响的分析方法研究.国家自然科学基金资助项目[R]. 1999.
[22]孙晓丹.震源对大跨度空间结构地震动输入的影响[D].哈尔滨工业大学. 2005.
[23]陶夏新,王国新.近场强地震动模拟中对破裂的方向性效应和上盘效应的表达[J].地震学报,2003,25(2):191-198.
[24]陶夏新等.兰州市活断层地震危害性评价报告[R]. 2007.
[25]王海云.近场强地震动预测的有限度断层震源模型[D].中国地震局工程力学研究所. 2004.
[26]谢礼立,陶夏新,王国新.强地震动估计和地震危险性评定[J].东北地震研究,2001,17(1):1-8.
[27]王前信.地面运动相位差对单层长建筑抗震分析的影响[R].中国科学院工程力学研究所研究报告集第三集. 1997.
[28]张冬丽.基于数值格林函数方法的近场长周期强地震动模拟[D].中国地震局工程力学研究所. 2005.
[29]张冬丽,陶夏新,周正华.关于有限断层计算模型的研究——考虑位错时、空不均匀分布的滑动时间函数[J].西北地震学报,2005,27(3):193-198.
[30]张敏政.强震震源和强震地震动的模拟(上)[J].世界地震工程,1988,(2):28-29.
[31]钟菊芳.同一测点不同地震动分量空间相干性分析[J].地震研究,2005,28(4):378-382.
[32]周正华.近断层强地面运动数值模拟[R].哈尔滨工业大学. 2003.
[33] C.H.Loh, Analysis of the spatial variation of seismic waves and ground movements from SMART-1 Array data [J], E.E.S.D, vol.13:561-581.
[34] D.J.Andrews. A Stochastic Fault Model, 1. Static Case [J]. J. Geophys. Res. 1980, (85):3867-3877.
[35] D.J.Andrews. A stochastic fault model, 2.Time-Independent case [J]. J. Geophys.Res.1980, (86):821-834.
[36] D.M.Boore. Stochastic Simulation of high-frequency Ground Motions Based on Seismological Models of the Radiated Spectra [J]. Bull. Seism. Soc. Am. 1983, (73):1865-1894.
[37] H.Hao, C.S.Oliveira, J. Penzien. Multiple-station ground motion processing and simulation based on SMATR-1 array data [J], nuclear engineering and design, 1989.293-310.
[38] J.G.Aderson, S.E.Hough. A Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at High Frequency [J]. Bull.Seismol.Soc.Am.1984,(74):1969-1993.
[39] K.Aki and P.G.Richards. Quantitative Seismology Theory and Methods [M]. Vols. 1, 2, Freeman, 1980, San Francisco, 1-932.
[40] K.Irikura. Semi-empirical Estimation of Strong Ground Motions during Large Earthquake [J]. Bull. Disaster Prevention Research Institute, 1983,(33):63-104.
[41] N.A.Haskell. Total Energy and Energy Spectral Density of Elastic Wave Radiation from Propagation Faults [J]. Bull.Seismol.Soc.Am.1964 ,(54):1811-1841.
[42] N.A.Abrahason, B.A.Bolt, R.B.Darragh, J.Penzien, andY.B.Tsai. TheSMART-1 accelerograph array (1980-1987): a review [J]. Earthquake Spectra, 1987.Vol.7, No.1:263-287.
[43] P.K.Somerville, K.Irikura, R.Graves, S.Sawada, D.Wald, N.Abrahamson, Y.Iwasaki, T.Kagawa, N.Smith, A.Kowada. Characterizing crustal Earthquake Slip Models for the Prediction of Strong Ground Motion [J]. Seism.Res.Lett.1999, 70(1):59-80.
[44] R.Harichandran, E.Vanmarcke. Stochastic Variation of Earthquake Ground in Space and Time [J], ASCE. J. EM. 112(2).
[45] SUN Xiaodan, TAO Xiaxin, Tang Aiping, LU Jianbo. Hybrid Slip Model for Near-field Ground Motion Prediction Based on Uncertainty of Source Parameters [J]. Transaction of Tianjin University. Accepted.
