摘要
震级均值ma是震级m以上事件的震级平均值.研究了九寨沟7. 0级地震余震序列的震级均值ma之后,发现两个与ma有关的线性关系:(1) lg N'=a'-b'ma,(2) ma=c+dm.第一个关系式不仅与G-R关系的形式相同,并且也可以用来估计完备震级Mc.令ΔN=lg N-lg N',lg N从目录统计得到,lg N'是(1)式给出的预测值.在ΔN与ma的散点图上,ΔN第一次突破0轴对应的ma值可以很好地估计完备性震级Mc.第二个关系式称为震均关系(A-M关系),只能从实际目录统计,不能从已有的统计关系推导出来.若震级是连续随机变量且G-R关系在完备震级Mc以上的任意的震级范围[m,∞]成立,将A-M关系代入极大似然法求b值的Aki-Utsu公式,可得到b值函数B(m)=-r/[c-(1-d) m].对B(m)积分可得(3) lg N=p+klg(c-qm),其中q=1-d.从(3)式可导出(4) F(M≥m)=[(cqm)/(c-qm0]k.(3)和(4)分别是有上限的震级-频度关系及其条件概率分布函数.按以下步骤确定参数c、q、p、k:第一步,拟合线性关系(1) lg N'=a'-b'ma,用ΔN=lg N-lg N'确定完备震级Mc,并统计Mc以上余震序列的震级均值mca.第二步,利用余震序列的最大震级不可能超过主震震级Mm的特点,假定余震序列震级上限mu=Mm+0. 5,通过点(mu,mu)和点(Mc,mca)求解A-M关系(2) ma=c+dm,获得参数c、q.第三步,拟合lg(c-qm)和相应的lg N,确定参数p、k.根据以上步骤,用震后2 h的余震目录拟合各项参数,获得概率分布函数F(M≥m)=[(0. 62-0. 0827m)/(0. 62-0. 0827m0]8. 8602.据此估计在后续累计发生0级以上余震10000次的条件下,至少发生一次的概率为63%、10%和1%对应的的震级分别为4. 8、5. 4、5. 9级.据蒋海昆等(2006)的多震型序列定义,后续须至少发生一次6. 4级以上地震,才能认为九寨沟7. 0级余震序列是多震型序列,而6. 4级以上地震至少发生一次的概率仅为4. 02E-4.根据这些概率计算,在震后2 h可以作出的预测意见为:九寨沟7. 0级地震的余震序列类型为主震-余震型,最大余震震级可能在5级左右或5～6级.迄今为止的事实表明,虽然随着余震的不断发生,以后的参数c、q、p、k会发生一定的波动,但不至于改变震后2 h作出余震预测意见.这表明将A-M关系和G-R关系结合起来,可以在震后最短时间内为预测余震序列类型和最大可能震级提供可靠判据.
The average magnitude ma is defined as the mean magnitude of earthquakes with magnitude m and larger.After investigating the aftershock sequence of Jiuzhaigou earthquake,MS 7,we have found out two linear relationships of ma:(1)lgN′=a′-b′ma,(2)ma=c+dm.The first relation has the same form as the G-R relation,and can be used to estimate the completeness magnitude Mc.LetΔN=lgN-lgN′,where lgN can be directly obtained from the statistics of sequence catalog and lgN′can be calculated from equation(1).Then the completeness magnitude Mc can be estimated by the value of ma where theΔN just crosses the 0-axis of the graph ofΔN versus ma.The second relation is called A-M relationship.It can only be obtained from observing the statistical graphs of ma vs.m,and cannot be derived from any existing statistical relations.Suppose that G-R relation is applicable for any continuous range[m,∞]where m is above the completeness magnitude Mc,a function of b-value will be written as B(m)=-r/[c-(1-d)m]by replacing the mean magnitude with A-M relation in the Aki-Utsu’s formula for b-value.Then equation(3)lgN=p+klg(c-qm)can be obtained from the integral of B(m),and equation(4)F(M≥m)=[(c-qm)/(c-qm0)]k will be derived from equation(3).In equations(3)and(4),the parameter q=1-d.Equation(3)is a new magnitude-frequency relationship with upper-bound magnitude and equation(4)is the conditional probability distribution function for limited magnitude range.The parameters c,q,p and k can be determined by following procedures.The first step,fit the linear relationship(1)lgN′=a′-b′ma and determine the complete magnitude Mc by observing the graph ofΔN versus ma.Then estimate mca,the mean magnitude of the aftershocks with magnitude Mc and larger.Next,assume mu,the upper-limit magnitude of the aftershock sequence as Mm+0.5,in the light of the characteristic that the maximum magnitude of the aftershock sequence do not exceed the magnitude of the mainshock,Mm.Solve the A-M relation ma=c+dm by fitting points(mu,mu)and(Mc,mca)for estimating these parameters c,q.Finally,the parameters p,k can be assessed by fitting lg(c-qm)and its corresponding lgN.By above steps,parameters c,q,p,k,will be estimated as 0.62,0.0827,4.8628,8.8602,respectively,with the aftershock catalog of 2 hours just after Jiuzhaigou mainshock.Then the probability distribution function will be determined as F(M≥m)=[(0.62-0.0827 m)/(0.62-0.0827 m0)]8.8602.Given that 10000 successive aftershocks cumulatively occur with magnitude above 0,the at-least-once probabilities for magnitudes 4.8,5.4,5.9 will be63%,10%and 1%,respectively.According to the definition of the type of multiplet mainshocks proposed by Jiang Haikun et al.(2006),the sequence of Jiuzhaigou earthquake MS7.0 will never be identified as the type of multiplet mainshocks unless the shock with magnitude above 6.4 occurs at least once in successive sequence.But the at-least-once probability of magnitude 6.4 is only4.02 E-4 calculated by the probability distribution function F(M≥m)=[(0.62-0.0827 m)/(0.62-0.0827 m0)]8.8602.These probabilities imply that the sequence of Jiuzhaigou earthquake MS7 will be the type of mainshock-aftershock and the largest aftershock will be magnitude about 5 or between 5 and 6.The successive events by now proves that this prediction is stable and reliable,although parameters c,k,p,q fluctuate somewhat with successive occurrence of aftershocks.From this study,we conclude that combining A-M relation with G-R relation will give a new magnitude-frequency distribution with upper-bound magnitude.And this distribution will provide a method for predicting the type and the maximum possible magnitude of an aftershock sequence as soon as possible after the mainshock.
作者
叶友清
苏金蓉
易桂喜
杨贤和
YE You-qing;SU Jin-rong;YI Gui-xi;YANG Xian-he(Sichuan Earthquake Agency,Chengdu 610041,China)
出处
《地球物理学进展》
CSCD
北大核心
2019年第2期489-499,共11页
Progress in Geophysics
基金
国家自然科学基金(41574047)
国家重点研发计划(2018YFC1504501-02)共同资助
作者简介
第一作者:叶友清,男,1965年生,高级工程师,从事地震地质、统计地震学和地震预报研究.(E-mail:yeyq206@126.com);通讯作者:苏金蓉,女,1971年生,高级工程师,从事数字地震学分析研究.(E-mail:sujr0816@163.com)
