影响b值计算误差的Monte Carlo实验研究
|
摘要
本文假设地震的发生与时间的关系遵循稳态泊松模型,假设地震震级M服从参数为1/β的指数分布,其中β=b/loge,在此基础上生成地震目录。用最小二乘法估算b值,分别从样本数量、震级间隔、震级误差三方面分析b值误差的大小。统计分析结果表明,b值的标准偏差随着样本数量的增多而减小;随着震级间隔的增大而减小;震级误差使b值的标准误差变大。本文可以为利用真实地震目录求b值时选择适当的方法提供参考。
In this paper,we assume that relationship between earthquake occurrence and time follows stationary Poisson model;and earthquake magnitude Mis an exponential distribution with parameter 1/β,β=b/loge.Earthquake catalog are generated based on this assumption.We use the least square method to estimate b values,and analysis the error of b values from number of samples,magnitude interval,and magnitude respectively.Statistical analysis shows that the standard deviation of b values decreases with the increase of the number of samples,the standard deviation of b values decreases with the increase of the magnitude interval,and magnitude error makes the standard deviation of b value bigger.
In this paper,we assume that relationship between earthquake occurrence and time follows stationary Poisson model;and earthquake magnitude Mis an exponential distribution with parameter 1/β,β=b/loge.Earthquake catalog are generated based on this assumption.We use the least square method to estimate b values,and analysis the error of b values from number of samples,magnitude interval,and magnitude respectively.Statistical analysis shows that the standard deviation of b values decreases with the increase of the number of samples,the standard deviation of b values decreases with the increase of the magnitude interval,and magnitude error makes the standard deviation of b value bigger.
引文
[1]Gutenberg B,Richter C F.Seismicity of the Earth and Associated Phenomena[M].2nd ed.Prince-ton N J:Princeton Univ Pr,1954.1-310.
[2]Rundle J B.Derivation of the complete Gutenberg-Richter magnitude-frequency relation using theprinciple of scale invariance[J].J Geophys Res,1989,94:12 337-12 342.
[3]Turcotte D L.Fractals and Chaos in Geology and Geophysics[M].Cambridge:Cambridge Universi-ty Press,1992.1-221.
[4]McGarr A.Dependence of magnitude statistics on strain rate[J].Bull Seism Soc Am,1976,66:33-44.
[5]Qin C Y,Papadimitriou E E,Papazachos B C,et al.Spatial distribution of time independent seis-micity of China[J].Pure Appl Geophys,1999,154:101-119.
[6]Mogi K.Study of elastic shocks caused by the fracture of heterogeneous materials and its relations toearthquake phenomena[J].Bull Earth Res Inst,1962,40:125-173.
[7]Mogi K.Magnitude-frequency relation for elastic shocks accompanying fracture of various materialsand some related problems in earthquakes(2)[J].Bull Earthq Res Inst,1962,40:831-853.
[8]Scholz C H.The frequency-magnitude relation of microfracturing in rock and its relation to earth-quakes[J].Bull Seism Soc Am,1968,58:399-415.
[9]吴开统,焦远碧,吕培苓,等.b值研究进展综述[J].地震,1986,6(1):50-53.
[10]Suyehiro S.Differences between after shocks and foreshocks in the relationship of magnitude to fre-quency of occurrence for the great Chilean earthquake of 1960[J].Bull Seism Soc Am,1966,56:185-200.
[11]Gibowicz S J.Variation of the frequency-magnitude relation during earthquake sequences in NewZealand[J].Bull Seism Soc Am,1973,63:517-528.
[12]Robinson R.Variation of energy release,rate of occurrence and b-value of earthquakes in the mainseismic region,New Zealand[J].Physics of the Earth and Planetary Interiors,1979,18(3):209-220.
[13]Smith W D.The b-value as an earthquake precursor[J].Nature,1981,289:136-139.
[14]李全林,陈锦标,于渌,等.b值时空扫描—监视破坏性地震孕育过程的一种手段[J].地球物理学报,1978,21(2):101-125.
[15]马鸿庆.华北地区几次大震前的b值异常变化[J].地球物理学报,1978,21(2):126-141.
[16]Westerhaus M,Wyss M,Yilmaz R,et al.Correlating variations of b values and crustal deformationduring the 1990smay have pinpointed the rupture initiation of the MW=7.4Izmit earthquake of 1999August 17[J].Geophys J Int,2002,148:139-152.
[17]Schorlemmer D,Nero G,Wiemer S,et al.Stability and significance tests for b-value anomalies:Ex-ample from the Tyrrhenian Sea[J].Geophys Res Lett,2003,30(16):1 835,doi:10.1029/2003GL017335.
