地震研究

利用振动台实验,通过设置多个采样频率监测仿真的正弦波形及天然地震波形,研究高频GNSS出现的频率混叠现象及其时频特征,并讨论合理的规避混叠现象的采样率设置方法。结果表明:混叠效应在时域和频域中均有所体现,混叠频率的幅度若高于GNSS的误差水平,其导致的失真将不能忽略; 震级与震中距是导致混叠现象的主要因素,活动断裂的孕震能力与地震危险性及站点与断层面距离是决定高频GNSS监测站采样频率的重要依据。

High rate GNSS measuring the kinematic displacements caused by earthquake with discrete and equal interval sampling rate. According the Nyquist Law,if analog signals have resolve energy at the frequencies higher than the half of sampling rate,the higher frequency signals masquerading as the low frequency signal in the time and frequency domains will contaminate the sampled data. This effect is called aliasing. In this paper,we investigate the aliasing of high rate GNSS by using shake table tests. First we used the sinusoids as input signals to confirm the aliasing effects in the high rate GNSS. Then we used an acceleration record of real earthquake as the input signal to study the mechanism of aliasing effects in the high rate GNSS.The results show that the aliasing occurs both in time domain and frequency domain,and shows non-negligible effect if the masqueraded amplitude is greater than the uncertainty of GNSS positioning. The earthquake magnitude and epicenter distance of GNSS site are two major factors which determine the amplitude of the aliasing effect. Therefore, sampling rate of GNSS should be set according to the seismogenic ability of monitoring fault and the distances between the fault plane and GNSS sites.

引言
1 振动台仿真实验及数据处理
2 实验结果及分析
3 讨论
4 结论

图1 振动台实验
Fig.1 Shake table tests

图2 2 Hz正弦波作为振动台输入时高频GNSS不同采样率下完整实验时间长度(a)及15～20 s放大显示(b)的位移时序<br/>Fig.2 GNSS time series in different sample rate in the whole time(a)and 15～20 s enlarged drawing(b) at different rates in the shake table tests by using the 2 Hz sinusoidsas as input signals

图2 2 Hz正弦波作为振动台输入时高频GNSS不同采样率下完整实验时间长度(a)及15～20 s放大显示(b)的位移时序
Fig.2 GNSS time series in different sample rate in the whole time(a)and 15～20 s enlarged drawing(b) at different rates in the shake table tests by using the 2 Hz sinusoidsas as input signals

图3 2 Hz正弦波作为振动台输入时高频GNSS不同采样率的幅度谱(a)及50 Hz时序对0.5、1、2.5、5、10 Hz频率高通滤波后重构的位移时序(b)<br/>Fig.3 Amplitude spectrums of GNSS time series sampled at different sample rate(a)in the shake tables tests by using the 2 Hz sinusoids as input signals and the time series constructed by the 50 Hz displacements high-pass filtered with corner at 0.5、1、2.5、5、10 Hz(b)

图3 2 Hz正弦波作为振动台输入时高频GNSS不同采样率的幅度谱(a)及50 Hz时序对0.5、1、2.5、5、10 Hz频率高通滤波后重构的位移时序(b)
Fig.3 Amplitude spectrums of GNSS time series sampled at different sample rate(a)in the shake tables tests by using the 2 Hz sinusoids as input signals and the time series constructed by the 50 Hz displacements high-pass filtered with corner at 0.5、1、2.5、5、10 Hz(b)

图4 Izmit MW7.4地震加速度记录作为输入时高频GNSS不同采样率时序及拾振器200 Hz位移时序(a)、10～30 s(P波与S波初动)放大图像(b)<br/>Fig.4 GNSS time series at different sample rates and displacement time series of 200 Hz vibration absorber(a)and 10～30 s(P wave and S vave first motion)enlarged drawing(b)in the shake table tests by using Izmit MW7.4 earthquake as input signals

图4 Izmit MW7.4地震加速度记录作为输入时高频GNSS不同采样率时序及拾振器200 Hz位移时序(a)、10～30 s(P波与S波初动)放大图像(b)
Fig.4 GNSS time series at different sample rates and displacement time series of 200 Hz vibration absorber(a)and 10～30 s(P wave and S vave first motion)enlarged drawing(b)in the shake table tests by using Izmit MW7.4 earthquake as input signals

图5 拾振器加速度、速度及位移时序的幅度谱<br/>Fig.5 Amplitude spectrums of acceleration,velocity and displacement time series of vibration pick-up

图5 拾振器加速度、速度及位移时序的幅度谱
Fig.5 Amplitude spectrums of acceleration,velocity and displacement time series of vibration pick-up

图6 Izmit MW7.4地震加速度记录作为输入时拾振器位移时序及高频GNSS不同采样率时序的幅度谱(a)及高于0.5、1、2.5 Hz频率部分(对应于1、2、5 Hz采样率)的位移时序(b)<br/>Fig.6 Amplitude spectrums of vibration pick-up displacement time series and GNSS time series at different sample rates in the shake tables tests by using the Izmit MW7.4 earthquake as input signals(a) and the constructed displacement time series of frequency higher than 0.5 Hz,1 Hz and 2.5 Hz(corresponding to sample rate of 1,2,5 Hz)(b)

