﻿ 中国大陆连续GPS时间序列垂向周期信号空间分布
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 大地测量与地球动力学  2023, Vol. 43 Issue (4): 356-363  DOI: 10.14075/j.jgg.2023.04.005

### 引用本文

MIAO Peiyu, XIAO Genru, GUO Zeng, et al. Spatial Distribution of Vertical Periodic Signals in Continents GPS Time Series in Chinese Mainland[J]. Journal of Geodesy and Geodynamics, 2023, 43(4): 356-363.

### Foundation support

Innovation Fund Designated for Graduate Students of ECUT, No.YC2022-s602; Open Fund of Key Laboratory of Marine Environmental Survey Technology and Application, MNR, No.MESTA-2020-A002; Key Research and Development Program of Jiangxi Province, No.20212BBE53031.

### Corresponding author

XIAO Genru, PhD, associate professor, majors in GPS crustal deformation and tectonic interpretation, E-mail: 48381790@qq.com.

### About the first author

MIAO Peiyu, postgraduate, majors in GPS time series analysis, E-mail: mpy17746616207@163.com.

### 文章历史

1. 东华理工大学测绘工程学院，南昌市广兰大道418号，330013;
2. 南京智绘星图信息科技有限公司，南京市玄武大道699号，210023

1 数据预处理 1.1 GPS数据处理

 图 1 基准站站点分布 Fig. 1 Distribution of reference stations
1.2 站点坐标时间序列数据预处理

 图 2 各站点历元数与粗差剔除率 Fig. 2 Epoch number and gross error rejection rate of each station
2 GPS时间序列分析

 $Y=Y_k+Y_t+v_t$ (1)

2.1 线性拟合获取趋势项

 $y_t=a t+b+x_t+\sum\limits_{j=1}^{n_j} g_i H\left(t_i-T_{g_j}\right)$ (2)

 图 3 YNYL站垂向时间序列 Fig. 3 Vertical time series of YNYL station
2.2 小波分析

 $C_{\varphi}=\int_R \frac{|\varphi(t)|^2}{|\omega|} \mathrm{d} \omega <\infty$ (3)

 $\varphi_{a b}(t)=\frac{1}{\sqrt{|a|}} \varphi\left(\frac{t-b}{a}\right), a, b \in R, a \neq 0$ (4)

 图 4 YNYL站垂向时间序列小波分析 Fig. 4 Wavelet analysis of vertical time series of YNYL station

2.3 周期项时间序列振幅拟合

GPS时间序列通常将周期信号视为具有年周期和半年周期的简谐波信号，拟合模型为：

 $\begin{gathered} U_t=c \cdot \sin (2 \pi t)+d \cdot \cos (2 \pi t)+ \\ e \cdot \sin (4 \pi t)+f \cdot \cos (4 \pi t)+v_t \end{gathered}$ (5)

 $A_{\mathrm{ann}}=\sqrt{c^2+d^2}, A_{\mathrm{semi}-\mathrm{ann}}=\sqrt{e^2+f^2}$ (6)

 $\mathrm{RMSE}=\sqrt{\frac{1}{N} \sum\limits_{i=1}^N\left(y_i-\bar{y}_i\right)}$ (7)

RMSE值越小表示其拟合效果越好。以YNYL站为例，其周期项拟合结果如图 5所示。为获取周期信号振幅的全国分布特征，对小波分析提取的主周期信号进行常振幅谐波拟合获取振幅值。

 图 5 YNYL站垂向周期项及拟合值 Fig. 5 Vertical periodic term and fitting values of YNYL station

 图 6 各站主周期谐波拟合RMSE Fig. 6 RMSE of main period harmonic fitting of each station
3 中国GPS站垂向趋势项与周期项分布特征

3.1 垂向速率分布特征

 图 7 垂向趋势项a的分布情况和垂向速率直方图 Fig. 7 National distribution and vertical rate histogram of vertical trend term a
3.2 周期项分布特征

3.2.1 年周期振幅分布特征

 图 8 周年振幅分布及各站周年项振幅统计 Fig. 8 Annual amplitude distribution and annual term amplitude statistics of each station

