自适应局部线性化方法的余震间隔时间预测
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摘要
研究了将自适应局部线性化方法应用于较强余震间隔时间的预测。首先对余震间隔时间数据进行预处理;再利用自适应局部线性化法找出合适的嵌入维数,并计算出待估计参数。最后用待估计参数预测余震间隔时间。对汶川地震发生后4.0级(含4.0级)以上的余震间隔时间数据进行了预测。实验结果表明,自适应局部线性化方法预测的余震间隔时间的平均均方根误差和平均绝对偏离明显低于标准局部线性化方法;自适应局部线性化方法预测的余震间隔时间绝对误差比标准局部线性化方法和最小二乘拟合方法的预测结果分别减少了7 d和20 d.
The approach to predicting time interval between aftershocks using adaptive local linear(ALL) is studied.Firstly,the data of time interval between aftershocks should be preprocessed.Then suitable embedding dimension is found using ALL,and the parameters to be estimated are calculated.Finally,time intervals between aftershocks are predicted by the parameters.The datasets of time intervals between aftershocks measuring above 4.0-magnitude(including 4.0 magnitude) after the Wenchuan earthquake are used to predict.Experimental results show that MRMSE(mean of root mean square errors) and MMAE(mean of mean absolute errors) of predictive time interval using ALL are much less than that of using original local linear(LL).The AE(absolute error) of predictive time interval using ALL decreases by 7 days and 20 days respectively than that of using LL and least square fitting.
The approach to predicting time interval between aftershocks using adaptive local linear(ALL) is studied.Firstly,the data of time interval between aftershocks should be preprocessed.Then suitable embedding dimension is found using ALL,and the parameters to be estimated are calculated.Finally,time intervals between aftershocks are predicted by the parameters.The datasets of time intervals between aftershocks measuring above 4.0-magnitude(including 4.0 magnitude) after the Wenchuan earthquake are used to predict.Experimental results show that MRMSE(mean of root mean square errors) and MMAE(mean of mean absolute errors) of predictive time interval using ALL are much less than that of using original local linear(LL).The AE(absolute error) of predictive time interval using ALL decreases by 7 days and 20 days respectively than that of using LL and least square fitting.
引文
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[17]刘蒲雄,陈修启,吕晓健,等.地震序列的后续显著地震的预测研究[J].地震学报,1996,18(1):27-33.LIU Pu-xiong,CHEN Xiu-qi,LV Xiao-jian,et al.Study on the forecasting method on the remarkable aftershock[J].ActaSeismologica Sinica,1996,18(1):27-33.
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[19]George D.A quantitative study of some aftershocks sequences in Greece[J].Pageoph,1994,143(4):603-616.
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[21]李爱国,覃征.自适应局部线性化法预测混沌时间序列[J].系统工程理论与实践,2004,24(6):67-71.LI Ai-guo,QIN Zheng.Adaptive local linear predicting chaotic time series[J].Journal of Systematic Engineering&Prac-tice,2004,24(6):67-71.
[2]丁鉴海,张国民,佘素荣,等.近年我国震后趋势判定与后续强震预测研究进展[J].华南地震,1999,19(1):1-7.DING Jian-hai,ZHANG Guo-min,SHE Su-rong,et al.Newprogress in study on post-seismic tendency determination and pre-diction for following strong shocks in recent years[J].South China Journal of Seismology,1999,19(1):1-7.
[3]张瑞青,吴庆举,李永华,等.汶川中强余震震源深度的确定及其意义[J].中国科学D辑:地球科学,2008,38(10):1 234-1 241.ZHANG Rui-qing,WU Qing-ju,LI Yong-hua,et al.Focal depths for moderate-sized aftershocks of the Wenchuan Ms8.0earthquake and their implications[J].Science in China Series D-Earth Sciences,2008,38(10):1 234-1 241.
[4]Amir M F,Conrad L,Mohammad M,et al.Aftershock Analysis for the 1997 Ghaen-Birjand(Ardekul)Earthquake[J].Journal of Seismology and Earthquake Engineering,2003,5(2):1-10.
[5]Mostafa A Z,Mohammad M.Prediction of aftershocks pattern distribution using Self-Organising Feature Maps(SOFM)andits application on the Birjand-Ghaen and Izmit Earthquakes[J].Journal of Seismology and Earthquake Engineering,2003,5(3):1-15.
[6]黄媛,吴建平,张天中.汶川8.0级大地震及其余震序列重定位研究[J].中国科学D辑:地球科学,2008,38(10):1 242-1 249.HUANG Yuan,WU Jian-ping,ZHANG Tian-zhong.Relocation of the M8.0 Wenchuan earthquake and its aftershock se-quence[J].Science in China Series D-Earth Sciences,2008,38(10):1 242-1 249.
