地震同震滑动分布反演的总体最小二乘方法

发布时间：2018-07-01 19:36

本文选题：同震滑动分布 + 总体最小二乘　；参考：《测绘学报》2017年03期

【摘要】：同震滑动分布参数与地表形变间的线性关系依赖于格林函数矩阵的构造,格林函数矩阵元素与破裂面位置、几何参数、破裂方式及位错模型假设等因素有关。本文尝试考虑格林函数矩阵元素的误差来补偿上述原因在一定程度上对反演参数的影响,采用同时顾及系数矩阵(格林函数矩阵)和观测向量两者误差的总体最小二乘方法反演同震滑动分布。首先确定了系数矩阵元素和观测向量的协因数矩阵,考虑到格林函数矩阵的病态性(秩亏),借助拉普拉斯二阶平滑得到正则化矩阵,采用总体最小二乘正则化法反演同震滑动分布。并对2009年意大利中部拉奎拉(L’Aquila)Mw6.3级地震实例进行同震滑动分布反演研究。结果表明,拉奎拉地震的走向为144.37°,倾角为59.06°,滑动分布的最大滑动量为0.95m,平均滑动角为-96.4°,主要滑动深度为4~15km的范围,地震矩为3.63×10~(18)N·m,对应的矩震级为Mw6.34。总体最小二乘与最小二乘法的滑动分布解存在一定差别,但差别的量级在10-4以内。
[Abstract]:The linear relationship between the coseismic slip distribution parameters and the surface deformation depends on the construction of the Green function matrix. The elements of the Green function matrix are related to the location of the rupture surface, the geometric parameters, the rupture mode and the hypothesis of the dislocation model. In this paper, we try to consider the error of Green function matrix element to compensate for the influence of the above reasons on the inversion parameters to some extent. The coearthquake slip distribution is inversed by the global least squares method which takes into account the errors of the coefficient matrix (Green function matrix) and the observation vector simultaneously. Firstly, the cofactor matrix of coefficient matrix and observation vector is determined. Considering the ill-condition (rank deficiency) of Green function matrix, the regularization matrix is obtained by Laplacian second-order smoothing. The coseismic slip distribution is inversed by the global least squares regularization method. The coseismic slip distribution of the Mw6.3 earthquake in L'Aquila, central Italy, in 2009 is inversed. The results show that the L'Aquila earthquake has a strike of 144.37 掳, a dip angle of 59.06 掳, a maximum slip of 0.95m and an average slip angle of -96.4 掳. The main slip depth is within the range of 4~15km, and the seismic moment is 3.63 脳 10 ~ (18) N ~ (m), corresponding to the magnitude of the moment is Mw6.34. There are some differences in the sliding distribution between the total least squares and the least squares, but the order of difference is less than 10-4.
【作者单位】：东华理工大学测绘工程学院;流域生态与地理环境监测国家测绘地理信息局重点实验室;武汉大学测绘学院;
【基金】：国家自然科学基金(41664001;41204003;41574002;41431069) 江西省杰出青年人才资助计划项目(20162BCB23050) 测绘地理信息公益性行业科研专项(201512026) 国家重点研发计划(2016YFB0501405) 江西省教育厅科技项目(GJJ150595)~~
【分类号】：P315

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