[46] T.C.Hanks, R.K.McGuire. The Character of High-Frequency Strong Ground Motion [J].Bull.Seismol.Soc.Am.1981, (7):2071-2095.
[47] Tao Xiaxin, J.G.Anderson. Near Field Strong ground Motion Simulation[C]. Proc. of ICANCEER. 2002.
[48] TAO Xiaxin and WANG Haiyun, A random source model for near filed strong ground motion prediction[C]. Proc. of 13WCEE, Vancouver. Paper No.1945.
[49] Wang Guoxin, Tao Xiaxin. Strong ground Motion of the 1994 M6.7 Northridge Earthquake Simulated by Stochastic Approach [C]. Proc. of IASPEI Assembly.2001.
[50] Y.Zeng, J.G.Anderson, Y.Guang. A composite Source Model for Computing Elastic Synthetic Strong Ground Motions. Reference [J]. Geophys. Res. Lett.1994, (21):725-778.
[2]陈原,李杰.一致激励条件下非线性工程场地地震动相干函数分析[J].防灾减灾工程学报,2006,26(4):369-376.
[3]陈原,李杰.考虑岩土介质随机特性的工程场地地震动相干函数研究[J].世界地震工程,2007,23(3):1-6.
[4]丁海平,刘启方,金星,袁一凡.基岩地震动的一个相干函数模型-走滑断层情形[J].地震学报,2004,26(1):62-67.
[5]冯启民,胡聿贤.空间相关地面运动的数学模型[J].地震工程与工程振动,1981,1(2):1-8.
[6]冯启民.地震动随机理论[J].世界地震工程.1986, 11(3):11-16.
[7]金星,廖振鹏.地震动随机场的物理模拟[J].地震工程与工程振动,1994,14(3):11-19.
[8]李小军,赵风新,胡聿贤.空间相关地震动场模拟的研究[J].地震学报,1997,19(2):212-215.
[9]金星,陈超,张明宇.震源对地震动空间相关性影响的定量研究[J].地震工程与工程振动,2000,20(1):1-10.
[10]金星,陈超,张明宇.单侧破裂震源对地震动空间相关性影响的远场分析[J].地震学报,2000,22(5):509-516.
[11]金星,陈超,张明宇.双侧破裂震源对地震动空间相关性影响的远场分析[J].自然灾害学报,2001,10(1):51-58.
[12]金星,刘启方.断层附近强地震动半经验合成方法的研究[J].地震工程与工程震动. 2002,22(4):22-27.
[13]李杰,廖松涛.工程场地地震动相干函数的数值模拟[J].地震工程与工程振动,2003,23(2):12-17.
[14]李杰.非一致激励条件下工程场地地震动相干函数的数值模拟——Ⅰ分析原理和方法[J].地震工程与工程振动,2006,26(1):30-35.
[15]廖振鹏著.工程波动理论导论(第二版)[M].科学出版社,2002.
[16]刘先明,叶继红,李爱群.空间相关多点地震动合成的简化方法[J].工程抗震,2003,(3):30-36.
[17]刘启方.断层附近强地面运动的初步研究[D].中国地震局工程力研究所. 2001.
[18]倪永军.考虑时间-空间变化的人工随机场模拟[J].地震学报,2002,24(4):407-412.
[19]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.
[20]屈铁军,王前信.空间相关的多点地震动合成基本公式[J].地震工程与工程振动,1998,18(1):8-15.
[21]孙平善.断层对地震动影响的分析方法研究.国家自然科学基金资助项目[R]. 1999.
[22]孙晓丹.震源对大跨度空间结构地震动输入的影响[D].哈尔滨工业大学. 2005.
[23]陶夏新,王国新.近场强地震动模拟中对破裂的方向性效应和上盘效应的表达[J].地震学报,2003,25(2):191-198.
[24]陶夏新等.兰州市活断层地震危害性评价报告[R]. 2007.
