﻿ 基于移去-恢复法的区域大气负荷影响精化——以滇西地区为例
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 大地测量与地球动力学  2022, Vol. 42 Issue (6): 631-636  DOI: 10.14075/j.jgg.2022.06.015

引用本文

SHEN Longjie, ZHANG Chuanyin, XU Pengfei, et al. Refinement of Regional Atmospheric Load Effects Based on Removal-Recovery Method: A Case Study of Western Yunnan[J]. Journal of Geodesy and Geodynamics, 2022, 42(6): 631-636.

Foundation support

Basic Research Fund of Chinese Academy of Surveying and Mapping, No.AR2114; Open Fund of Key Laboratory of Marine Environmental Survey Technology and Application, MNR, No.MESTA-2020-A001; The Excellent Platform of Lanzhou Jiaotong University, No.201806.

Corresponding author

ZHANG Chuanyin, PhD, researcher, majors in gravity field and vertical datum construction, E-mail: zhangchy@casm.ac.cn.

文章历史

1. 兰州交通大学测绘与地理信息学院, 兰州市安宁西路88号, 730070;
2. 中国测绘科学研究院, 北京市莲花池西路28号, 100830;
3. 甘肃省地理国情监测工程实验室, 兰州市安宁西路88号, 730070;
4. 地理国情监测技术应用国家地方联合工程研究中心, 兰州市安宁西路88号, 730070

1 理论与方法

1.1 全球负荷形变场的球谐分析

 $\begin{array}{*{20}{c}} {{h_{\rm{w}}}(R, \theta , \lambda ) = }\\ {R\sum\limits_{n = 1}^N {\sum\limits_{m = 0}^n {\left[ {\Delta {C_{nm}}\cos m\lambda + \Delta {S_{nm}}\sin m\lambda } \right]} } {{\bar P}_{nm}}(\sin \varphi )} \end{array}$ (1)

 $\begin{array}{*{20}{c}} {\zeta = \frac{{GM}}{{\gamma r}}\sum\limits_{n = 2}^\infty {{{\left( {\frac{a}{r}} \right)}^n}} \left( {1 + k_n^\prime } \right) \cdot }\\ {\sum\limits_{m = 0}^n {\left( {\Delta {{\bar C}_{nm}}\cos m\lambda + \Delta {{\bar S}_{nm}}\sin m\lambda } \right)} {{\bar P}_{nm}}} \end{array}$ (2)

 $\begin{array}{*{20}{c}} {{g_t} = \frac{{GM}}{{{r^2}}}\sum\limits_{n = 2}^\infty {(n + 1)} \left( {1 + \frac{2}{n}h_n^\prime - \frac{{n + 1}}{n}k_n^\prime } \right) \cdot }\\ {{{\left( {\frac{a}{r}} \right)}^n}\sum\limits_{m = 0}^n {\left( {\Delta {{\bar C}_{nm}}\cos m\lambda + \Delta {{\bar S}_{nm}}\sin m\lambda } \right)} {{\bar P}_{nm}}} \end{array}$ (3)

 $\begin{array}{*{20}{c}} {{H_t} = \frac{{GM}}{{\gamma r}}\sum\limits_{n = 2}^\infty {{{\left( {\frac{a}{r}} \right)}^n}} h_n^\prime \cdot }\\ {\sum\limits_{m = 0}^n {\left( {\Delta {{\bar C}_{nm}}\cos m\lambda + \Delta {{\bar S}_{nm}}\sin m\lambda } \right)} {{\bar P}_{nm}}} \end{array}$ (4)

1.2 区域负荷影响的格林函数积分公式

 $\Delta \mathit{\Theta }(\varphi , \lambda ) = G{\rho _{\rm{w}}}\iint_s {\frac{{\Delta {h_{\rm{w}}}\left( {{\varphi ^\prime }, {\lambda ^\prime }} \right)}}{L}} G(\psi ){\rm{d}}S$ (5)

 $\begin{array}{*{20}{c}} {G_i^V(\psi ) = \frac{{\gamma R}}{M} \cdot }\\ {\sum\limits_{n = 0}^\infty {\left( {\frac{{k_\infty ^\prime }}{{2\sin (\psi /2)}} + \sum\limits_{n = 0}^\infty {\left( {k_n^\prime + k_\infty ^\prime } \right)} {P_n}(\cos \psi )} \right)} } \end{array}$ (6)

 $G_d^V(\psi ) = \frac{{\gamma R}}{M}\frac{1}{{2\sin (\psi /2)}}$ (7)

 $\begin{array}{l} \begin{array}{*{20}{c}} {G(\psi ) = - \frac{\gamma }{M}\left( {\frac{{k_\infty ^\prime - 2h_\infty ^\prime }}{{2\sin (\psi /2)}} + } \right.}\\ {\left. {\sum\limits_{n = 0}^\infty {\left( {(n + 1)k_n^\prime - k_\infty ^\prime - 2\left( {h_n^\prime - h_\infty ^\prime } \right){P_n}(\cos \psi )} \right)} } \right) + } \end{array}\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\frac{\gamma }{M}\frac{1}{{4\sin (\psi /2)}} \end{array}$ (8)

 $\begin{array}{c} G_{i}^{r}(\psi)= \\ \frac{R}{M}\left(\frac{h_{\infty}^{\prime}}{2 \sin (\psi / 2)}+\sum\limits_{n=0}^{\infty}\left(h_{n}^{\prime}+h_{\infty}^{\prime}\right) P_{n}(\cos \psi)\right) \end{array}$ (9)

2 研究区与实验数据处理 2.1 研究区概况

2.2 实验数据 2.2.1 全球大气压变化数据

 图 1 全球大气压数据分布 Fig. 1 Distribution of global atmospheric pressure data
2.2.2 区域高分辨率大气压变化数据

 图 2 区域高分辨率大气压数据分布 Fig. 2 Distribution of regional high resolution atmospheric pressure data
2.2.3 CORS站大地高变化数据

2.3 数据处理流程

1) 对全球等效水高变化格网进行球谐分析展开，得到360阶次负荷变化球谐系数模型，并通过球谐综合计算得到滇西地区参考等效水高和负荷影响模型值格网；

2) 将区域等效水高变化格网数据移去参考等效水高，获得区域等效水高变化残差格网数据，并利用负荷格林函数积分理论计算区域残余负荷影响模型值格网；

3) 将全球负荷影响模型值格网与区域残余负荷影响模型值格网结合，恢复为滇西地区区域高精度负荷影响格网模型。

3 实验结果与分析

3.1 地壳形变

 图 3 大气压变化对滇西地区大地高的影响 Fig. 3 The influence of atmospheric pressure change on the geodetic height in western Yunnan

 图 4 CORS站大地高变化时间序列 Fig. 4 Time series of geodetic height variation at CORS stations

 图 5 CORS站大气负荷时间序列 Fig. 5 Time series of atmospheric load at CORS stations

3.2 时变重力场

 图 6 大气压变化对滇西地区地面重力的影响 Fig. 6 Influence of atmospheric pressure change on surface gravity in western Yunnan
4 结语