[7]陈海通,孙次昌,黎向东,等.强震类型划分和后续强震预测方法探索[J].地震学报,2000,22(2):194-199.CHEN Hai-tong,SUN Ci-chang,LI Xiang-dong,et al.Research on strong earthquake type division and forecast method forsubsequent strong earthquakes[J].Acta Seismologica Sinica,2000,22(2):194-199.
[8]刁守中,王红卫,华爱军.中国大陆地区地震序列显著地震的时间分布特征[J].中国地震,1995,11(4):315-326.DIAO Shou-zhong,WANG Hong-wei,HUA Ai-jun.The time distribution characteristics of significant seismic of earthquakesequence in the Chinese mainland[J]Earthquake Research in China,1995,11(4):315-326.
[9]华爱军,刁守中,王红卫.强余震“等待时间”判别方案预报效能的研究[J].地壳形变与地震,1996,16(2):47-52.HUA Ai-jun,DIAO Shou-zhong,WANG Hong-wei.Study on prediction ability of method for distinguishing the waiting time ofstrong aftershick[J].Crustal Deformation and Earthquake,1996,16(2):47-52.
[10]Baiesi M,Paczuski M.Complex networks of earthquakes and aftershocks[J].Nonlinear Processes in Geophysics,2005,12(1):1-11.
[11]董国胜.强余震预报规律的探讨及其应用[J].四川地震,1991,(4):30-33.DONG Guo-sheng.A study of strong post-earthquake prediction law and its application[J].Earthquake Researth in Si-chuan,1991,(4):30-33.
[12]平建军,李永庆,张清荣.地震序列较强余震快速响应灰色预测的方法探讨[J].地震学报,1999,21(1):70-74.PING Jian-jun,LI Yong-qing,ZHANG Qing-rong.Method discussion for quick respond grey prediction of stronger after-shocks of an earth-quake sequence[J].Acta Seismologica Sinica,1999,21(1):70-74.
[13]平建军,刘荣环,贾炯,等.地震序列较强余震灰色及最小二乘拟合预测方法的应用研究[J].华北地震科学,2005,23(1):6-13.PING Jian-jun,LIU Rong-huan,JIA Jiong,et al.The application study of the predict method of the gray and the method ofleast square in the earthquake array strong aftershock[J].North China Earthquake Sciences,2005,23(1):6-13.
[14]平建军,贾炯,刘荣环,等.地震序列较强余震最小二乘拟合预测的方法研究[J].华北地震科学,2007,25(3):1-5.PING Jian-jun,JIA Jiong,LIU Rong-huan,et al.Study of the prediction of relatively strong aftershocks in the earthquakesequence with least square fitting method[J].North China Earthquake Sciences,2007,25(3):1-5.
[15]周翠英,王红卫,王梅,等.强余震持续时间的早期估计[J].中国地震,1997,13(2):164-171.ZHOU Cui-ying,WANG Hong-wei,WANG Mei.Early estimation of strong aftershock duration time[J].Earthquake Re-search In China,1997,13(2):164-171.
[16]胡先明.中国大陆强余震的统计特征与发震可能性的判别[J].地震研究,1995,18(2):151-160.HU Xian-ming.Statistical characteristics of strong aftershocks in Chinese mainland and estimation of the seismogenic possi-bility[J].Journal of Seismological Research,1995,18(2):151-160.
[17]刘蒲雄,陈修启,吕晓健,等.地震序列的后续显著地震的预测研究[J].地震学报,1996,18(1):27-33.LIU Pu-xiong,CHEN Xiu-qi,LV Xiao-jian,et al.Study on the forecasting method on the remarkable aftershock[J].ActaSeismologica Sinica,1996,18(1):27-33.
[18]蒋海昆,曲延军,李永莉,等.中国大陆中强地震余震序列的部分统计特征[J].地球物理学报,2006,49(4):1 110-1 117.JIANG Hai-kun,QU Yan-jun,LI Yong-li,et al.Some statistic features of aftershock sequences in Chinese mainland[J].Chinese Journal of Geophysics,2006,49(4):1 110-1 117.
[19]George D.A quantitative study of some aftershocks sequences in Greece[J].Pageoph,1994,143(4):603-616.
[20]George D.Relative seismic quiescence before large aftershocks[J].Pure and Applied Geophysics,2000,157:1 407-1 421.
[21]李爱国,覃征.自适应局部线性化法预测混沌时间序列[J].系统工程理论与实践,2004,24(6):67-71.LI Ai-guo,QIN Zheng.Adaptive local linear predicting chaotic time series[J].Journal of Systematic Engineering&Prac-tice,2004,24(6):67-71.
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