 图 9 年周期项最大值出现月份统计 Fig. 9 Statistics for the month in which the maximum value of the annual term occurs
3.2.2 半年周期振幅分布特征

 图 10 半年周期项振幅分布及各站半年周期项振幅统计 Fig. 10 Half year amplitude distribution and half year term amplitude statistics of each station

 图 11 半年周期项最大值出现月份及统计 Fig. 11 Month and statistics of the maximum value of the semi annual term
3.2.3 不同周期振幅量级对比

4 中国大陆连续GPS时间序列垂向周期振幅模型

 $\begin{gathered} Y=a x+b y+c x^2+ \\ d x y+e y^2+f \end{gathered}$ (12)
 图 12 各站点年周期、半年周期振幅与经纬度分布 Fig. 12 Distribution of amplitude, longitude and latitude of annual cycle and semi annual cycle of each station

 $\mathrm{SSE}=\sum\limits_{i=1}^m\left(y_i-\tilde{y}_i\right)^2$ (9)

 图 13 中国大陆区域分块 Fig. 13 Regional block of Chinese mainland

 图 14 全国模型与分区域模型振幅差值 Fig. 14 Amplitude difference of national model and subregional model

5 结语

1) 时间序列分析中得到的线性趋势项能够表示中国大陆垂向运动的大致趋势，西域块体天山地区、青藏高原南部、鄂尔多斯块体等地有明显上升趋势，天津沿海地区、华南沿海地区等地有下沉趋势。

2) 通过对选取的260个基准站的周期项振幅进行对比分析可知，年周期振幅大于半年周期振幅，前者通常是后者的3倍以上，年周期运动和半年周期运动具有不同的空间分布特征。季节项中川滇地区的年周期运动和半年周期运动最为明显。从整体上来看，年周期项最大值出现月份在沿海地区和内陆地区具有一定的差异性，相同纬度条件下沿海地区的年周期项最大值出现月份晚于内陆。

3) 年周期模型、半年周期模型相较于全国模型分别提高31.59百分点、9.41百分点，但二项式拟合方法容易受到异常值的影响，今后可对模型进行改进。通过小波分析可知，GPS时间序列的季节信号具有调制特征，没有被准确拟合的季节信号会进入到残差序列中。

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Spatial Distribution of Vertical Periodic Signals in Continents GPS Time Series in Chinese Mainland
MIAO Peiyu1     XIAO Genru1,2     GUO Zeng1     YANG Jiamin1
1. Faculty of Geomatics, East China University of Technology, 418 Guanglan Road, Nanchang 330013, China;
2. Nanjing Zhixing Map Information Technology Co Ltd, 699 Xuanwu Road, Nanjing 210023, China
Abstract: The continuous GPS reference station data of the Chinese Continental Tectonic Environment Monitoring Network are used to reveal the spatial distribution characteristics of the amplitude and phase of the vertical period. The results show that the vertical period signal of each station exhibits obvious seasonal variations, the average amplitude of the semi-annual period signal is only 1/4 of that of the annual period signal, and shows different spatial distributions. The amplitude of the annual cycle signal gradually decreases from west to east in space, with smaller amplitude in southeast coastal areas and larger amplitude in Sichuan and Yunnan; the amplitude of the semiannual cycle gradually decreases from southwest to northeast, and the semiannual cycle phenomenon is more obvious in north China and Sichuan and Yunnan. There is a big difference between phases of annual cycle and semi-annual cycle signals; the peak of annual cycle signal appears between February and August, and the peak of semi-annual cycle signal mostly appears in January and May, and there are obvious zoning characteristics. The peak of the annual cycle signal gradually appears later with increasing latitude, and the peak of the annual cycle signal appears later in coastal areas than inland at the same latitude; the peak of the semi-annual cycle signal appears mostly in May in southwest, northeast, and north China, and in January in south, central and northwest China.
Key words: GPS time series; PPP; least squares method; wavelet analysis; Kriging interpolation; spatial distribution