系数矩阵误差对地壳应变参数反演的影响  

The Effect of the Random Coefficient Matrix on Adjustment of the Inversion of Crustal Strain Parameters Model

作　　者：王乐洋[1,2] 许光煜 WANG Leyang XU Guangyu(Faculty of Geomatics, East China Institute of Technology,Nanchang 330013, China Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG,Nanchang 330013, Chin School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China)

机构地区：[1]东华理工大学测绘工程学院,江西南昌330013 [2]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 [3]武汉大学测绘学院,湖北武汉430079

出　　处：《武汉大学学报（信息科学版）》2017年第10期1453-1460,共8页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41664001;41204003);江西省杰出青年人才资助计划(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);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开放基金(WE2015005);对地观测技术国家测绘地理信息局重点实验室开放基金(K201502);东华理工大学博士科研启动基金(DHBK201113)~~

摘　　要：针对地壳应变参数反演模型中系数矩阵含随机和非随机元素及观测数据存在相关性等情况,以部分变量误差(partial-errors-in-variables,PEIV)模型为基础,采用了地壳应变参数反演的加权总体最小二乘算法,该算法不受系数矩阵和权矩阵结构的限制,能够快速、有效解决系数矩阵含有随机误差的模型问题。结合推导得到的最小二乘改正项公式,对地壳反演模型中坐标点误差对反演参数求解的影响进行了分析。通过对模拟数据和川滇地区的实际数据进行处理,得出系数矩阵误差对地壳应变参数反演的影响主要受GPS站点坐标值量级以及应变参数量级的牵制。Theweighted total least squares method based on partial errors-in-variables （PEIV for short） model is used to solve the inversion parameters of crustal strain model.It not only considers the error of observation （displacement or velocity field）,but also the error effects from the coefficient matrix,generally composed of monitoring points coordinates.When taking the special structure of the coefficient matrix in the geodetic inversion model into account,we insure that the repeated coordinates have the same residual and that the constants are not allocated any correction.The method usedin this paper can meet these requirements as it separates the random elements from the constant elements taking advantage of the partial errors-in-variables model.All calculation formulae for crust strain （rate） parameters inversion based on partial errors-in-variables using monitoring point displacement or velocity fields are deduced.In addition,the derivate correction of weighted least squares （WLS） is used to analyze the effect of the random coefficient.The discrepancy between the weighted least squares solution and WTLS solution was also investigated.Because of the complexity of the WTLS solution,we propose a formulation to relate the WLS／and WTLS solutions based on Xu （J Geod 86： 661-675,2012）.A simulation using data from the Sichuan-Yunnan region permits a comparison and analysis of the effect of the random design matrix.The experimental results reveal that the effect of the random coefficient matrix on adjustment of the inversion of crustal strain （rate） parameters model is mainly depend on the order of value of the GPS coordinates and the crustal strain parameters themselves.

关 键 词：大地测量反演 加权总体最小二乘 川滇地区 系数矩阵 地壳应变 部分变量误差模型 

分 类 号：P207[天文地球—测绘科学与技术]