基于拉普拉斯变换构建校正窄频速度记录的传递函数

孙艺璇, 徐国林

孙艺璇,徐国林. 2023. 基于拉普拉斯变换构建校正窄频速度记录的传递函数. 地震学报,45(1):107−115. DOI: 10.11939/jass.20210182
引用本文: 孙艺璇,徐国林. 2023. 基于拉普拉斯变换构建校正窄频速度记录的传递函数. 地震学报,45(1):107−115. DOI: 10.11939/jass.20210182
Sun Y X,Xu G L. 2023. A transfer function based on Laplace transform for correcting narrow-frequency velocity recording. Acta Seismologica Sinica45(1):107−115. DOI: 10.11939/jass.20210182
Citation: Sun Y X,Xu G L. 2023. A transfer function based on Laplace transform for correcting narrow-frequency velocity recording. Acta Seismologica Sinica45(1):107−115. DOI: 10.11939/jass.20210182

基于拉普拉斯变换构建校正窄频速度记录的传递函数

基金项目: 国家自然科学基金(52268051)资助
详细信息
    作者简介:

    孙艺璇,在读硕士研究生,主要从事结构地震反应分析方法研究,e-mail:1374714132@qq.com

    通讯作者:

    徐国林,博士,教授,主要从事结构地震反应分析方法研究,e-mail:guolin.xu@swfu.edu.cn

  • 中图分类号: P315.31

A transfer function based on Laplace transform for correcting narrow-frequency velocity recording

  • 摘要: 受窄频地震仪平坦响应范围影响,窄频速度记录存在低频成分失真问题,导致地震记录可用范围受限。针对此问题,本文推导基于拉普拉斯变换和双线性变换的传递函数,实现由窄频地震记录向宽频地震记录的校正,并以日本Hi-net速度记录为例进行验证,将校正后的速度记录与同台KiK-net加速度积分所得的速度记录予以对比。结果显示,原始速度记录在低频处存在失真,而校正后的波形与KiK-net加速度积分速度记录波形一致,这表明改进的传递函数能有效地解决原速度记录中的低频成分失真问题,有效地拓宽了低频可使用范围,而且相较于Nakata校正速度记录方法,以本文给出的传递函数校正的速度记录在振幅和波形等方面的精度更高。
    Abstract: Affected by the flat response range of the narrow-band seismograph, the narrow-band velocity recording has the problem of low-frequency component distortion, which limits the usable range of the seismic recording. To solve this problem, this paper deduces an improved transfer function based on the Laplace transform and bilinear transform to realize the correction from narrow-band seismic records to broadband ones. And then the Japanese Hi-net velocity records are used as an example for correction, and the corrected velocity records are compared with the KiK-net acceleration integral velocity records from the same station. The results show that the original velocity records are distorted at low frequencies, while the corrected waveforms are consistent with the KiK-net acceleration integral velocity records. The analyse show that the improved transfer function can effectively solve the distortion of the low-frequency components in the original velocity records, which effectively widens the usable range of low-frequency. Moreover, compared with the Nakata-corrected velocity recording method, the velocity recording corrected with the transfer function given in this paper is more accurate in terms of amplitude and waveform.
  • 图  3   算例记录的速度反应谱

    (a) 茨城县地震;(b) 宫城地震;(c) 磐城县地震;(d) 福岛县地震

    Figure  3.   Velocity response spectrum of example recordings

    (a) Ibaraki earthquake;(b) Miyagi earthquake;(c) Iwaki earthquake;(d) Fukushima earthquake

    图  1   算例速度频谱图

    (a) 茨城县地震;(b) 宫城地震;(c) 磐城县地震;(d) 福岛县地震

    Figure  1.   Velocity spectra of examples

    (a) Ibaraki earthquake;(b) Miyagi earthquake;(c) Iwaki earthquake;(d) Fukushima earthquake

    图  2   算例不同频段的速度时程图

    (a) 茨城县地震;(b) 宫城地震;(c) 磐城县地震;(d) 福岛县地震

    Figure  2.   Velocity time histories of the examples in different frequency bands

    (a) Ibaraki earthquake;(b) Miyagi earthquake;(c) Iwaki earthquake;(d) Fukushima earthquake

    图  4   利用Nakata方法与本文方法校正所得的福岛县地震结果对比

    (a) 频谱图;(b) 分频段时程图

    Figure  4.   Comparison of the corrected results of the Fukushima earthquake by the Nakata method with those by the method proposed in this paper

