贝叶斯框架下利用GPS数据反演震源参数的一种改进MCMC算法  

An improved MCMC algorithm for inversion of source parameters using GPS data under the Bayesian framework

作　　者：王乐洋 席灿 WANG LeYang;XI Can(Key Laboratory of Mine Environmental Monitoring and Improving around Poyang Lake of Ministry of Natural Resources,East China University of Technology,Nanchang 330013,China;School of Surveying and Geoinformation Engineering,East China University of Technology,Nanchang 330013,China;Jiangxi Province Engineering Research Center of Surveying,Mapping and Geographic Information,Nanchang 330025,China)

机构地区：[1]东华理工大学自然资源部环鄱阳湖区域矿山环境监测与治理重点实验室,南昌330013 [2]东华理工大学测绘与空间信息工程学院,南昌330013 [3]江西省测绘地理信息工程技术研究中心,南昌330025

出　　处：《地球物理学报》2024年第9期3367-3385,共19页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(42174011)资助。

摘　　要：随着机器软硬件设施的飞速发展,贝叶斯算法在各个领域得到了广泛应用.在贝叶斯的框架下,以采样方式的MCMC方法去求解震源参数问题时,马尔科夫链的收敛对于得到合理正确的震源参数至关重要.基于此,本文在已有研究的基础上,改进了MCMC方法的随机步长生成方式,使其随机步长整体符合正态分布;并考虑到初值对马尔科夫链的收敛至关重要,提出以非线性启发式搜索算法结合贝叶斯框架下的MCMC算法共同反演地震震源参数.论文以MPSO算法提供初值,以一组随机生成的值作为对照,针对美浓地震,以GPS位移数据验证了改进MCMC算法在收敛速度上优于原始算法,置信区间更为合理;同时验证了以MPSO为贝叶斯算法提供初值的情况下,不仅克服了启发式搜索算法的不稳定性,且改进算法收敛速度更快.为了验证改进算法能大大缩减采样所需要的次数,拓展本文改进算法在不同类型地震中的应用,本文将改进算法以10万次采样反演了博德鲁姆-科斯MW6.6倾滑型地震震源参数.反演结果支持博德鲁姆-科斯地震断层为北向倾斜断层,形变场拟合东西方向(EW)均方根误差为1.43 mm,南北方向(SN)均方根误差为3.23 mm,垂直方向均方根误差为9.69 mm,优于大部分同类型已有文献.With the rapid development of machine hardware and software facilities,the Bayesian algorithm has been widely used in various fields.In the Bayesian framework,the convergence of the Markov chain is very important for obtaining reasonable and correct source parameters when the sampling MCMC method is used to solve the source parameter problem.Based on existing research,this paper improves the random step generation method of the MCMC method,so that the random step size conforms to the normal distribution as a whole.Considering that the initial value is also crucial to the convergence of the Markov chain,a nonlinear heuristic search algorithm combined with the MCMC algorithm under the Bayesian framework is proposed to jointly invert the seismic source parameters.The MPSO algorithm is used to provide the initial value,and a set of randomly generated values is used as a control.Under the Meinong earthquake,the GPS displacement data verify that the improved MCMC algorithm is superior to the original algorithm in terms of convergence speed,and the confidence interval is more reasonable.At the same time,it is verified that the MPSO provides the initial value for the Bayesian algorithm,which not only overcomes the instability of the heuristic search algorithm but also improves the convergence speed of the improved algorithm.In order to verify that the improved algorithm can greatly reduce the number of times required for sampling and expand the application of the improved algorithm in different types of earthquakes,this paper inverts the source parameters of the Bodrum-Kos MW6.6 dip-slip earthquake with 100000 times of sampling.The inversion results support that the Bodrum-Kos seismic fault is a north-dipping fault.The root mean square error of the deformation field fitting in the east-west direction(EW)is 1.43 mm,the root mean square error in the north-south direction(SN)is 3.23 mm,and the root mean square error in the vertical direction is 9.69 mm,which is better than most of the existing literature of the same type.

关 键 词：贝叶斯框架 MCMC算法 震源参数反演 美浓地震 博德鲁姆-科斯地震 

分 类 号：P228[天文地球—大地测量学与测量工程] P315[天文地球—测绘科学与技术]