适用于弱震的中国东南地区地震资料稀疏情况的极值灾害模型(英文)
|
摘要
由于岗布尔(Gunbel)第三极值分布模型的独特优点(例如其震级上限ω等),地震专家把该模型应用到地震危险性研究。然而由于其复杂的非线性分布,以及地震数据的局限,极大地限制了在地震研究中的应用。为此,论述了以下两个方面的研究:挖掘拓宽和有效利用观测数据;确定初始参数以确保非线性拟合模型的收敛。该方法还能应用于弱震区地震发生规律的研究,为了阐述该方法的独特优点,对不同地震构造背景下的两组——中国东南的弱震区及希腊西部强震区地震数据进行了分析。研究证明对以上两个地震区的结果稳定且拟合误差小。
The Gumbel extreme model,especially the third distribution G(M)=exp-(ω-m/ω-μ)1/λ is used usually to earthquake risk research because of its prominent advantages,such as the upper bound to magnitude ω etc.Due to the complications of nonlinearity and the limitation of sparse observations,however,its importance has been largely underestimated.The methodology developed here concentrates on two aspects: exploring widening and adaptable use of the observations and finding the proper starting parameters to guarantee the convergence in the nonlinear fitting.Moreover,this new method makes it possible to study the occurrence pattern of large earthquakes in low seismicity regions.In order to expound the distinctive advantage of this method,two data sets from different seismotectonic backgrounds,a low seismicity region from southeastern China and a high seismicity region from western Greece,are analysed.Both of these results are good and stable,as with low fitting errors.
The Gumbel extreme model,especially the third distribution G(M)=exp-(ω-m/ω-μ)1/λ is used usually to earthquake risk research because of its prominent advantages,such as the upper bound to magnitude ω etc.Due to the complications of nonlinearity and the limitation of sparse observations,however,its importance has been largely underestimated.The methodology developed here concentrates on two aspects: exploring widening and adaptable use of the observations and finding the proper starting parameters to guarantee the convergence in the nonlinear fitting.Moreover,this new method makes it possible to study the occurrence pattern of large earthquakes in low seismicity regions.In order to expound the distinctive advantage of this method,two data sets from different seismotectonic backgrounds,a low seismicity region from southeastern China and a high seismicity region from western Greece,are analysed.Both of these results are good and stable,as with low fitting errors.
引文
1 Gutenberg B and Richter C F.Frequency of earthquakes inCalifornia[J].Bull.Seism.Soc.Am.,1944,34:185-188.
2 Rundle J B.Derivation of the complete Gutenberg-Richtermagnitude-frequency relation using the principle of scale in-variance[J].J.Geophys.Res.,1989,94(B9):12 337-12 342.
3 Turcotte D L.A fractal approach to probabilistic seismic haz-ard assessment[J].Tectonophysics,1989,167:171-177.
4 Turcotte D L.Fractals and chaos in geology and geophysics[M].Cambridge University Press,1992.
5 Pacheco J F,Scholz C H and Sykes L R.Changes in fre-quency-size relationship from small to large earthquakes[J].Nature,1992,355:71-73.
6 Qin C,et al.Spatial distribution of time independent seismic-ity of China[J].Pure Appl.Geoph.,1999,154:101-119.
7 Qin C.The Thickness of seismogenic layer under the areassurrounding the Ordos block,Northern China[J].Pure Ap-pl.Geoph.,2002,159:2613-2628.
8 Mogi K.Regional variations in magnitude-frequency rela-tion of earthquakes[J].Bulletin of the Earthquake ResearchInstitute,1967,45:313-325.
9 Scholz C H.The frequency magnitude relation of microfrac-turing in rock and its relation to earthquakes[J].Bull.Seism.Soc.Am.,1968,58:399-415.
10 Scholz C H.The mechanics of earthquakes and faulting[M].Cambridge Unversity Press,1990.
11 Makropoulos K C and Burton P W.Seismic hazard inGreece.I.Magnitude recurrence[J].Tectonophysics,1985,117:205-257.
12 Burton P W,et al.Extreme earthquake perceptibility studyin Greece and its surrounding area[J].Natural Hazards,2004,32:277-312.
13 Burton P W.Pathways to seismic hazard evaluation:ex-treme and characteristic earthquakes in areas of low andhigh seismicity[J].Natural Hazards,1990,3:275-291.
14 Berrill J B and Davis R O.Maximum entropy and the mag-nitude distribution[J].Bull.Seism.Soc.Am.,1980,70:1 823-1 831.
15 Main I G and Burton P W.Information theory and the earth-quake frequency-magnitude distribution[J].Bull.Seism.Soc.Am.,1984,74:1 409-1 426.
16 Ratkowsky D A.Nonlinear regression modelling[R].Mar-cel Dekker,INC,New York and Basel,1983.
17 Gumbel E J.Simplified plotting of statistical observations[J].Transactions,1945,26:69-81.
18 Nordquist J N.Theory of largest values applied to earth-quake magnitude[J].Tran.Am.Geophys.Union,1945,26:29-31.
19 Yegulalp T M.Forecasting for largest earthquakes[J].Management Science,1974,21:418-421.
20 Yegulalp TM and Kuo J T.Statistical prediction of the oc-currence of maximum magnitude earthquakes[J].Bull.Seism.Soc.Am.,1974,64:393-414.
21 Burton P W.Perceptible earthquake in the United Kingdom[J].Geophys.J.R.Astro.Soc.,1978,54:475-479.
22 Burton P W.Seismic risk in southern Europe through to In-dia examined using Gumbel’s third distribution of extremevalues[J].Geophys.J.R.Astro.Soc.,1979,59:249-280.
