多个地震台网相互融合测定震级的贝叶斯算法  

A Bayesian algorithm for magnitude determination by merging multiple seismic networks

作　　者：司政亚 庄建仓 蒋长胜[1] SI ZhengYa;ZHUANG JianCang;JIANG ChangSheng(Institute of Geophysics,China Earthquake Administration,Beijing 100081,China;Beijing Earthquake Agency,Beijing 100080,China;Institute of Statistical Mathematics,Tokyo 106-8569,Japan)

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]北京市地震局,北京100080 [3]日本统计数理研究所,东京106-8569

出　　处：《地球物理学报》2022年第6期2167-2178,共12页Chinese Journal of Geophysics

基　　金：中国地震科学实验场专项项目(2019CSES0105,2019CSES0106);国家自然科学基金(41774067)联合资助。

摘　　要：流动地震台网由于台站台基响应、震级测定方法和操作方式等多种因素的影响,测定震级与区域内的固定地震台网震级测量结果存在差异,从而使其记录到的而标准台网没有记录到的大量局域小地震不能直接补充到标准目录中.即使流动地震台网的震级测定公式中的量规函数经过校正,两者在具体地震事件的震级测定上的差异仍不可避免,因此急需解决这一普遍性问题的快速计算方法.本文先假定震级的观测值服从正态分布,其中对固定台网而言,测定震级的平均值为未知的真实震级,对流动台网而言,测定震级的平均值为真实震级的一个线性函数,然后基于贝叶斯原理,推导得出了不同台网观测震级的后验概率密度函数.应用于实际观测资料时,可用最大似然估计来获得该算法中的矫正参数,并计算后验的地震震级,即矫正震级.我们将该算法实际应用于西昌流动地震台网(XC)与中国地震台网(CN)的震级融合问题中.基于矫正震级与原始测定震级的对比研究表明,矫正震级与固定地震台网原始测定震级之间存在一定偏离度的线性对应分布,而西昌流动地震台网测定震级相比矫正震级整体偏小.本文所提出的多台网震级融合的贝叶斯算法为流动台网测定的不精确震级提供了一种震级矫正的快速算法,考虑固定台网与流动台网测定震级的一致性,固定台网测定震级的稳定性和准确性也得到同步提高.The earthquake magnitude determined by a temporary seismic network usually differs from that given by a permanent seismic network due to several factors,including the undetermined site response,the determination method,and the operation mode.This problem cannot even be solved by correcting the gauge function in the magnitude determination formula for the temporary seismic network.Therefore,a large number of small earthquakes recorded only by temporary seismic networks that cannot be directly added to the standard catalogs.This paper aims to provide a novel fast algorithm for solving this problem.Assuming that an observed magnitude follows the Gaussian distribution,with a mean of its unknown true value if it is determined by the permanent seismic network,or with a mean as a linear function of its true value if it is given by a temporary seismic network,we derive the posterior probability density function of the magnitude given its observation values by different networks,based on the Bayesian formula.The parameters in the posterior probability density function can be estimated from observation data by using the maximum likelihood method,and then the posterior estimate of the earthquake magnitude,namely the revised magnitude,can be calculated.This algorithm is applied to earthquake catalogs recorded by the Xichang(XC)temporary seismic network and by the China(CN)seismic network.We find that the revised magnitude approximately follows a linear relationship against its observed value given by the CN seismic network,generally larger than its value measured by the XC seismic network.The proposed method provides a fast algorithm for correcting the unprecise magnitudes determined by temporary seismic networks,and simultaneously,improves the stability and accuracy of the magnitudes estimated by the permanent seismic network by taking account of the consistency of the magnitudes measured by the temporary seismic network.

关 键 词：流动地震台网 震级标度 震级矫正 贝叶斯算法 

分 类 号：P315[天文地球—地震学]