地壳形变分析的抗差最小二乘配置迭代解法

Analysis of crustal deformation based on iterative solutions of Robust Least Squares Collocation

利用最小二乘配置进行地壳形变分析,其结果的合理性关键在于经验协方差函数的拟合.考虑到观测数据存在粗差的情况,提出基于观测值中位数初值的抗差最小二乘配置方法和基于中位参数法的抗差最小二乘配置方法.两种方法首先分别利用观测值中位数给出观测值初始权阵以及利用中位参数法给出最小二乘配置初始解,然后均在给定协方差函数参数初始值的情况下,应用合适的等价权进行抗差估计并通过迭代计算,最终获得稳健的协方差函数参数估值及最小二乘配置解.利用本文提出的两种方法以及传统方法分别对庐山地震的GPS垂直位移数据和意大利L'Aquila地震的InSAR同震位移数据进行处理分析.结果表明:相对传统方法,基于观测值中位数初值的抗差最小二乘配置方法效果更好,更具稳健性.

The rationality of the results obtained by the least squares collocation（LSC） method in analysis of crustal deformation depends on the fitting of the empirical covariance function. The Robust Least Square Collocation method based on Observation Initial Median Values （RLSC-OIMV） and the Robust Least Square Collocation method based on Median Parameter （RLSC-MP） are proposed consdiering the observation data contains outliers. Firstly, the observation median value is used to obtain the initial weight matrix of observation data and the median parameters method is used to obtain the initial solution of least squares collocation in RLSC-OIMV and RLSC-MP, respectively. With the initial parameters of covariance function, the equivalent weight scheme is then applied to obtain the robust parameters estimation of covariance function and least squares collocation solutions through iteration. We apply the two proposed methods and the traditional methods to analyze GPS vertical displacement data of the Lushan earthquake and the InSAR coseismic displacement data of the L＇Aquila earthquake in Italy. The results show that the RLSC-OIMV is better and more robust than other methods.