23 Burton P W.Variation in seismic risk parameters in Brit-ain,Proceeding of the 2nd international symposium on theanalysis of seismicity and on seismic hazard[A].Liblice,Czechoslovakia,May 18-23,1981,495-530.
24 Burton P W,et al.Seismic risk in Turkey,the Aegean andthe eastern Mediterranean:the occurrence of large magni-tude earthquakes[J].Geophys.J.R.Astro.Soc.,1984,78:475-506.
25 Kijko A and Sellevoll MA.Estimation of earthquake hazardparameters from incomplete files.Part I,Utilization of ex-treme and complete catalogues with different threshold mag-nitudes[J].Bull.Seism.Soc.Am.,1989,79:645-654.
26 Gringorten I I.A plotting rule for extreme probability paper[J].J.Geophys.Res.,1963,68:813-814.
27 Burton P W and Makropoulos K C.Seismic risk of the Cir-cum-pacific earthquakes:II.Extreme values using Gumbel's third distribution and the relationship with strain energyrelease[J].Pure Appl.Geophys.,1985,123:849-869.
28 Wessel P and Smith W H F.The Generic Mapping Tools(GMT)software[S].1995.
2 Rundle J B.Derivation of the complete Gutenberg-Richtermagnitude-frequency relation using the principle of scale in-variance[J].J.Geophys.Res.,1989,94(B9):12 337-12 342.
3 Turcotte D L.A fractal approach to probabilistic seismic haz-ard assessment[J].Tectonophysics,1989,167:171-177.
4 Turcotte D L.Fractals and chaos in geology and geophysics[M].Cambridge University Press,1992.
5 Pacheco J F,Scholz C H and Sykes L R.Changes in fre-quency-size relationship from small to large earthquakes[J].Nature,1992,355:71-73.
6 Qin C,et al.Spatial distribution of time independent seismic-ity of China[J].Pure Appl.Geoph.,1999,154:101-119.
7 Qin C.The Thickness of seismogenic layer under the areassurrounding the Ordos block,Northern China[J].Pure Ap-pl.Geoph.,2002,159:2613-2628.
8 Mogi K.Regional variations in magnitude-frequency rela-tion of earthquakes[J].Bulletin of the Earthquake ResearchInstitute,1967,45:313-325.
9 Scholz C H.The frequency magnitude relation of microfrac-turing in rock and its relation to earthquakes[J].Bull.Seism.Soc.Am.,1968,58:399-415.
10 Scholz C H.The mechanics of earthquakes and faulting[M].Cambridge Unversity Press,1990.
11 Makropoulos K C and Burton P W.Seismic hazard inGreece.I.Magnitude recurrence[J].Tectonophysics,1985,117:205-257.
12 Burton P W,et al.Extreme earthquake perceptibility studyin Greece and its surrounding area[J].Natural Hazards,2004,32:277-312.
13 Burton P W.Pathways to seismic hazard evaluation:ex-treme and characteristic earthquakes in areas of low andhigh seismicity[J].Natural Hazards,1990,3:275-291.
14 Berrill J B and Davis R O.Maximum entropy and the mag-nitude distribution[J].Bull.Seism.Soc.Am.,1980,70:1 823-1 831.
15 Main I G and Burton P W.Information theory and the earth-quake frequency-magnitude distribution[J].Bull.Seism.Soc.Am.,1984,74:1 409-1 426.
16 Ratkowsky D A.Nonlinear regression modelling[R].Mar-cel Dekker,INC,New York and Basel,1983.
17 Gumbel E J.Simplified plotting of statistical observations[J].Transactions,1945,26:69-81.
18 Nordquist J N.Theory of largest values applied to earth-quake magnitude[J].Tran.Am.Geophys.Union,1945,26:29-31.
19 Yegulalp T M.Forecasting for largest earthquakes[J].Management Science,1974,21:418-421.
20 Yegulalp TM and Kuo J T.Statistical prediction of the oc-currence of maximum magnitude earthquakes[J].Bull.Seism.Soc.Am.,1974,64:393-414.
21 Burton P W.Perceptible earthquake in the United Kingdom[J].Geophys.J.R.Astro.Soc.,1978,54:475-479.
22 Burton P W.Seismic risk in southern Europe through to In-dia examined using Gumbel’s third distribution of extremevalues[J].Geophys.J.R.Astro.Soc.,1979,59:249-280.
23 Burton P W.Variation in seismic risk parameters in Brit-ain,Proceeding of the 2nd international symposium on theanalysis of seismicity and on seismic hazard[A].Liblice,Czechoslovakia,May 18-23,1981,495-530.
24 Burton P W,et al.Seismic risk in Turkey,the Aegean andthe eastern Mediterranean:the occurrence of large magni-tude earthquakes[J].Geophys.J.R.Astro.Soc.,1984,78:475-506.
25 Kijko A and Sellevoll MA.Estimation of earthquake hazardparameters from incomplete files.Part I,Utilization of ex-treme and complete catalogues with different threshold mag-nitudes[J].Bull.Seism.Soc.Am.,1989,79:645-654.
26 Gringorten I I.A plotting rule for extreme probability paper[J].J.Geophys.Res.,1963,68:813-814.
27 Burton P W and Makropoulos K C.Seismic risk of the Cir-cum-pacific earthquakes:II.Extreme values using Gumbel's third distribution and the relationship with strain energyrelease[J].Pure Appl.Geophys.,1985,123:849-869.
28 Wessel P and Smith W H F.The Generic Mapping Tools(GMT)software[S].1995.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心