地震动空间相干函数模型中拟合参数的修正

丁海平 张铭哲

丁海平,张铭哲. 2022. 地震动空间相干函数模型中拟合参数的修正. 地震学报,44(3):501−511 doi: 10.11939/jass.20210006
引用本文: 丁海平,张铭哲. 2022. 地震动空间相干函数模型中拟合参数的修正. 地震学报,44(3):501−511 doi: 10.11939/jass.20210006
Ding H P,Zhang M Z. 2022. Modification of fitting parameters in coherency model for spatial variation of seismic ground motion. Acta Seismologica Sinica,44(3):501−511 doi: 10.11939/jass.20210006
Citation: Ding H P,Zhang M Z. 2022. Modification of fitting parameters in coherency model for spatial variation of seismic ground motion. Acta Seismologica Sinica44(3):501−511 doi: 10.11939/jass.20210006

地震动空间相干函数模型中拟合参数的修正

doi: 10.11939/jass.20210006
基金项目: 国家自然科学基金项目(51678383)资助
详细信息
    作者简介:

    丁海平,博士,教授,主要从事地震工程与防震减灾工程方面的研究,e-mail:hpding@126.com

    通讯作者:

    丁海平,博士,教授,主要从事地震工程与防震减灾工程方面的研究,e-mail:hpding@126.com

  • 中图分类号: P315.9

Modification of fitting parameters in coherency model for spatial variation of seismic ground motion

  • 摘要: 采用SMART-1台阵第5次和第45次地震的水平向分量加速度记录,首先计算了不同间距台站对的地震动空间相干函数;然后讨论了台站距离对相干函数拟合结果的影响,即某一特定距离的相干函数与所有不同距离的相干函数的拟合结果存在明显差异。为减小这一差异,提出了一种对各个不同距离的相干函数拟合参数进行二次回归的方法,并选用Loh相干函数模型进行了验证,最后给出了基于Loh相干函数模型的拟合参数的修正结果。结果表明本文提出的修正方法将大大提高相干函数模型中参数的拟合精度。

     

  • 图  1  SMART-1地震台阵布置图

    Figure  1.  The layout of SMART-1 accelerograph array

    图  2  两次地震震中位置示意图

    Figure  2.  Schematic diagram of the epicenter location of two earthquakes

    图  3  不同间距的相干系数γ与根据所有不同间距的相干系数γ12的拟合曲线对比(以第5次地震为例)

    Figure  3.  Comparison between fitting curves with lagged coherency γ of different distances and fitting curves with lagged coherency γ12 of all distance (taking the 5th earthquake as an example)

    (a) d=200 m;(b) d=282 m;(c) d=400 m;(d) d=800 m;(e) d=980 m;(f) d=1 000 m;(g) d=1 200 m; (h) d=1 732 m;(i) d=1 800 m;(j) d=2 000 m;(k) d=2 200 m;(l) d=3 000 m

    图  4  不同间距的相干系数γ与根据所有不同间距的相干系数γ12的拟合曲线对比 (以第45次地震为例)

    Figure  4.  Comparison between fitting curve with lagged coherency γ of different distances and fitting curve with lagged coherency γ12 of all distance(taking the 45th earthquake as an example)

    (a) d=200 m;(b) d=282 m;(c) d=400 m;(d) d=800 m;(e) d=980 m;(f) d=1 000 m;(g) d=1 200 m; (h) d=1 732 m;(i) d=1 800 m;(j) d=2 000 m;(k) d=2 200 m;(l) d=3 000 m

    图  5  第5次(蓝色)和第45次(红色)地震的参数a (a),b (b)值随距离的变化及修正结果

    Figure  5.  Changes of parameters a (a) and b (b) with distance and modified results of the 5th (blue) and the 45th (red) earthquakes

    图  6  基于Loh相干函数模型,不同间距的相干系数γ、由所有不同间距的相干系数γ12和修正后的相干系数γs拟合曲线对比(以第5次地震为例)

    Figure  6.  Based on Loh coherency function model,comparison of fitting curve with lagged coherency γ of different distances,fitting curve with lagged coherency γ12 of all distance and fitting curve with lagged coherency γs of modified parameter (taking the 5th earthquake as an example)