    (a) Spectrum map;(b) Time histories in different frequency bands

    表  1   校正窄频速度记录的传递函数系数

    Table  1   Transfer function coefficient for correcting narrow-band velocity recording

    aibi
    i=01.044 9841.000 370
    i=1−1.998 024−1.999 999
    i=20.956 9900.999 629
    下载: 导出CSV

    表  2   本研究所用的日本同台站地震记录

    Table  2   Earthquake records at the same station in Japan

    编号Hi-net
    站点
    地震名称发震时间(JST)震中位置震源
    深度/km
    M方向KiK-net
    站点
    记录信噪比
    年-月-日时:分:秒北纬/°东经/°速度加速度
    1 N.TSKH 茨城县地震 2008-05-08 01:45:00 36.227 141.607 51 7.0 EW IBRH19 72.45 48.55
    2 N.TSKH 宫城地震 2011-04-07 03:54:00 38.20 141.92 66 7.1 EW IBRH19 23.97 12.10
    3 N.TSKH 磐城县地震 2011-07-31 03:54:00 36.90 141.22 57 6.5 NS IBRH19 102.16 52.60
    4 N.TSKH 福岛县地震 2021-02-13 08:00:00 37.73 141.70 55 7.3 EW IBRH19 85.30 55.51
    下载: 导出CSV

    表  3   本文方法和Nakata方法校正速度记录峰值对比

    Table  3   Comparison of the peak value of the correction velocity recording by this method with that by the Nakata method

    地震原始Hi-net速度记录
    峰值/(10−5 m·s−1
    KiK-net积分速度记录
    峰值/(10−5 m·s−1
    校正的Hi-net速度记录峰值/(10−5 m·s−1
    本文方法Nakata方法
    茨城县地震5.08.28.25.5
    宫城地震2.45.45.13.3
    磐城县地震3.94.34.13.5
    福岛县地震5.910.29.76.5
    下载: 导出CSV
  • 冯静,高孟潭,胥广银,陈鲲. 2013. Hi-net速度微分与KiK-net加速度对比研究[J]. 地震学报,35(6):902–913. doi: 10.3969/j.issn.0253-3782.2013.06.013

    Feng J,Gao M T,Xu G Y,Chen K. 2013. A comparative study on Hi-net velocity differential and KiK-net acceleration[J]. Acta Seismologica Sinica,35(6):902–913 (in Chinese).

    金星,马强,李山有. 2004. 利用数字化速度记录实时仿真位移与加速度时程[J]. 地震工程与工程振动,24(6):9–14. doi: 10.3969/j.issn.1000-1301.2004.06.002

    Jin X,Ma Q,Li S Y. 2004. Real-time simulation of ground displacement and acceleration using digital velocity record[J]. Earthquake Engineering and Engineering Vibration,24(6):9–14 (in Chinese).

    李永振,金震,梁永朵,于沈平,刘琳婷. 2012. 利用数字化加速度记录仿真速度及位移时程应用研究[J]. 防灾减灾学报,28(3):32–36. doi: 10.3969/j.issn.1674-8565.2012.03.006

    Li Y Z,Jin Z,Liang Y D,Yu S P,Liu L T. 2012. Study of simulation speed and displacement time history recorded by digital acceleration[J]. Journal of Disaster Prevention and Reduction,28(3):32–36 (in Chinese).

    马强,金星,李山有. 2003. 单自由度系统地震动力反应的实时计算方法[J]. 地震工程与工程振动,23(5):61–68. doi: 10.3969/j.issn.1000-1301.2003.05.011

    Ma Q,Jin X,Li S Y. 2003. Real-time algorithm of seismic dynamic response for SDOF system[J]. Earthquake Engineering and Engineering Vibration,23(5):61–68 (in Chinese).

    潘岳怡,牟剑英,谢夜玉,符衡,张清. 2019. 广西地区测震记录与强震动记录一致性分析:以广西北流MS5.2地震为例[J]. 华北地震科学,37(增刊):38–42.

    Pan Y Y,Mou J Y,Xie Y Y,Fu H,Zhang Q. 2019. Consistency analysis of seismic records and strong motion records in Guangxi:Taking the Guangxi Beiliu MS5.2 earthquake as an example[J]. North China Earthquake Sciences,37(S1):38–42 (in Chinese).

