海城地震窗地震活动异常提取及其预报效能
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摘要
一个时间序列可以分解为趋势周期(含季节周期)部分和不规则随机部分.趋势周期部分是序列的潜在部分,它反映了增长、下降和周期影响的长期变动规律,具有确定性或可预测性;不规则随机部分包含残差、突然等因素引起的突变量,具有不可预测性.当趋势周期部分被确定后,它可通过计算得到.本文研究了1975年海城MS7.3地震孕育、发生的断裂构造背景,合理地确立地震窗的范围来选取地震资料.在此基础上,对海城地震窗地震月频次时间序列进行分解,采用自回归单整移动平均(ARIMA)模型确定了趋势周期部分,并计算得到了不规则随机部分;分析了不规则随机部分中的突变量异常特征对华北地区MS6.0和地震窗附近MS5.0以上地震的反应.结果表明,该异常特征具有较高预测效能,对地震预测有较好参考价值.
An original time series signal can be decomposed into a trend-cycle,including seasonal cycle,component and an irregular component.The trendcycle part is defined as underlying level of the series,and is a manifestation of medium-long term variation influenced by fluctuation and cycles referring to generally deterministic or predictable change of a series.The irregular component contains the residual variation and random abrupt changes,etc.,being unpredictable.Knowing the trend-cycle component,the irregular part can be calculated.Based on the investigation of the faults associated with the 1975 Haicheng M S 7.3earthquake,this study reasonably determined the area window of the Haicheng earthquake series.Then the time series of monthly earthquakesin the Haicheng seismicity window was decomposed.The trend-cycle component of the series was determined using ARIMA ( atuo regression integrated moving average ) model and the irregular variation was also extracted.The reaction of the anomalous abrupt variation to the M S ≥6.0earthquakes in North China and M S ≥5.0earthquakes near the seismicity window was analyzed.The result shows that the anomaly of abrupt seismicity variation may be taken as an indicator with prediction ability.This is of significance in earthquake prediction.
An original time series signal can be decomposed into a trend-cycle,including seasonal cycle,component and an irregular component.The trendcycle part is defined as underlying level of the series,and is a manifestation of medium-long term variation influenced by fluctuation and cycles referring to generally deterministic or predictable change of a series.The irregular component contains the residual variation and random abrupt changes,etc.,being unpredictable.Knowing the trend-cycle component,the irregular part can be calculated.Based on the investigation of the faults associated with the 1975 Haicheng M S 7.3earthquake,this study reasonably determined the area window of the Haicheng earthquake series.Then the time series of monthly earthquakesin the Haicheng seismicity window was decomposed.The trend-cycle component of the series was determined using ARIMA ( atuo regression integrated moving average ) model and the irregular variation was also extracted.The reaction of the anomalous abrupt variation to the M S ≥6.0earthquakes in North China and M S ≥5.0earthquakes near the seismicity window was analyzed.The result shows that the anomaly of abrupt seismicity variation may be taken as an indicator with prediction ability.This is of significance in earthquake prediction.
引文
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Bartlett M S.1946.On the theoretical specification of sampling properties of autocorrelated time series[J].J R Stat Soc,B8(27):20--47.
Box G,Pierce D.1970.Distribution of residual autocorrelations in ARIMA time series models[J].J Am Stat Assoc,65(332):1509--1526.
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Dickey D,Fuller W.1979.Distribution of the estimators for autoregressive time series with a unit root[J].J Am StatAssoc,74(336):427--431.
Divine D V,Polzehl J,Godtliebsen F.2008.A propagation-separation approach to estimate the autocorrelation in a time-series[J].Nonlinear Processes Geophysics,15(4):591--599.
Findley D F,Monsell B C,Bell W R,Otto M C,Chen B C.1998.New capabilities and methods of the X-12-ARIMAseasonal adjustment program[J].Journal of Business and Economic Statistics,16(2):127--177.
Fischer B.1995.Decomposition of Time Series:Comparing Different Methods in Theory and Practice[R].EurostatWorking Group Document:20--96.
Hamilton J.1994.Time Series Analysis[M].Princeton:Princeton University Press:20--95.
Harvey A.1989.Structural Time Series and the Kalman Filter,Forecasting[M].Cambridge:Cambridge Univ Press:20--90.
Ramsey F L.1974.Characterization of the partial autocorrelation function[J].Annals of Statistics,2(6):1296--1301.
Said S E,Dickey D A.1984.Testing for unit roots in autoregressive-moving average models of unknown order[J].Biometrika,71(3):599--608.
Schwarz G.1978.Estimating dimension of a model[J].Ann Stat,6(2):461--464.
陆远忠,李胜乐,邓志辉,潘怀文,车时,李志雄.2002.基于GIS的地震分析预报系统[M].成都:成都地图出版社:11--72.
许绍燮.1989.地震预报能力评价[G]∥国家地震局科技监测司编.地震预报方法实用化研究文集(地震学专辑).北京:学术书刊出版社:586--590.
薛丁,曹刚,纪建国.2007.河北邢台余震窗地震活动对华北地区6级以上地震的预测反应[J].山西地震,(2):13--15.
张培震,邓起东,张国民,马瑾,甘卫军,闵伟,毛凤英,王琪.2003.中国大陆的强震活动与活动地块[J].中国科学:D辑,33(S1):12--20.
Akaike H.1973.Information theory and an extension of the maximum likelihood principle[C]∥Petrov B N,Csaki F eds.2nd International Symposium on Information Theory.Budapest:Akademiai Kiado:267--281.
Barndorff-Nielsen O,Schou G.1973.On the parametrization of autoregressive models by partial autocorrelations[J].JMultivariate Anual,3(3):408--419.
Bartlett M S.1946.On the theoretical specification of sampling properties of autocorrelated time series[J].J R Stat Soc,B8(27):20--47.
Box G,Pierce D.1970.Distribution of residual autocorrelations in ARIMA time series models[J].J Am Stat Assoc,65(332):1509--1526.
Box G P E,Jenkis G M.1978.Time Series Analysis:Forecasting and Contro[M].San Francisco:San Francisco Press:20--79.
Dickey D,Fuller W.1979.Distribution of the estimators for autoregressive time series with a unit root[J].J Am StatAssoc,74(336):427--431.
Divine D V,Polzehl J,Godtliebsen F.2008.A propagation-separation approach to estimate the autocorrelation in a time-series[J].Nonlinear Processes Geophysics,15(4):591--599.
Findley D F,Monsell B C,Bell W R,Otto M C,Chen B C.1998.New capabilities and methods of the X-12-ARIMAseasonal adjustment program[J].Journal of Business and Economic Statistics,16(2):127--177.
Fischer B.1995.Decomposition of Time Series:Comparing Different Methods in Theory and Practice[R].EurostatWorking Group Document:20--96.
Hamilton J.1994.Time Series Analysis[M].Princeton:Princeton University Press:20--95.
Harvey A.1989.Structural Time Series and the Kalman Filter,Forecasting[M].Cambridge:Cambridge Univ Press:20--90.
Ramsey F L.1974.Characterization of the partial autocorrelation function[J].Annals of Statistics,2(6):1296--1301.
Said S E,Dickey D A.1984.Testing for unit roots in autoregressive-moving average models of unknown order[J].Biometrika,71(3):599--608.
Schwarz G.1978.Estimating dimension of a model[J].Ann Stat,6(2):461--464.
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