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《Chinese Journal of Geophysics》 2013-01

## Measuring three-dimensional surface displacements from combined InSAR and GPS data based on BFGS method

HU Jun1,LI Zhi-Wei1*,ZHU Jian-Jun1,DING Xiao-Li1,2, WANG Chang-Cheng1,FENG Guang-Cai1,SUN Qian1 1 School of Geosciences and Info-Physics,Central South University,Changsha 410083,China 2 Department of Land Surveying and Geo-Informatics,The Hong Kong Polytechnic University,Hong Kong,China
InSAR has the advantages of wide spatial coverage,high spatial resolution and high precision,but it can only measure one-dimensional surface displacements in line-of-sight(LOS).While GPS can monitor three-dimensional surface displacements,it is generally with very low spatial resolution.In this paper,the method of combining InSAR and GPS to measure three-dimensional surface displacements with high spatial resolution is studied.Firstly,it is proved that a local optimization method is sufficient to achieve the global optimization solutions of the objective function model,which is used to optimize the InSAR and GPS integration.Then the BFGS method is introduced in this study to estimate the optimal value of the three-dimensional surface displacement velocities.Compared to the global optimization method or the analytical optimization method,the BFGS method is very simple in computing and easy to converge,and has good resistance to numerical instability.In the last of the paper,the results of numerical simulations and real data experiments over Southern California are presented.They show a great improvement of accuracy when the proposed methods are used.Especially,when the observation or interpolation errors lead to ill-condition in the coefficient matrix of normal equations,the analytical optimization method can result in great errors,while the BFGS method works very well.
【Fund】： 国家自然科学基金(40974006 40774003);; 香港研究资助局项目(PolyU5161/06E PolyU5155/07E);; 教育部新世纪优秀人才支持计划(NCET-08-0570);; 中央高校基本科研业务费专项资助(2011JQ001 2009QZZD004);; 教育部首批博士研究生学术新人奖(085201001)联合资助
【CateGory Index】： P228.4;P225
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