    图  7  基于LOH相干函数模型,不同间距的相干系数γ、根据所有不同间距的相干系数γ12和修正后的相干系数γs拟合曲线对比(以第45次地震为例)

    Figure  7.  Based on Loh coherency function model,comparison of fitting curve of lagged coherency γ of different distances,fitting curve of lagged coherency of all distance γ12 and fitting curve with lagged coherency of modified parameter γs (taking the 45th earthquake as an example)

    图  8  不同间距的相干系数经修正前γ、后γs的拟合曲线与根据所有不同间距的相干系数γ12拟合曲线的比较(以两次地震为例)

    Figure  8.  Comparison of fitting curve of lagged coherency γ of different distances,fitting curve of lagged coherency γ12 of all distance and fitting curve with lagged coherency γs of modified parameter (take two earthquakes as examples)

    表  1  台站间距和对应的台站对及数量

    Table  1.   Distance between stations and the corresponding number of station pairs

    台站距离d/m台站对台站对个数台站距离d/m台站对台站对个数
    200 C00−I03 4 1 200 I06−M12 2
    282 I03−I06 2 1 732 M06−O09 2
    400 I03−I09 2 1 800 I03−O03 2
    800 I03−M03 2 2 000 C00−O03 4
    980 I03−M06 2 2 200 I03−O09 2
    1 000 C00−M03 4 3 000 M03−O09 2
    下载: 导出CSV

    表  2  基于Loh相干函数模型的拟合系数结果

    Table  2.   Fitting coefficient results based on Loh coherency function model

    台站距离d/m第5次地震 第45次地震
    ab ab
    200 0.476 49 0.000 72 0.299 25 0.001 60
    282 0.328 58 0.000 38 0.359 96 0.001 10
    400 0.300 20 0.000 29 0.461 33 0.000 88
    800 0.305 26 0.000 21 0.408 63 0.000 46
    980 0.325 09 0.000 11 0.449 52 0.000 23
    1 000 0.260 01 0.000 13 0.496 97 0.000 38
    1 200 0.208 47 0.000 08 0.471 04 0.000 16
    1 732 0.193 98 0.000 04 0.475 44 0.000 06
    1 800 0.180 25 0.000 04 0.425 02 0.000 05
    2 000 0.169 69 0.000 06 0.449 15 0.000 07
    2 200 0.161 71 0.000 04 0.374 76 0.000 05
    3 000 0.164 18 0.000 00 0.321 45 0.000 01
    12d 0.189 77 0.000 08 0.357 08 0.000 36
    下载: 导出CSV

    表  3  ab二次拟合系数的修正结果

    Table  3.   Modified results of a and b

    地震a1a2a3b1b2b3
    第5次 0.733 53 −0.133 37 −0.482 98 0.000 10 −0.114 25 −0.805 45
    第45次 −0.000 57 −3.410 92 0.432 46 0.000 82 0.573 00 −2.470 90
    下载: 导出CSV