[18]Schorlemmer D,Wiemer S,Wyss M.Earthquake statistics at Parkfield:1.Stationarity of b values[J].J Geophys Res,2004,109:B12307,doi:10.1029/2004JB003234.
[19]Wyss M,Sammis C G,Nadeau R M.Fractal dimension and b-value on creeping and locked patchesof the San Andreas fault near Parkfield,California[J].Bull Seism Soc Am,2004,94:410-421.
[20]Wyss M,Stefansson R.Nucleation points of recent mainshocks in southern Iceland,mapped by b-values[J].Bull Seism Soc Am,2006,96:599-608.
[21]黄玮琼,时振梁,曹学锋.b值统计中的影响因素及危险性分析中b值的选取[J].地震学报,1989,11(4):351-361.
[22]Aki K.Maximum likelihood estimate of bin the formula log N=a-bMand its confidence limits[J].Bull Earthquake Res Inst,Tokyo Univ.1965,43:237-239.
[23]张建中,宋良玉.地震b值的估计方法及其标准误差-应用蒙特卡罗方法估计b值精度[J].地震学报,1981,3(3):292-301.
[24]Shi Y L,Blot B A.The standard error of the magnitude-frequency b value[J].Bull Seism Soc Am,1982,72(5):1 677-1 687.
[25]秦长源.地震震级误差对b值的影响[J].地震学报,2000,22(4):337-344.
[26]任雪梅,高孟潭,冯静.地震目录的完整性对b值计算的影响[J].震灾防御技术,2011,6(3):257-268.
[27]苏有锦,李永莉,李忠华,等.川滇地区区域地震目录完整性最小震级分析[J].地震研究,2003,26(Sup):10-16.
[28]龙锋,闻学泽,倪四道.区域最小完整性震级时空分布的确定以龙门山断裂带为例[J].地震,2009,29(3):27-36.
[29]王鹏,郑建常,赵金花,等.山东地区最小完整性震级的确定R-S检验[J].华北地震科学,2011,29(3):19-22.
[30]李志海,蒋长胜,黄瑜,等.新疆地区地震目录最小完整性震级和台网科学布局研究[J].地震学报,2011,33(6):763-775.
[31]韩立波,蒋长胜,李艳娥,等.用于地震可预测性CSEP计划的南北地震带地区地震最小完整性震级Mc研究[J].地震,2012,32(1):17-27.
[32]刘杰,傅征祥,孟桂萍,等.地震发生中长期预测中的非稳态泊松模型[J].地震,1998,18(3):219-225.
[33]陈培善,白彤霞,李保昆.b值和地震复发周期[J].地球物理学报,2003,46(4):510-519.
[35]金星,廖诗荣,陈绯雯.地震台网实时速报系统研究[J].福建地震,2006,22(3-4):1-10.
[36]Tinti S,Mulargia F.Effects of magnitude uncertainties on estimating the parameters in the Guten-berg-Richter frequency-magnitude law[J].Bull Seism Soc Am,1985,75:1 681-1 697.
[37]Tinti S,Mulargia F.Application of the extreme value approaches to the apparent magnitude distri-bution of the earthquakes[J].Pure and Applied Geophysics,1985,123:199-220.
[2]Rundle J B.Derivation of the complete Gutenberg-Richter magnitude-frequency relation using theprinciple of scale invariance[J].J Geophys Res,1989,94:12 337-12 342.
[3]Turcotte D L.Fractals and Chaos in Geology and Geophysics[M].Cambridge:Cambridge Universi-ty Press,1992.1-221.
[4]McGarr A.Dependence of magnitude statistics on strain rate[J].Bull Seism Soc Am,1976,66:33-44.
[5]Qin C Y,Papadimitriou E E,Papazachos B C,et al.Spatial distribution of time independent seis-micity of China[J].Pure Appl Geophys,1999,154:101-119.
[6]Mogi K.Study of elastic shocks caused by the fracture of heterogeneous materials and its relations toearthquake phenomena[J].Bull Earth Res Inst,1962,40:125-173.
[7]Mogi K.Magnitude-frequency relation for elastic shocks accompanying fracture of various materialsand some related problems in earthquakes(2)[J].Bull Earthq Res Inst,1962,40:831-853.
[8]Scholz C H.The frequency-magnitude relation of microfracturing in rock and its relation to earth-quakes[J].Bull Seism Soc Am,1968,58:399-415.
[9]吴开统,焦远碧,吕培苓,等.b值研究进展综述[J].地震,1986,6(1):50-53.
