区域地壳运动速度场的几类最小二乘配置解法

Building up Regional Crustal Movement Velocity Field with Several Kinds of Least Squares Collocation

在最小二乘配置方法中,关键在于协方差拟合函数的参数求解。而在拟合函数确定的情况下,直接影响其结果的是如何确定距离同协方差的关系。在传统的确定方案中,为保证协方差的非负定性,对信号量采取截断或者取模;为方便解算,对距离进行分段,这些硬性的处理均会对协方差拟合函数造成影响。对于块体的刚体旋转模型(RRM),其各信号值在距离与方向间具有一定相关性。直接采用观测点间的位置信息对信号量进行拟合,可以避免初始信号的硬性处理。实例验证,该方法的拟合精度高于传统的最小二乘配置解法。

In the least square collocation method,the key is to calculate the parameters of the covariance function.But in the case of the determined the fitting function,the mode of confirming the relationship between distance and covariance has a direct impact on the result.In the traditional solution,in order to ensure the positive property of the covariance function and the efficiency of the program,some inflexible operation will cause the initial signal polluted.There are also some position relativity in the initial signal which acquired by rotation in the rigid body model（RRM）.In this paper,we get the signal value from the position information directly,avoiding the inflexible operation.The velocity field obtained in this paper is more accurate than the traditional least square collocation.