基于L_1范数正则化的强震动加速度记录基线漂移识别方法
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摘要
本文提出了一种基于L_1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。
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 L_1-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 convexityoptimized tool automatically in this L_1-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.
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 L_1-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 convexityoptimized tool automatically in this L_1-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.
引文
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.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 accelerograms[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.Wang G Q,Zhou X Y. 2004. Baseline correction of near fault ground motion recordings of the 1999 Chi-Chi,Taiwan earthquake[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 nearfield[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.
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 ChiChi,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.
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.
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.
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.
Efron B,Hastie T,Johnstone I,Tibshirani R. 2004. Least angle regression[J]. Ann Statist,32(2):407–499.
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,Version1 .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.
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.
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.
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.
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.
Wu Y M,Wu C F. 2007. Approximate recovery of coseismic deformation from Taiwan strong-motion records[J]. J Seismol,
11 (2):159–170.
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 accelerograms[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.Wang G Q,Zhou X Y. 2004. Baseline correction of near fault ground motion recordings of the 1999 Chi-Chi,Taiwan earthquake[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 nearfield[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.
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 ChiChi,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.
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.
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.
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.
Efron B,Hastie T,Johnstone I,Tibshirani R. 2004. Least angle regression[J]. Ann Statist,32(2):407–499.
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,Version1 .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.
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.
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.
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.
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.
Wu Y M,Wu C F. 2007. Approximate recovery of coseismic deformation from Taiwan strong-motion records[J]. J Seismol,
11 (2):159–170.