| 火山Mogi模型反演的总体最小二乘联合平差方法 |
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| 引用本文： | 王乐洋,余航.火山Mogi模型反演的总体最小二乘联合平差方法[J].武汉大学学报(信息科学版),2018,43(9):1333-1341. |
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| 作者姓名： | 王乐洋 余航 |
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| 作者单位： | 1.东华理工大学测绘工程学院, 江西 南昌, 330013 |
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| 基金项目： | 国家自然科学基金41664001国家自然科学基金41204003江西省杰出青-人才资助计划20162BCB23050国家重点研发计划2016YFB0501405江西省教育厅科技项目GJJ150595 |
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| 摘 要： | 针对垂直位移与水平位移的Mogi模型，提出采用总体最小二乘联合（total least squares joint，TLS-J）平差方法进行求解。该方法可同时顾及联合平差函数模型中观测向量与系数矩阵的误差项，且采用3种判别函数最小化法确定相对权比，用以权衡垂直位移与水平位移观测数据在联合求解过程中所占的比重。针对平差过程中出现的病态问题，结合L曲线法确定岭参数。通过实际算例，系统研究了总体最小二乘联合平差方法在长白山天池火山Mogi模型反演中的应用。研究结果表明，以判别函数为$\sum\limits_{i=1}^{n1}{\left| {{{\hat{\bar{e}}}}_{1i}} \right|}+\sum\limits_{j=1}^{n2}{\left| {{{\hat{\bar{e}}}}_{2j}} \right|}$的函数最小化能获得合理的压力源参数估值结果和相对权比大小，具有一定的实际参考价值。
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| 关 键 词： | 总体最小二乘 联合平差 相对权比 Mogi模型 病态 |
| 收稿时间： | 2017-07-06 |
Application of Total Least Squares Joint Adjustment to Volcano Inversion of Mogi Model |
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| Institution: | 1.Faculty of Geomatics, East China University of Technology, Nanchang 330013, China2.School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China3.Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, East China University of Technology, Nanchang 330013, China4.Key Laboratory for Digital Land and Resources of Jiangxi Province, East China University of Technology, Nanchang 330013, China |
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| Abstract: | In this paper, a total least squares joint (TLS-J) adjustment method is proposed to the inversion of Mogi model with vertical and horizontal observational data. The proposed method considers the errors in both observation vector and coefficient matrix of the functional model of joint adjustment problem. Three forms of the minimum discriminate function methods are adopted to determine the weight scaling factor which are used to weigh the vertical and horizontal observation data. In view of the existing ill-posed problems in the joint adjustment, the L-curve method is adopted to determine the ridge parameter. Through practical examples, the total least squares joint method is systematically applied to the inversion of the Mogi model of Changbaishan Tianchi volcano. The results show that the discriminant function as the minimum can obtain the reasonable value of pressure source parameters and the relative weight ratio, which has a certain referential value to practical applications. |
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