地震同震滑动分布反演的总体最小二乘方法

doi:10.11947/j.AGCS.2017.20160212

测绘学报 ›› 2017, Vol. 46 ›› Issue (3): 307-315.doi: 10.11947/j.AGCS.2017.20160212

地震同震滑动分布反演的总体最小二乘方法

王乐洋^1,3, 李海燕¹, 温扬茂², 许才军²

1. 东华理工大学测绘工程学院, 江西南昌 330013;
2. 武汉大学测绘学院, 湖北武汉 430079;
3. 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, 江西南昌 330013

收稿日期:2016-05-19 修回日期:2016-10-25 出版日期:2017-03-20 发布日期:2017-04-11
作者简介:王乐洋(1983-),男,博士,副教授,主要研究方向为大地测量反演及大地测量数据处理。E-mail:wleyang@163.com
基金资助:
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）

Total Least Squares Method Inversion for Coseismic Slip Distribution

WANG Leyang^1,3, LI Haiyan¹, WEN Yangmao², XU Caijun²

1. Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, China;
2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
3. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China

Received:2016-05-19 Revised:2016-10-25 Online:2017-03-20 Published:2017-04-11
Supported by:
National Natural Science Foundation of China (Nos.41664001;41204003;41574002;41431069);Support Program for Outstanding Youth Talents in Jiangxi Province (No.20162BCB23050);National Department Public Benefit Research Foundation (Surveying, Mapping and Geoinformation) (No.201512026);National Key Research and Development Program(No.2016YFB0501405);Science and Technology Project of the Education Department of Jiangxi Province (No.GJJ150595)

摘要/Abstract

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3.63×10¹⁸N·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。

关键词: 同震滑动分布, 总体最小二乘, 反演, 正则化, 拉奎拉地震

Abstract: The coefficient matrix (Green matrix) is composed of surface point offset caused by unit slip of sub-fault patches. The elements of the coefficient matrix are related to the location, geometry of rupture surface, assumption of model and other factors. In this paper, we attempted to consider the Green'function matrix (coefficient matrix) errors in order to compensate for the effects of above-mentioned factors to some extent. The total least squares (TLS) method, which both errors of coefficient matrix and observation vector are considered, is proposed for fault slip inversion. So we dealt with the errors in both of coefficient matrix and observation at same time. And by analysis of the relations between observation vector and coefficient matrix elements, we obtained the covariance matrix of coefficient matrix elements and observation vector. Considering the coefficient matrix was ill-posed, we used the second-order Laplace smoothing to constrain the slip parameters each other, then we used the regularized total least squares method to estimate slip distribution. the total least squares (TLS)slip inversion method was applied to simulate oblique fault event and Mw6.3 earthquake occurred in L'Aquila (central Italy) on April 6, 2009, respectively. To L'Aquila earthquake, the results by total least squares method indicate that the inverted geodetic moment is 3.63×10¹⁸ N·m (Mw6.34). With a maximum slip of 0.95 m, and a average rake of -96.4°, the main slip occurred at depth of 4 km-15 km. The difference of slip distribution solutions between total least squares and least squares method is less than 10^-4 order.

Key words: coseismic slip distribution, total least squares inversion, regularization, L'Aquila earthquake

中图分类号:

P227

王乐洋, 李海燕, 温扬茂, 许才军. 地震同震滑动分布反演的总体最小二乘方法[J]. 测绘学报, 2017, 46(3): 307-315.

WANG Leyang, LI Haiyan, WEN Yangmao, XU Caijun. Total Least Squares Method Inversion for Coseismic Slip Distribution[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(3): 307-315.

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地震同震滑动分布反演的总体最小二乘方法

Total Least Squares Method Inversion for Coseismic Slip Distribution

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