Statistical analysis of ETAS parameters in the early stage of the 2013 Lushan MS7.0 earthquake sequence
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摘要: 为考察2013年4月20日芦山MS7.0地震震后序列参数的早期特征， 利用“传染型余震序列”(ETAS)模型和最大似然法进行了参数估计. 设定截止震级Mc=ML2.0， 拟合时段为震后0.31—24.12天， 计算获得α=1.89， p=1.22， 同时利用最大似然法估计获得b=0.72. 与中国大陆地区其它中强震的余震序列参数的比较表明， 芦山MS7.0地震序列参数表现为触发次级余震的能力较弱和序列衰减速率较快的特征， 反映出余震区相对较高的应力水平. 为检测结果的稳定性， 设定不同的截止震级Mc以及不同的拟合截止时间， 分别进行参数拟合和参数标准差估计. 结果表明， Mc的选取对α值影响明显， 对p值影响则较小. 此外， 震后10天内获得的参数拟合结果随时间变化较为明显， 而其后各参数变化总体较为平稳.Abstract: The epidemic-type aftershock sequence (ETAS) model was fitted to the aftershock sequence of the April 20, 2013 Lushan MS7.0 earthquake with cutoff magnitude Mc=ML2.0 and a fitting time interval from 0.31 days to 24.12 days after the earthquake. The maximum likelihood estimates of the model parameters are α=1.89, p=1.22 and b=0.72. Comparing to other earthquake sequences in China continent, the Lushan MS7.0 earthquake sequence is characterized by a weak triggering ability in generating secondary aftershocks, a quick decay rate of aftershocks, indicating a high stress level in the aftershock region. To examine the stability of parameters, the ETAS parameters and their standard errors are estimated with different cutoff magnitudes Mc and different ending times of the fitting interval. It is observed that Mc affects the value of α significantly but has less influence on p. Furthermore, the temporal variation of the ETAS parameters changed obviously within 10 days after the main shock, but became more stable beyond this time interval.
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Keywords:
- Lushan MS7.0 earthquake /
- aftershock /
- earthquake sequence /
- ETAS model
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图 1 芦山MS7.0地震序列目录的完整性分析 (a) 芦山MS7.0地震序列的震级-序号图.子图为序列第1—240个事件的放大图， 垂直虚线标出了ML2.0以上地震完整的位置， 约为第190个事件， 即主震后0.31天；(b)震级-序号法给出的地震密度分布
Figure 1. Catalogue completeness of the Lushan MS7.0 earthquake sequence (a) Magnitude-rank distribution of the Lushan MS7.0 earthquake sequence. Grey subplot shows the partial enlarged view of the first 240 events, and the vertical dashed line indicates the completeness of ML≥2.0 aftershocks, which is the position of the 190th event or 0.31 days after the main shock；(b) Seismic rate distribution given by magnitude-rank analysis
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图 2 利用ETAS模型拟合给出的芦山MS7.0地震序列ML2.0以上地震的条件强度曲线(a)和M - t图(b). 纵坐标上的频度指每天发生的地震次数
Figure 2. Temporal variation of the conditional intensity from fitting the ETAS model to the Lushan MS7.0 earthquake sequence with cutoff magnitude ML2.0 (a) and M - t plot (b).The frequency on the ordinate axis means the earthquake number per day
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图 3 芦山MS7.0地震序列ML2.0以上地震的累积地震数与ETAS模型拟合曲线的比较 (a)累积地震数与ETAS拟合曲线在“转换时间”域τ的比较； (b) M-τ图，τ为将时间转换为稳态泊松分布的“转换时间”
Figure 3. Comparison of the observed and modeled cumulative numbers of the Lushan MS7.0 earthquake sequence with magnitude larger than ML2.0. (a) Observation (black curve) and ETAS formula (thick gray dashed line) in the transformed time (τ) domain; (b) M-τ plot where τ is the transformed time which is according to the stationary Poisson process
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图 4 ETAS模型参数α， p和b随拟合截止时间的变化(a)和M - tend图(b)
Figure 4. Parameters α, p and b against the end time tend in ETAS fitting (a) and the M - tend plot (b)
表 1 不同截止震级下ETAS模型拟合参数
Table 1 Parameters of ETAS model with different cutoff magnitude
注： 总地震数是指地震序列中 Mc以上地震的总数， 拟合地震数是指拟合所用的震后0.31—24.12天内的地震数． 
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陈运泰, 杨智娴, 张勇, 刘超. 2013. 从汶川地震到芦山地震[J]. 中国科学: 地球科学, 43(6): 1064-1072. 蒋长胜, 吴忠良. 2011. 玉树MS7.1地震前的中长期加速矩释放(AMR)[J]. 地球物理学报, 54(6): 1501-1510. 蒋海昆, 郑建常, 吴琼, 曲延军, 李永莉. 2007. 传染型余震序列模型震后早期参数特征及其地震学意义[J]. 地球物理学报, 50(6): 1778-1786. 刘杰, 易桂喜, 张致伟, 官致军, 阮祥, 龙锋, 杜方. 2013. 2013年4月20日四川芦山MS7.0级地震介绍[J]. 地球物理学报, 56(4): 1404-1407. 中华人民共和国中央人民政府. 2013. 民政部: 芦山地震已造成193人死亡, 25人失踪[EB/OL]. [2013-04-23]. http://www.gov.cn/jrzg/2013-04/23/content_2386791.htm. Akaike H. 1974. A new look at the statistical model identification[J]. IEEE Trans Automat Control, 19(6): 716-723.
