地震研究

采用时间序列的“传染型余震序列”(ETAS)模型和最大似然法,对2016年1月21日门源MS6.4地震序列参数进行估计。选用截止震级MC=ML1.0对门源地震余震序列整体的参数进行连续滑动拟合。结果表明:在主震发生后的早期阶段,α值有明显的不稳定变化,震后3天稳定在1.0～1.4; p值在震后第1～6天由0.98逐渐上升到1.77,其后逐渐下降到1.42,最后相对稳定在1.1～1.3; b值则在震后早期有缓慢升高的变化,但变化幅度不大,由0.77增至0.82,其后稳定在0.81～0.82。门源MS6.4地震后的早期阶段震源区的应力积累水平逐渐减弱,在序列衰减逐渐减缓的过程中,伴随着激发次级余震能力减弱的现象。

Using time series “epidemic type aftershock sequence”(ETAS)model and the maximum likelihood method,we estimate the parameters of aftershocks sequence of the Menyuan MS6.4 earthquake on Jan.21,2016,and then select the cutoff magnitude MC=ML1.0 to do continuous sliding fitting on these parameters. The result shows the α value changed unstable in the early stage after the main shock,then it was stable in the range of 1.0～1.43 days after the mainshock. The p value increased gradually from 0.98 to 1.77 within 1～6 days after the mainshock and then gradually decreased to 1.42,and finally remained steady at 1.1～1.3. And the b value increased from 0.77 to 0.82 in the early stage after the mainshock,and then remained steady at 0.81～0.82. The stress accumulation level was gradually weakened in the focal area in the early stage after the main shock,and in the process of gradually slowing down the aftershock attenuation,there appeared a weak triggering ability in generating secondary aftershocks.

引言
1 资料选取和序列完整性分析
2 序列ETAS模型拟合情况
3 序列ETAS模型参数稳定性分析
4 结论

图1 门源MS6.4地震序列空间分布图<br/>Fig.1 Spatial distribution of the Menyuan MS6.4 earthquake sequence

图1 门源MS6.4地震序列空间分布图
Fig.1 Spatial distribution of the Menyuan MS6.4 earthquake sequence

图2 门源MS6.4地震序列目录的完整性分析(a)纬度-时间图;(b)经度-时间图;(c)空间分布图;(d)震级-序号图<br/>Fig.2 Catalogue completeness analysis for the Menyuan MS6.4 earthquake sequence (a)latitude-time plot;(b)longitude-time plot;(c)spatial distribution plot;(d)magnitude-rank plot

图2 门源MS6.4地震序列目录的完整性分析(a)纬度-时间图;(b)经度-时间图;(c)空间分布图;(d)震级-序号图
Fig.2 Catalogue completeness analysis for the Menyuan MS6.4 earthquake sequence (a)latitude-time plot;(b)longitude-time plot;(c)spatial distribution plot;(d)magnitude-rank plot

图3 利用ETAS模型拟合ML≥1.0地震的条件强度曲线(a)和M-t图(b)<br/>Fig.3 Conditional intensity curve of ML≥1.0 earthquakes fitted by the ETAS model(a)and M-t plot(b)

图3 利用ETAS模型拟合ML≥1.0地震的条件强度曲线(a)和M-t图(b)
Fig.3 Conditional intensity curve of ML≥1.0 earthquakes fitted by the ETAS model(a)and M-t plot(b)

图4 利用ETAS模型对ML≥1.0地震的拟合情况(a)累计地震数与ETAS拟合曲线在“转换时间”(τ)域的比较; (b)M-τ图,τ为将时间转换为稳态泊松分布的“转换时间”<br/>Fig.4 Fitting situation of ML≥1.0 earthquakes based on ETAS model (a)comparison of cumulative earthquake number and ETAS fitting curve in transformed time(τ)domain; (b)M-τ plot,in which τ is the transformed time which is according to the stationary Poisson process

图4 利用ETAS模型对ML≥1.0地震的拟合情况(a)累计地震数与ETAS拟合曲线在“转换时间”(τ)域的比较; (b)M-τ图,τ为将时间转换为稳态泊松分布的“转换时间”
Fig.4 Fitting situation of ML≥1.0 earthquakes based on ETAS model (a)comparison of cumulative earthquake number and ETAS fitting curve in transformed time(τ)domain; (b)M-τ plot,in which τ is the transformed time which is according to the stationary Poisson process

图5 ETAS模型参数α、p和b随拟合截止时间的变化<br/>Fig.5 Parameters α,p and b varied with the end time in ETAS fitting

图5 ETAS模型参数α、p和b随拟合截止时间的变化
Fig.5 Parameters α,p and b varied with the end time in ETAS fitting

何文贵,刘百篪,袁道阳等.2000.冷龙岭活动断裂的滑动速率研究[J].西北地震学报,22(1):90-97.
蒋长胜,韩立波,郭路杰.2014.新疆于田地区2008年以来3次地震序列参数的早期特征[J].地震学报,36(2):165-174.
蒋长胜,吴忠良,韩立波等.2013a.地震序列早期参数估计和余震概率预测中截止震级MC的影响:以2013年甘肃岷县漳县6.6级地震为例[J].地球物理学报,56(12):4048-4057.
蒋长胜,庄建仓,龙锋等.2013b.2013年芦山MS7.0地震序列参数的早期特征:传染型余震序列模型计算结果[J].地震学报,35(5):661-669.
蒋海昆,曲延军,李永莉等.2006.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,49(4):1110-1117.
蒋海昆,郑建常,吴琼等.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.
Akaike H.1974.A new look at the statistical model identification[J].IEEE Trans Automat Control,19(6):716-723.
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 Tottoriprefecture earthquake[J].J Geophys Res,111(B4):170-176.
Kagan Y Y,Bird P,Jackson D D.2010.Earthquake patterns in diverse tectonic zones of the globe[J].Pure Appl Geophys,167(6):721-741.
Ogata Y.1988.Statistical models for earthquake occurrences and residual analysis for pointprocesses[J].J Amer Statist Assoc,83(401):9-27.
Ogata Y.1989.Statistical model for standard seismicity and detection of anomalies by residualanalysis[J].Tectonophysics,169(1):159-174.
Ogata Y.2001.Increased probability of large earthquakes near aftershock regions with relativequiescence[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.
Utsu T.1961.A statistical study of on the occurrence of aftershocks[J].Geophys Mag,30:521-605.
Wang Q,Jackson D D,Zhuang J C.2010.Missing links in earthquake clustering models[J].Geophys Res Lett,37(21):620-626.
Zhuang J C.2011.Next-day earthquake forecasts for the Japan region generated by the ETASmodel[J].Earth Planets Space,63(3):207-216.
Zhuang J,Harte D,Werner M J, et al.2012.Basic models of seismicity:temporal models[G]//Community Online Resource for Statistical Seismicity Analysis.

备注

引言

1 资料选取和序列完整性分析

2 序列ETAS模型拟合情况

3 序列ETAS模型参数稳定性分析

4 结论

期刊信息