图6 Izmit MW7.4地震加速度记录作为输入时拾振器位移时序及高频GNSS不同采样率时序的幅度谱(a)及高于0.5、1、2.5 Hz频率部分(对应于1、2、5 Hz采样率)的位移时序(b)
Fig.6 Amplitude spectrums of vibration pick-up displacement time series and GNSS time series at different sample rates in the shake tables tests by using the Izmit MW7.4 earthquake as input signals(a) and the constructed displacement time series of frequency higher than 0.5 Hz,1 Hz and 2.5 Hz(corresponding to sample rate of 1,2,5 Hz)(b)

方荣新,施闯,陈克杰,等.2011.GPS地震仪:PANDA软件测试结果与验证[J].武汉大学学报(信息科学版),36(4):453-456.
刘刚,聂兆生,方荣新,等.2014.高频GNSS形变波的震相识别:模拟实验与实例分析[J].地球物理学报,57(9):2813-2825,doi:10.6038/cjg20140908.
万永革.2007.数字信号处理的MATLAB实现[M].北京:科学出版社.
张培震,邓起东,张竹琪,等.2013.中国大陆的活动断裂、地震灾害及其动力过程[J].中国科学:地球科学,43(10):1607-1620.
BILICH A,CASSIDY J,LARSON K M.2008.GPS Seismology:Application to the 2002 MW7.9 Denali Fault Earthquake[J].Bull Seismol Soc Am,98(2):593-606.
BLEWITT G,HAMMOND W C,KREEMER C,et al.2009.GPS for real-time earthquake source determination and tsunami warning systems[J].Geod,83(3):335-343.
DAVIS J P,SMALLEY J R.2009.Love wave dispersion in central North America determined using absolute displacement seismograms from high-rate GPS[J].Geophys Res Lett,114(B11):292-310,doi:10.1029/2009JB006288.
DELOUIS B,NOCQUET J-M,VALLÉE M.2010.Slip distribution of the February 27,2010 MW8.8 Maule Earthquake,central Chile,from static and high-rate GPS,InSAR and broadband teleseismic data[J].Geophys Res Lett,37(17),L17305,doi:10.1029/2010GL043899.
FANG R,SHI C,SONG W W,et al.2013.Determination of earthquake magnitude using GPS displacement waveforms from real-time precise point positioning[J].Geophys J Int,196(1):461-472,doi:10.1093/gji/ggt378.
GALETZKA J,MELGAR D,GENRICH J F,et al.2015.Slip pulse and resonance of the Kathmandu basin during the 2015 Gorkha earthquake,Nepal[J].Science,349(6252):1091-1095.
HUNG H K,RAU R J.2013.Surface waves of the 2011 Tohoku earthquake:Observations of Taiwan's dense high-rate GPS network[J].J Geophys Res,118(1):332-345,doi:10.1029/2012JB009689.
LARSON KM,BODIN P,GOMBERG J.2003.Using 1-Hz GPS Data to Measure Deformations Caused by the Denali Fault Earthquake[J].Science,300(5624):1421,doi:10.1126/science.1084531.
LI H,WANG D,CAI Y J,et al.2012.Baseline Correction of Digital Strong-Motion Data-Examples from the 2008 Wenchuan,China,Earthquake[J].Adv Mater Res,378-379,247-250.
LOU Y,ZHANG W,SHI C,et al.2013.High-rate(1-Hz and 50-Hz)GPS Seismology:Application to the 2013 MW6.6 Lushan earthquake[J].Journal of Asian Earth Sciences,79:426-431,doi:http://dx.doi.rog/10.1016/j.jseases.2013.10.016.
MELGAR D,BOCK Y,CROWELL W B.2012.Real-time centroid moment tensor determination for large earthquakes from local and regional displacement records[J].Geophys Res Lett,188(2):703-718.
SMALLEY R.2009.High-rate GPS:How High do We Need to go?[J].Seismol Res Lett,80(6):1054-1061.
WRIGHT T J,HOULIÉ N,HILDYARD M,et al.2012.Real-time,reliable magnitudes for large earthquakes from 1Hz GPS precise point positioning:The 2011 Tohoku-Oki(Japan)earthquake[J].Geophys Res Lett,39(1),L12302,doi:10.1029/2012GL051894.
YANG S M,NIE Z S,JIAZ G,et al.2011.Co-seismic displacements of 2011 Japan MW9.0 earthquake recorded by far-field GPS stations[J].Geodesy and Geodynamics,2(3),12-15,doi:10.3724/SP.J.1246.2011.00012.
YUE H,LAY T.2011.Inversion of high-rate(1 sps)GPS data for rupture process of the 11 March 2011 Tohoku earthquake(MW9.1)[J].Geophys.Res Lett,38(7):752-767,doi:10.1029/2011GL048700.

备注

引言

1 振动台仿真实验及数据处理

2 实验结果及分析

3 讨论

4 结论

期刊信息