    任枭,刘瑞丰,杨辉,徐志国,孙丽,黄志斌,邹立晔. 2009. 中国数字地震台网所使用的仪器及其传递函数的计算方法[J]. 地震地磁观测与研究,30(5):113–119.

    Ren X,Liu R F,Yang H,Xu Z G,Sun L,Huang Z B,Zou L Y. 2009. The status and transfer function of instruments deployed in China Digital Seismological Networks[J]. Seismological and Geomagnetic Observation and Research,30(5):113–119 (in Chinese).

    盛谦,崔臻,刘加进,冷先伦. 2012. 传递函数在地下工程地震响应研究中的应用[J]. 岩土力学,33(8):2253–2258. doi: 10.3969/j.issn.1000-7598.2012.08.003

    Sheng Q,Cui Z,Liu J J,Leng X L. 2012. Application study of transfer function for seismic response analysis of underground engineering[J]. Rock and Soil Mechanics,33(8):2253–2258 (in Chinese).

    文雪康,袁莹,唐建明,刘胜,陈明春. 2020. 速度、加速度检波器在超深层地震勘探中应用效果分析:以川南赤水地区为例[J]. 地球物理学进展,35(4):1489–1496. doi: 10.6038/pg2020DD0343

    Wen X K,Yuan Y,Tang J M,Liu S,Chen M C. 2020. Analysis and application of velocity and acceleration geophone in ultra deep seismic exploration:A case study of Chishui area in south Sichuan basin[J]. Progress in Geophysics,35(4):1489–1496 (in Chinese).

    谢剑波. 2014. 地震记录的时间域反褶积、仿真及在地震计方位角相对测量中的应用[J]. 地球物理学报,57(1):167–178. doi: 10.6038/cjg20140115

    Xie J B. 2014. Deconvolution,simulation of seismic records in the time domain and application in the relative measurements of seismometer orientation[J]. Chinses Journal of Geophysics,57(1):167–178.

    杨笑梅,郭钦华. 2007. 二维复杂工程场址设计地震动的修正分析方法[J]. 世界地震工程,23(2):112–117. doi: 10.3969/j.issn.1007-6069.2007.02.018

    Yang X M,Guo Q H. 2007. The modified method for determining design ground motions of 2D complex engineering site[J]. World Earthquake Engineering,23(2):112–117 (in Chinese).

    俞言祥, 汪素云, 胡聿贤. 1999. 用宽频带数字记录计算长周期地震动反应谱[C]//中国地震学会成立20周年纪念文集. 北京: 地震出版社: 113–121.

    Yu Y X, Wang S Y, Hu Y X. 1999. Calculation of long-period ground motion response spectrum using broadband digital records[C]//Celebration of the 20th Anniversary of the Founding of China Seismological Society. Beijing: Seismological Press: 113–121 (in Chinese).

    张宁,徐国林. 2022. 基于Hi-net速度记录计算地震反应谱[J]. 地震工程与工程振动,42(1):243–249.

    Zhang N,Xu G L. 2022. Calculation of earthquake response spectrum based on Hi-net velocity records[J]. Earthquake Engineering and Engineering Dynamics,42(1):243–249 (in Chinese).

    周云耀,蔡亚先,吕永清,程骏玲. 2002. CT-1地震计传递函数测试仪的设计[J]. 大地测量与地球动力学,22(3):117–121. doi: 10.14075/j.jgg.2002.03.028

    Zhou Y Y,Cai Y X,Lü Y Q,Cheng J L. 2002. Design of CT-1 transfer function test system of seismometer[J]. Journal of Geodesy and Geodynamics,22(3):117–121 (in Chinese).

    Maeda T,Obara K,Furumura T,Saito T. 2011. Interference of long-period seismic wavefield observed by the dense Hi-net array in Japan[J]. J Geophys Res:Solid Earth,116(B10):B10303. doi: 10.1029/2011JB008464

    Nakata N. 2013. Combination of Hi-net and KiK-net data for deconvolution interferometry[J]. Bull Seismol Soc Am,103(6):3073–3082. doi: 10.1785/0120130101

图(4)  /  表(3)
计量
  • 文章访问数:  395
  • HTML全文浏览量:  147
  • PDF下载量:  109
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-11-28
  • 修回日期:  2022-05-16
  • 网络出版日期:  2022-09-14
  • 发布日期:  2023-01-16

目录

    /

    返回文章
    返回