Aki K.1965. Maximum likelihood estimate of b in the formula logn=a-bm and its confidence limits[J]. Bull Earthquake Re Inst, 43(2): 237-239.
Daley D D, Vere-Jones D. 2003. An Introduction to Theory of Point ProcessesVolume 1: Elementary Theory and Methods[M]. Second Edition. Springer: New York: 17-33.
Guo Z, Ogata Y. 1997. Statistical relations between the parameters of aftershocks in time, space and magnitude[J]. J Geophys Res, 102(B2): 2857-2873.
Huang Q. 2006. Search for reliable precursors: A case study of the seismic quiescence of the 2000 Western Tottori prefecture earthquake[J]. J Geophys Res, 111(B4): B04301, doi:10.1029/2005JB003982.
Jiang C S, Wu Z L. 2012. Testing the forecast of aftershocks: A simple method with an example of application[J]. Research in Geophysics, 2(1): 29-33.
Kagan Y Y, Bird P, Jackson D D. 2010. Earthquake patterns in diverse tectonic zones of the globe[J]. Pure Appl Geophys, 167(6/7): 721-741.
Ogata Y. 1978. The asymptotic behavior of maximum likelihood estimators for stationary point processes[J]. Ann Inst Statist Math, 30(2): 243-261.
Ogata Y. 1988. Statistical models for earthquake occurrences and residual analysis for point processes[J]. J Amer Statist Assoc, 83(401): 9-27.
Ogata Y. 1989. Statistical model for standard seismicity and detection of anomalies by residual analysis[J]. Tectonophy-sics, 169(1/3): 159-174.
Ogata Y. 1992. Detection of precursory relative quiescence before great earthquakes through a statistical model[J]. J Geophys Res, 97(B13): 19845-19871.
Ogata Y. 1998. Space-time point-process models for earthquake occurrences[J]. Ann Inst Statist Math, 50(2): 379-402.
Ogata Y. 2001. Increased probability of large earthquakes near aftershock regions with relative quiescence[J]. J Geophys Res, 106(B5): 8729-8744.
Omori F. 1894. On aftershocks of earthquakes[J]. J Coll Sci Imp Univ Tokyo, 7: 111-200.
Peng Y J, Zhou S Y, Zhuang J C. 2012. An approach to detect the abnormal seismicity increase in Southwestern China triggered co-seismically by 2004 Sumatra MW9.2 earthquake[J]. Geophys J Int, 189(3): 1734-1740.
Schoenberg F P, Chu A, Veen A. 2010. On the relationship between lower magnitude thresholds and bias in ETAS parameter estimates[J]. J Geophys Res, 115(B4): B04309, doi:10.1029/2009JB006387.
Shi Y, Bolt B A. 1982. The standard error of the magnitude frequency b-value[J]. Bull Seismol Soc Am, 72(5): 1677-1687.
Sornette D, Werner M J. 2005. Apparent clustering and apparent background earthquakes biased by undetected seismicity[J]. J Geophys Res, 110(B9): B09303, doi:10.1029/2005JB003621.
Stein S, Liu M. 2009. Long aftershock sequences within continents and implications for earthquake hazard assessment[J]. Nature, 462: 87-89.
Utsu T. 1961. A statistical study on the occurrence of aftershocks[J]. Geophys Mag, 30: 521-605.
Utsu T. 1965. A method for determining the value of b in a formula logn=a-bm showing the magnitude frequency for earthquakes[J]. Geophys Bull Hokkaido Univ, 13: 99-103.
Wang Q, Jackson D D, Zhuang J C. 2010a. Missing links in earthquake clustering models[J]. Geophys Res Lett, 37(21): L21307, doi:10.1029/2010GL044858.
Wang Q, Schoenberg F P, Jackson D D. 2010b. Standard errors of parameter estimates in the ETAS model[J]. Bull Seismol Soc Am, 100(5A): 1989-2001.
Zhuang J C. 2000. Statistical modeling of seismicity patterns before and after the 1990 Oct 5 Cape Palliser earthquake, New Zealand[J]. NZJ Geol Geophys, 43(3): 447-460.
Zhuang J, Harte D, Werner M J, Hainzl S, Zhou S. 2012. Basic Models of Seismicity: Temporal Models[M/OL]. Community Online Resource for Statistical Seismicity Analysis. doi:10.5078/corssa-79905851. http://www.corssa.org.
Zhuang J, Ogata Y. 2006. Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks[J]. Physical Review E, 73(4): 046134, doi:10.1103/PhysRevE.73.046134.
Zhuang J, Ogata Y, Vere-Jones D. 2002. Stochastic declustering of space-time earthquake occurrences[J]. J Amer Stat Assoc, 97(458): 369-380.
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