[10]Suyehiro S.Differences between after shocks and foreshocks in the relationship of magnitude to fre-quency of occurrence for the great Chilean earthquake of 1960[J].Bull Seism Soc Am,1966,56:185-200.
[11]Gibowicz S J.Variation of the frequency-magnitude relation during earthquake sequences in NewZealand[J].Bull Seism Soc Am,1973,63:517-528.
[12]Robinson R.Variation of energy release,rate of occurrence and b-value of earthquakes in the mainseismic region,New Zealand[J].Physics of the Earth and Planetary Interiors,1979,18(3):209-220.
[13]Smith W D.The b-value as an earthquake precursor[J].Nature,1981,289:136-139.
[14]李全林,陈锦标,于渌,等.b值时空扫描—监视破坏性地震孕育过程的一种手段[J].地球物理学报,1978,21(2):101-125.
[15]马鸿庆.华北地区几次大震前的b值异常变化[J].地球物理学报,1978,21(2):126-141.
[16]Westerhaus M,Wyss M,Yilmaz R,et al.Correlating variations of b values and crustal deformationduring the 1990smay have pinpointed the rupture initiation of the MW=7.4Izmit earthquake of 1999August 17[J].Geophys J Int,2002,148:139-152.
[17]Schorlemmer D,Nero G,Wiemer S,et al.Stability and significance tests for b-value anomalies:Ex-ample from the Tyrrhenian Sea[J].Geophys Res Lett,2003,30(16):1 835,doi:10.1029/2003GL017335.
[18]Schorlemmer D,Wiemer S,Wyss M.Earthquake statistics at Parkfield:1.Stationarity of b values[J].J Geophys Res,2004,109:B12307,doi:10.1029/2004JB003234.
[19]Wyss M,Sammis C G,Nadeau R M.Fractal dimension and b-value on creeping and locked patchesof the San Andreas fault near Parkfield,California[J].Bull Seism Soc Am,2004,94:410-421.
[20]Wyss M,Stefansson R.Nucleation points of recent mainshocks in southern Iceland,mapped by b-values[J].Bull Seism Soc Am,2006,96:599-608.
[21]黄玮琼,时振梁,曹学锋.b值统计中的影响因素及危险性分析中b值的选取[J].地震学报,1989,11(4):351-361.
[22]Aki K.Maximum likelihood estimate of bin the formula log N=a-bMand its confidence limits[J].Bull Earthquake Res Inst,Tokyo Univ.1965,43:237-239.
[23]张建中,宋良玉.地震b值的估计方法及其标准误差-应用蒙特卡罗方法估计b值精度[J].地震学报,1981,3(3):292-301.
[24]Shi Y L,Blot B A.The standard error of the magnitude-frequency b value[J].Bull Seism Soc Am,1982,72(5):1 677-1 687.
[25]秦长源.地震震级误差对b值的影响[J].地震学报,2000,22(4):337-344.
[26]任雪梅,高孟潭,冯静.地震目录的完整性对b值计算的影响[J].震灾防御技术,2011,6(3):257-268.
[27]苏有锦,李永莉,李忠华,等.川滇地区区域地震目录完整性最小震级分析[J].地震研究,2003,26(Sup):10-16.
[28]龙锋,闻学泽,倪四道.区域最小完整性震级时空分布的确定以龙门山断裂带为例[J].地震,2009,29(3):27-36.
[29]王鹏,郑建常,赵金花,等.山东地区最小完整性震级的确定R-S检验[J].华北地震科学,2011,29(3):19-22.
[30]李志海,蒋长胜,黄瑜,等.新疆地区地震目录最小完整性震级和台网科学布局研究[J].地震学报,2011,33(6):763-775.
[31]韩立波,蒋长胜,李艳娥,等.用于地震可预测性CSEP计划的南北地震带地区地震最小完整性震级Mc研究[J].地震,2012,32(1):17-27.
[32]刘杰,傅征祥,孟桂萍,等.地震发生中长期预测中的非稳态泊松模型[J].地震,1998,18(3):219-225.
[33]陈培善,白彤霞,李保昆.b值和地震复发周期[J].地球物理学报,2003,46(4):510-519.
[35]金星,廖诗荣,陈绯雯.地震台网实时速报系统研究[J].福建地震,2006,22(3-4):1-10.
[36]Tinti S,Mulargia F.Effects of magnitude uncertainties on estimating the parameters in the Guten-berg-Richter frequency-magnitude law[J].Bull Seism Soc Am,1985,75:1 681-1 697.
[37]Tinti S,Mulargia F.Application of the extreme value approaches to the apparent magnitude distri-bution of the earthquakes[J].Pure and Applied Geophysics,1985,123:199-220.
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