中文摘要：

在剔除粗差的基础上,以GPS连续站低频拟合残差时间序列在站心坐标系下的空间分布作为研究对象,运用分形理论中测度关系求分维方法求得全国27个连续站残差空间分布的分维及其无标度区间,并讨论了落入无标度区间的点占总点数的百分比情况;同时,利用相关系数及F检验方法对无标度区间内是否符合线性特征进行显著性检验。主要结果如下：1）除DXIN、QION和XIAA三个连续站残差序列无标度区内线性相关系数在0.99~0.995之间外,其他24个台站无标度区间内的线性相关系数都在0.995以上;27个连续站无标度区内线性回归F检验在α=0.005时全部拒绝不符合线性分布的零假设（H0：b=0）,表明GPS残差序列在无标度区内符合分形特征,即具有较高的自相似性特征。2）除BJFS、LUZH和XIAM三个连续站无标度区间内的点数占各自总点数的40%左右外,其余24个台站无标度区间内的点数占各自总点数的50%甚至60%,说明残差序列中符合分形规律的点约占自身总点数的一半或以上,表明自然分形规律在残差序列中占有一定的权重。3）27个连续站在无标度区间内的分维值在1.71~1.97之间,即各台站分维值为非整数值且存在着差异性;另外,在构建涉及指数的GPS观测模型或噪声模型时,如果选取其分维值作为各自的模型指数,则有可能减少模型的系统误差。

英文摘要：

In this paper, based on the excluding gross error, we get the space distribution of the continuous GPS sites＇s high frequency in the station coordinate system （NEU coordination system）. Then, we use the fractal theory （the measure of relations） to calculate the fractal dimension and its scale-free zone. Finally, we calculate the correlation coefficient and F significant test method in the scale free zone. The main results are as follows：First, aside from the three consecutive points DXIN, QION and XIAA, where the residual series scale free region between the correlation coefficients of 0.99-0. 995, the other 24 units have reached a correlation coefficient of 0. 995 or more. The 27 consecutive sites＇ scale-free zone in the linear regression F-tests rejects the null hypothesis when all scalefree zone in double logarithmic coordinate system can be used least squares linear fit when a： 0. 005. This is consistent with GPS residual sequence fractal features, thus supporting these conclusions. Sec- ond, the percentage of points in the scale-free zone to total points is about 50%-60% at 24 consecutive sites and 40 at the three consecutive sites（BJFS, LUZH and XIAM）. This indicates that about half the observations fall under the laws of the fractal nature. Consequently, the noise residual series or sequence （constructed time series and noise models） can play a guiding role. Third, 27 GPS sites fit the fractal characteristics very well in its scale-free zone （the fractal dimension is not the integer）, with a fractal dimension range between 1.71 and 1.97. This indicates that GPS part of the residual se- quence is contained under the laws of the fractal nature of the observations and should not generally be considered as noise, as supported by our more sophisticated understanding and analysis of GPS obser vations.