地壳应变参数反演的总体最小二乘方法

摘要

The inversion of strain (rate) parameters based on total least squares (TLS) is studied,not only considering the error of observation (displacement or velocity field),but also considering the error effects of the coefficient matrix generally composed of monitoring points coordinates.All calculation formulae of crust strain (rate) parameters inversion based on total least squares (TLS) using monitoring points displacement or velocity field are deduced.Because there are constant part independent from monitoring points coordinates and coordinates part in the coefficient matrix,it is divided into two parts.The stochastic model of strain parameter inversion using coordinate displacement with TLS is solved by matrix vec operator.Through a simulated example,the comparisons and analysis of strain (rate) parameters are carried out between the total least squares (TLS) results and least squares (LS) results.The rationality and effectiveness of total least squares (TLS) in crust strain (rate) parameters inversion are confirmed.%采用总体最小二乘方法研究地壳应变(率)参数的反演,不仅考虑观测值的误差,同时考虑通常由监测点坐标组成的反演参数的系数矩阵的误差影响,推导了利用监测点位移或速度反演地壳应变(率)参数的总体最小二乘方法的求解公式；基于反演参数的系数矩阵中既含有不依赖于监测点坐标的常数部分又含有监测点坐标部分,将系数矩阵分为两部分,通过矩阵拉直运算求解总体最小二乘方法反演应变参数的随机模型；通过模拟算例比较分析了利用总体最小二乘方法与最小二乘方法反演地壳应变参数的差别,证实了总体最小二乘方法研究地壳应变参数的合理性和实效性.