[25]王海云.近场强地震动预测的有限度断层震源模型[D].中国地震局工程力学研究所. 2004.
[26]谢礼立,陶夏新,王国新.强地震动估计和地震危险性评定[J].东北地震研究,2001,17(1):1-8.
[27]王前信.地面运动相位差对单层长建筑抗震分析的影响[R].中国科学院工程力学研究所研究报告集第三集. 1997.
[28]张冬丽.基于数值格林函数方法的近场长周期强地震动模拟[D].中国地震局工程力学研究所. 2005.
[29]张冬丽,陶夏新,周正华.关于有限断层计算模型的研究——考虑位错时、空不均匀分布的滑动时间函数[J].西北地震学报,2005,27(3):193-198.
[30]张敏政.强震震源和强震地震动的模拟(上)[J].世界地震工程,1988,(2):28-29.
[31]钟菊芳.同一测点不同地震动分量空间相干性分析[J].地震研究,2005,28(4):378-382.
[32]周正华.近断层强地面运动数值模拟[R].哈尔滨工业大学. 2003.
[33] C.H.Loh, Analysis of the spatial variation of seismic waves and ground movements from SMART-1 Array data [J], E.E.S.D, vol.13:561-581.
[34] D.J.Andrews. A Stochastic Fault Model, 1. Static Case [J]. J. Geophys. Res. 1980, (85):3867-3877.
[35] D.J.Andrews. A stochastic fault model, 2.Time-Independent case [J]. J. Geophys.Res.1980, (86):821-834.
[36] D.M.Boore. Stochastic Simulation of high-frequency Ground Motions Based on Seismological Models of the Radiated Spectra [J]. Bull. Seism. Soc. Am. 1983, (73):1865-1894.
[37] H.Hao, C.S.Oliveira, J. Penzien. Multiple-station ground motion processing and simulation based on SMATR-1 array data [J], nuclear engineering and design, 1989.293-310.
[38] J.G.Aderson, S.E.Hough. A Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at High Frequency [J]. Bull.Seismol.Soc.Am.1984,(74):1969-1993.
[39] K.Aki and P.G.Richards. Quantitative Seismology Theory and Methods [M]. Vols. 1, 2, Freeman, 1980, San Francisco, 1-932.
[40] K.Irikura. Semi-empirical Estimation of Strong Ground Motions during Large Earthquake [J]. Bull. Disaster Prevention Research Institute, 1983,(33):63-104.
[41] N.A.Haskell. Total Energy and Energy Spectral Density of Elastic Wave Radiation from Propagation Faults [J]. Bull.Seismol.Soc.Am.1964 ,(54):1811-1841.
[42] N.A.Abrahason, B.A.Bolt, R.B.Darragh, J.Penzien, andY.B.Tsai. TheSMART-1 accelerograph array (1980-1987): a review [J]. Earthquake Spectra, 1987.Vol.7, No.1:263-287.
[43] P.K.Somerville, K.Irikura, R.Graves, S.Sawada, D.Wald, N.Abrahamson, Y.Iwasaki, T.Kagawa, N.Smith, A.Kowada. Characterizing crustal Earthquake Slip Models for the Prediction of Strong Ground Motion [J]. Seism.Res.Lett.1999, 70(1):59-80.
[44] R.Harichandran, E.Vanmarcke. Stochastic Variation of Earthquake Ground in Space and Time [J], ASCE. J. EM. 112(2).
[45] SUN Xiaodan, TAO Xiaxin, Tang Aiping, LU Jianbo. Hybrid Slip Model for Near-field Ground Motion Prediction Based on Uncertainty of Source Parameters [J]. Transaction of Tianjin University. Accepted.
[46] T.C.Hanks, R.K.McGuire. The Character of High-Frequency Strong Ground Motion [J].Bull.Seismol.Soc.Am.1981, (7):2071-2095.
[47] Tao Xiaxin, J.G.Anderson. Near Field Strong ground Motion Simulation[C]. Proc. of ICANCEER. 2002.
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