    表  4  a b的统一修正结果

    Table  4.   Unified modified results of a and b

    a1 a2 a3 b1 b2 b3
    −0.022 1.759 9 0.416 3 0.011 9 1.531 3 −4.367
    下载: 导出CSV
  • [1] 丁海平,罗翼,饶威波,朱越. 2018. 截止频率的取值对地震动空间相干函数统计结果的影响[J]. 地震学报,40(5):664–672.
    [2] Ding H P,Luo Y,Rao W B,Zhu Y. 2018. The influence of cut-off frequency on the statistical results of spatial coherency function of seismic ground motion[J]. Acta Seismologica Sinica,40(5):664–672 (in Chinese).
    [3] 李英民,吴哲骞,陈辉国. 2013. 地震动的空间变化特性分析与修正相干模型[J]. 振动与冲击,32(2):164–170. doi: 10.3969/j.issn.1000-3835.2013.02.032
    [4] Li Y M,Wu Z Q,Chen H G. 2013. Analysis and modeling for characteristics of spatially varying ground motion[J]. Journal of Vibration and Shock,32(2):164–170 (in Chinese).
    [5] 刘先明,叶继红,李爱群. 2004. 竖向地震动场的空间相干函数模型[J]. 工程力学,21(2):140–144. doi: 10.3969/j.issn.1000-4750.2004.02.024
    [6] Liu X M,Ye J H,Li A Q. 2004. Space coherency function model of vertical ground motion[J]. Engineering Mechanics,21(2):140–144 (in Chinese).
    [7] 屈铁军,王君杰,王前信. 1996. 空间变化的地震动功率谱的实用模型[J]. 地震学报,18(1):55–62.
    [8] Qu T J,Wang J J,Wang Q X. 1996. A practical model for the power spectrum of spatial variant ground motion[J]. Acta Seismologica Sinica,18(1):69–79.
    [9] 饶威波,丁海平,罗翼. 2018. 台站间距d 的分布对地震动空间相干函数的影响[J]. 地震工程与工程振动,38(3):103–109.
    [10] Rao W B,Ding H P,Luo Y. 2018. The influence of the distribution of station distance d on the ground motion’s coherence function[J]. Earthquake Engineering and Engineering Dynamics,38(3):103–109 (in Chinese).
    [11] Abrahamson N A,Bolt B A,Darragh R B,Penzien J,Tsai Y B. 1987. The SMART-I accelerograph array (1980−1987):A review[J]. Earthq Spectra,3(2):263–287. doi: 10.1193/1.1585428
    [12] Abrahamson N A,Schneider J F,Stepp J C. 1991. Empirical spatial coherency functions for application to soil-structure interaction analyses[J]. Earthq Spectra,7(1):1–27. doi: 10.1193/1.1585610
    [13] Abrahamson N A. 1993. Spatial variation of multiple support inputs[C]//Proceedings of the 1st U.S. Seminar on Seismic Evaluation and Retrofit of Steel Bridges. San Francisco, California: A Caltrans and University of California at Berkeley Seminar.
    [14] Bi K M,Hao H,Chouw N. 2013. 3D FEM analysis of pounding response of bridge structures at a canyon site to spatially varying ground motions[J]. Adv Struct Eng,16(4):619–640. doi: 10.1260/1369-4332.16.4.619
    [15] Chopra A K,Wang J T. 2010. Earthquake response of arch dams to spatially varying ground motion[J]. Earthq Eng Struct Dyn,39(8):887–906.
    [16] der Kiureghian A. 1996. A coherency model for spatially varying ground motions[J]. Earthq Eng Struct Dyn,25(1):99–111. doi: 10.1002/(SICI)1096-9845(199601)25:1<99::AID-EQE540>3.0.CO;2-C
    [17] Hao H. 1989. Effects of Spatial Variation of Ground Motions on Large Multiply-Supported Structures[R]. Berkeley: University of California: 18–27.
    [18] Harichandran R S,Vanmarcke E H. 1986. Stochastic variation of earthquake ground motion in space and time[J]. J Eng Mech,112(2):154–174. doi: 10.1061/(ASCE)0733-9399(1986)112:2(154)
    [19] Li C,Hao H,Li H N,Bi K M,Chen B K. 2017. Modeling and simulation of spatially correlated ground motions at multiple onshore and offshore sites[J]. J Earthq Eng,21(3):359–383. doi: 10.1080/13632469.2016.1172375
    [20] Liu C,Gao R. 2018. Design method for steel restrainer bars on railway bridges subjected to spatially varying earthquakes[J]. Eng Struct,159:198–212. doi: 10.1016/j.engstruct.2018.01.001
    [21] Loh C H. 1985. Analysis of the spatial variation of seismic waves and ground movements from SMART-1 array data[J]. Earthq Eng Struct Dyn,13(5):561–581. doi: 10.1002/eqe.4290130502
    [22] Park D,Sagong M,Kwak D Y,Jeong C G. 2009. Simulation of tunnel response under spatially varying ground motion[J]. Soil Dyn Earthq Eng,29(11/12):1417–1424.
    [23] Wu Y X,Gao Y F,Zhang N,Li D Y. 2016. Simulation of spatially varying ground motions in V-shaped symmetric canyons[J]. J Earthq Eng,20(6):992–1010. doi: 10.1080/13632469.2015.1010049
    [24] Zerva A. 2009. Spatial Variation of Seismic Ground Motions: Modeling and Engineering Applications[M]. New York: CRC Press: 96–119.
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出版历程
  • 收稿日期:  2021-01-17
  • 修回日期:  2021-03-27
  • 网络出版日期:  2022-08-10
  • 刊出日期:  2022-06-27

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