A method for identifying the baseline drift of strong-motion records based on L1-norm regularization
-
摘要: 本文提出了一种基于L1范数正则化的基线校正新方法，即以拟合速度时程误差最小为目标，以基线漂移本身尽可能小为约束条件，经过凸优化多次迭代自动求解出满足条件的基线漂移，避免了人为选取基线漂移分段次数和基线漂移起止时刻的主观干扰；随后利用该方法对多组加入了基线漂移噪声模型的强震动加速度记录进行验证。结果表明：本文方法对于识别和处理单段式、两段式和多段式的基线漂移噪声具有普适性，能敏锐地捕捉到速度时程发生漂移的趋势（斜率变化），无需预先设定加速度基线漂移模型也可有效地识别出多种基线漂移噪声的起止位置和漂移程度；地震记录事前部分对本文方法处理结果影响较大，当记录事前部分足够长时（如20 s），识别基线漂移噪声的准确性较高，位移时程可以较好地与原始位移匹配；而对于发生漂移的速度时程，本文方法可以不受地震事前部分长短的干扰，甚至在加速度记录出现明显丢头现象时，也能很好地实现峰值速度和整个速度时程的恢复。Abstract: To identify the accurate baseline drift in ground acceleration, velocity, and displacement time series is one of the basic and challenge problems in the research of strong ground motion. This study proposes a new baseline-correction method based on L1-norm regularization. It aims at minimizing the error of fitting velocity trace subject to let the sum of absolute values of acceleration baseline drift be small. As the baseline-offset is figured out by the convexity-optimized tool automatically in this L1-norm regularization based baseline-correction method, the subjective interferences can be well avoided such as selecting segmentation times and the start and end moments. And then representative noise models of acceleration baseline offset are added respectively to typical strong-motion records in order to test and verify the new method. The results shows that our method is universal for identifying and processing single-, double-, and multi-stage baseline drift noises. It can sensitively capture the trend （slope） change of the velocity trace while it’s no need to set segmentation times and positions of piecewise linear fitting in advance. The pre-event interval of strong-motion record has a great influence on the processing results of this method. If the pre-event interval is long enough （e.g. 20 seconds） in a record, the identification of the baseline drift noise will be much more accurate, and the recovered displacement trace will match better with the real one. Additionally, this method shows good performance to recover peak ground velocity and the whole velocity time series even if the record almost has no pre-event portion.
-
-
![]()
图 1 本文采用的典型加速度基线漂移噪声模型（修改自Akkar，Boore，2009）
tb和te分别为加速度记录的起、止时刻，t1和t2分别为加速度绝对值在第一次和最后一次大于50 m/s2时刻，t3为[t1，t2]中间时刻，am1和am2分别为加速度在强烈震动时段的加速度漂移幅值，af为加速度最终保持的漂移幅值
Figure 1. Representative sketches of acceleration baseline-offset noise models （modified from Akkar，Boore，2009）
tb and te are respectively the beginning and ending of the recording， the time t1 and t2 represent the first and last time that the recording’s absolute values are larger than 50 m/s2， t3 is the medium time between t1 and t2，am1 and am2 mean the two consecutive constant offsets during the strong ground shaking，af is the final offset
![]()
图 2 L1范数正则化方法对于两段式基线漂移噪声模型的识别和处理结果
（a） 地震加速度时程；（b） 速度时程；（c） 加速度基线；（d） 位移时程
Figure 2. The results of identifying and processing double-stage baseline-offset noise model based on the L1-norm regularization method
（a） Acceleration time history；（b） Velocity time history；（c） Acceleration baseline-offset；（d） Displacement time history
![]()
图 4 本文方法所识别的El Centro台南北向记录与加入两段式噪声模型后的基线漂移噪声差值
Figure 4. The difference between baseline-offset identified by this paper and added two-stage noise model for El Centro NS component
![]()
图 3 El Centro台南北向初始部分记录处理结果
Figure 3. Comparison of the original record with the results processed by the new method in the pre-event portion of El Centro NS components record
![]()
图 5 基于L1范数正则化方法对单段式基线漂移噪声模型的识别和处理结果
（a） 地震加速度时程；（b） 速度时程；（c） 加速度基线；（d） 位移时程
Figure 5. The results of identifying and processing on records added single-stage baseline-offset noise model based on the L1-norm regularization method
（a） Acceleration time history；（b） Velocity time history；（c） Acceleration baseline-offset；（d） Displacement time history
![]()
图 6 基于L1范数正则化方法对于多段式基线漂移噪声模型的识别和处理结果
（a） 地震加速度时程；（b） 速度时程；（c） 加速度基线；（d） 位移时程
Figure 6. The results of identifying and processing on records added multi-stage baseline-offset noise model based on the L1-norm regularization method
（a） Acceleration time history；（b） Velocity time history；（c） Acceleration baseline-offset；（d） Displacement time history
![]()
图 7 利用本文方法对加入不同噪声模型后的El Centro台NS向记录进行恢复的结果
（a） 单段式基线漂移噪声；（b） 两段式基线漂移噪声；（c） 多段式基线漂移噪声
Figure 7. Velocity trace recovered from El Centro NS component records with different noise models by the method proposed in this paper
（a） Single-stage baseline drift noises； （b） Double-baseline drift noises； （c） Multi-stage baseline drift noises
表 1 本文所列地震记录信息（PEER，2013）
Table 1 Information about digital accelerograms shown in this study （PEER，2013）
发震年 地震 MW P波到时/s 持时/s 分量方向 台站名称 场地类型* 震中距/km 1940 帝王谷地震 6.95 0.04 40 NS El Centro Array#9 D 12.99 1999 迪兹杰地震 7.14 5.39 56 EW Bolu D 41.27 1999 集集地震 7.62 20.65 90 NS TCU129 C 14.16 注：场地类型采用美国地震减灾计划（National Earthquake Hazards Reduction Program，NEHRP）给出的A，B，C，D和E等5类场地条件划分类型（ Huang et al，2010 ）.
