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.
-
Keywords:
- velocity record /
- transport function /
- Laplacetransform /
- bilinear transformation /
- Hi-net
-
-
![]()
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
ai bi i＝0 1.044 984 1.000 370 i＝1 −1.998 024 −1.999 999 i＝2 0.956 990 0.999 629 
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/kmM 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 5.0 8.2 8.2 5.5 宫城地震 2.4 5.4 5.1 3.3 磐城县地震 3.9 4.3 4.1 3.5 福岛县地震 5.9 10.2 9.7 6.5
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
-
期刊类型引用(3)
1. 李军红，崔宁. 基于拉普拉斯变换的常微分方程课程思政探究. 内江科技. 2025(01): 131-133 . 
百度学术
2. 吴文波，杨耀宁，禹谢华. 多层卷积神经网络在图像目标标注中的应用. 计算机仿真. 2025(02): 243-247 . 百度学术
3. 王锋. 港口桥式起重机械负载防摇控制方法研究. 自动化与仪表. 2024(01): 61-65 . 百度学术
其他类型引用(0)
计量
- 文章访问数: 395
- HTML全文浏览量: 147
- PDF下载量: 109
- 被引次数: 3