下载: 导出CSV
-
符伟,刘财. 2015. 基于L1正则化的地震谱反演方法[J]. 世界地质,34(2):505–510 doi: 10.3969/j.issn.1004-5589.2015.02.028 Fu W,Liu C. 2015. Seismic spectral-inversion technique based on L1-norm regulation method[J]. Global Geology,34(2):505–510 (in Chinese)
李欣,杨婷,孙文博,王贝贝. 2018. 一种基于光滑L1范数的地震数据插值方法[J]. 石油地球物理勘探,53(2):251–256 Li X,Yang T,Sun W B,Wang B B. 2018. A gradient projection method for smooth L1 norm regularization based seismic data sparse interpolation[J]. Oil Geophysical Prospecting,53(2):251–256 (in Chinese)
彭小波,李小军,刘泉. 2010. 数字加速度记录基线校正相关问题的初步研究[J]. 世界地震工程,26(增刊1):142–147 Peng X B,Li X J,Liu Q. 2010. Preliminary study on baseline correction of digital acceleration records[J]. World Earthquake Engineering,26(S1):142–147 (in Chinese)
彭小波,李小军,刘启方. 2011. 基于强震记录估算同震位移的研究进展及方法[J]. 世界地震工程,27(3):73–80 Peng X B,Li X J,Liu Q F. 2011. Advances and methods for the recovery of coseismic displacements from strong-motion accelero-grams[J]. World Earthquake Engineering,27(3):73–80 (in Chinese)
荣棉水,彭艳菊,喻畑,杨宇. 2014. 近断层强震观测记录基线校正的优化方法[J]. 土木工程学报,47(增刊2):308–314 Rong M S,Peng Y J,Yu T,Yang Y. 2014. Optimized baseline correction method for the near-fault observation strong motion records[J]. China Civil Engineering Journal,47(S2):308–314 (in Chinese)
王国权,周锡元. 2004. 9·21台湾集集地震近断层强震记录的基线校正[J]. 地震地质,26(1):1–14 doi: 10.3969/j.issn.0253-4967.2004.01.001 Wang G Q,Zhou X Y. 2004. Baseline correction of near fault ground motion recordings of the 1999 Chi-Chi,Taiwan earth-quake[J]. Seismology and Geology,26(1):1–14 (in Chinese)
于海英,江汶乡,解全才,杨永强,程翔,杨剑. 2009. 近场数字强震仪记录误差分析与零线校正方法[J]. 地震工程与工程振动,29(6):1–12 Yu H Y,Jiang W X,Xie Q C,Yang Y Q,Cheng X,Yang J. 2009. Baseline correction of digital strong-motion records in near-field[J]. Journal of Earthquake Engineering and Engineering Vibration,29(6):1–12 (in Chinese)
周宝峰,于海英,温瑞智,谢礼立. 2013. 一种识别永久位移的新方法[J]. 土木工程学报,46(增刊2):135–140 Zhou B F,Yu H Y,Wen R Z,Xie L L. 2013. A new way of permanent displacement identification[J]. China Civil Engineering Journal,46(S2):135–140 (in Chinese)
周巍. 2013. L1范数最小化算法及应用[D]. 广州: 华南理工大学: 14–23. Zhou W. 2013. L1-Norm Minimization Algorithms and Its Applications[D]. Guangzhou: South China University of Technology: 14–23（in Chinese）.
Akkar S,Boore D M. 2009. On baseline corrections and uncertainty in response spectra for baseline variations commonly encountered in digital accelerograph records[J]. Bull Seismol Soc Am,99(3):1671–1690 doi: 10.1785/0120080206
Allen R V. 1978. Automatic earthquake recognition and timing from single traces[J]. Bull Seismol Soc Am,68(5):1521–1532
Allen R V. 1982. Automatic phase pickers:Their present use and future prospects[J]. Bull Seismol Soc Am,72(6B):S225–S242
Boore D M. 2001. Effect of baseline corrections on displacements and response spectra for several recordings of the 1999 Chi-Chi,Taiwan,earthquake[J]. Bull Seismol Soc Am,91(5):1199–1211
Boore D M. 2005. On pads and filters:Processing strong-motion data[J]. Bull Seismol Soc Am,95(2):745–750 doi: 10.1785/0120040160
Boyd S P, Vandenberghe L. 2004. Convex Optimization[M]. New York: Cambridge University Press: 291–311.
Chao W A,Wu Y M,Zhao L. 2010. An automatic scheme for baseline correction of strong-motion records in coseismic deformation determination[J]. J Seismol,14(3):495–504 doi: 10.1007/s10950-009-9178-7
Chiu H C. 1997. Stable baseline correction of digital strong-motion data[J]. Bull Seismol Soc Am,87(4):932–944
Dai Z J,Li X J,Hou C L. 2014. An optimization method for the generation of ground motions compatible with multi-damping design spectra[J]. Soil Dyn Earthq Eng,66:199–205 doi: 10.1016/j.soildyn.2014.06.032
Donoho D L,Tsaig Y. 2008. Fast solution of L1-norm minimization problems when the solution may be sparse[J]. IEEE Trans Inf Theory,54(11):4789–4812 doi: 10.1109/TIT.2008.929958
Efron B,Hastie T,Johnstone I,Tibshirani R. 2004. Least angle regression[J]. Ann Statist,32(2):407–499 doi: 10.1214/009053604000000067
Huang Y N,Whittaker A S,Luco N. 2010. NEHRP site amplification factors and the NGA relationships[J]. Earthquake Spectra,26(2):583–593
Hershberger J. 1955. Recent developments in strong-motion analysis[J]. Bull Seismol Soc Am,45(1):11–21
Housner G W. 1947. Ground displacement computed from strong-motion accelerograms[J]. Bull Seismol Soc Am,37(4):299–305
Iwan W D,Moser M A,Peng C Y. 1985. Some observations on strong-motion earthquake measurement using a digital accelerograph[J]. Bull Seismol Soc Am,75(5):1225–1246
Jones J, Kalkan E, Stephens C. 2017. Processing and Review Interface for Strong Motion Data （PRISM） Software, Version 1.0.0: Methodology and Automated Processing[R].Reston: U S Geological Survey : 3–20.
Mallat S G,Zhang Z F. 1993. Matching pursuits with time-frequency dictionaries[J]. IEEE Trans Signal Process,41(12):3397–3415 doi: 10.1109/78.258082
PEER. 2013. PEER NGA-West2 ground motion database[EB/OL]. [2017–10–02]. https://peer.berkeley.edu/research/nga-west-2.
Schmidt M. 2005. Least Squares Optimization With L1-Norm Regularization[R]. Vancouver: Univercity of British Clumbia: 3–6.
Tibshirani R. 1996. Regression shrinkage and selection via the lasso[J]. J Roy Statist Soc Ser B,58(1):267–288
Trifunac M D. 1970. Low Frequency Digitization Errors and A New Method for Zero Baseline Correction of Strong-Motion Accelerograms[R]. Pasadena: Earthquake Engineering Research Laboratory: 7–24.
Trifunac M D,Lee V W. 1974. A note on the accuracy of computed ground displacements from strong-motion accelerograms[J]. Bull Seismol Soc Am,64(4):1209–1219
Wang G Q,Boore D M,Igel H,Zhou X Y. 2003. Some observations on colocated and closely spaced strong ground-motion records of the 1999 Chi-Chi,Taiwan,earthquake[J]. Bull Seismol Soc Am,93(2):674–693 doi: 10.1785/0120020045
Wang R J,Schurr B,Milkereit C,Shao Z G,Jin M P. 2011a. An improved automatic scheme for empirical baseline correction of digital strong-motion records[J]. Bull Seismol Soc Am,101(5):2029–2044 doi: 10.1785/0120110039
Wang R J,Parolai S,Ge M R,Jin M P,Walter T R,Zschau J. 2013. The 2011 MW9.0 Tohoku earthquake:Comparison of GPS and strong-motion data[J]. Bull Seismol Soc Am,103(2B):1336–1347 doi: 10.1785/0120110264
Wang Y F,Cao J J,Yang C C. 2011b. Recovery of seismic wavefields based on compressive sensing by an L1-norm constrained trust region method and the piecewise random subsampling[J]. Geophys J Int,187(1):199–213 doi: 10.1111/gji.2011.187.issue-1
Wu Y M,Wu C F. 2007. Approximate recovery of coseismic deformation from Taiwan strong-motion records[J]. J Seismol,11(2):159–170 doi: 10.1007/s10950-006-9043-x
计量
- 文章访问数: 1266
- HTML全文浏览量: 873
- PDF下载量: 80
