﻿ 我国陆海统一似大地水准面构建的三维重力矢量法
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The 3D Gravity Vectors Method in China Land and Ocean Quasi-geoid Determination
XING Zhibin , LI Shanshan
Information Engineering University, Zhengzhou 450000, China
Foundation support: The National Natural Science Foundation of China (No. 41274029); The National High-tech Research and Development Program of China (863 Program) (No. 2013AA122502)
First author: XING Zhibin (1990—), male, PhD candidate, majors in physical geodesy.E-mail:xzb0312@126.com
Abstract: The horizontal component of earth gravity field-vertical deflection is very sensitive to the information of terrain. Firstly, using 3D gravity vectors-grid vertical deflections which are calculated by gravity and terrain data by solving physical geodetic boundary value problems (GBVP), grid gravity anomaly and grid terrain data to calculate the differences of height anomaly, then, with the control of GPS/leveling points to form rigorous geometric conditions, after that, the grid height anomaly is calculated by L-S adjustment method. Finally, a quasi-geoid model with a high precision and resolution is achieved. Based on the method presented, a national quasi-geoid model is built which includes land and ocean by using more than 6600 GPS/leveling points data, 1'×1' grid vertical deflections, grid gravity anomaly and grid terrain data. Compared with the GPS/leveling points, the absolute precision of our national quasi-geoid is about 4 cm, while the relative precision is better than 7 cm.
Key words: 3D gravity vectors     vertical deflections     differences of height anomaly     LS adjustment     quasi-geoid model

1 格网高程异常差及其平差模型的建立 1.1 格网垂线偏差计算高程异常差的基本原理

(1)

 图 1 垂线偏差与高程异常差的关系 Fig. 1 Using deflection of the vertical to calculate height anomaly difference

(2)
(3)

1.2 计算高程异常差的平差模型

(4)

(5)

(6)

(7)

2 基于三维重力矢量的我国似大地水准面模型的建立 2.1 数据准备

 图 2 我国陆地1′×1′分辨率子午垂线偏差 Fig. 2 China land grid vertical deflections of meridian direction with a resolution of 1′×1′

 图 3 我国陆地1′×1′分辨率卯酉垂线偏差 Fig. 3 China land grid vertical deflections of prime direction with a resolution of 1′×1′

 图 4 我国陆地1′×1′分辨率重力异常 Fig. 4 China land grid gravity anomaly with a resolution of 1′×1′

 图 5 我国陆地1′×1′SRTM地形数据 Fig. 5 China land SRTM terrain data with a resolution of 1′×1′

 图 6 我国陆地GPS/水准点分布 Fig. 6 Distribution of China land GPS/leveling points

2.2 分区似大地水准面的确定

 图 7 区域1的控制点、检核点分布 Fig. 7 Distribution of control and check points of area 1

 图 8 区域2的控制点、检核点分布 Fig. 8 Distribution of control and check points of area 2

 图 9 区域3的控制点、检核点分布 Fig. 9 Distribution of control and check points of area 3

 图 10 区域4的控制点、检核点分布 Fig. 10 Distribution of control and check points of area 4

 图 11 区域5的控制点、检核点分布 Fig. 11 Distribution of control and check points of area 5

 图 12 区域6的控制点、检核点分布 Fig. 12 Distribution of control and check points of area 6

 图 13 陆地分区似大地水准面模型及精度 Fig. 13 The quasi-geoid model precision of different areas

 区域 控制点数 检核点数 残差特征值/m 残差范围/个 最大值 最小值 平均值 RMS < RMS < 2×RMS < 3×RMS 区域1 1389 3319 0.099 -0.099 7 0.001 8 0.039 2223 3178 3319 区域2 69 20 0.071 3 -0.113 5 -0.045 8 0.067 9 11 20 20 区域3 266 114 0.096 1 -0.112 0.002 8 0.049 5 70 112 114 区域4 285 290 0.092 9 -0.10 1 0.0002 7 0.041 8 187 281 290 区域5 93 58 0.101 7 -0.117 7 -0.003 1 0.057 3 37 57 58 区域6 290 456 0.097 3 -0.099 0 -0.003 4 0.041 2 293 440 456

 图 14 6个区域残差大小统计 Fig. 14 Statistic of six areas' residual

2.3 全国陆海统一似大地水准面确定

 图 15 陆海统一的似大地水准面模型 Fig. 15 China land and ocean quasi-geoid model

 图 16 残差分布统计 Fig. 16 The distribution of residual

 图 17 残差大小统计 Fig. 17 Statistic of residual

 最大值 残差特征值/m 残差范围/个 最小值 平均值 RMS < RMS < 2×RMS < 3×RMS 0.099 8 -0.100 1 0.001 5 0.040 1 2822 4058 4241

2.4 相对精度评定

2.4.1 相对精度评定方法

(1) 任选一检核点A，以A点为中心选择一定半径范围的检核点Bi(i=1, 2, …, nn为以A点为中心一定半径范围内的检核点的个数)。

(2) 内插A点的高程异常得到ζA，内插Bi的高程异常得到ζi(i=1, 2, …, n)，A点高程异常内插值与Bi点高程异常内插值做差，得

(3) A点的高程异常真值ζABi点的高程异常真值ζi做差，得

(4) 步骤(2)与步骤(3)计算所得的残差之间做差，称为相对高程异常差，得

2.4.2 似大地水准面相对精度分析

 最大值 残差特征值/m 残差范围/个 最小值 平均值 RMS < RMS < 2×RMS < 3×RMS 0.193 2 -0.186 0 0.000 8 0.049 0 34 779 46 777 49 295

 图 18 相对高程异常差分布统计 Fig. 18 Distribution of differences of relative height anomaly

 图 19 全国陆地相对精度分区统计 Fig. 19 Statistic of precision of different areas

 统计半径 区域 统计组数 残差特征值/m 残差范围/个 最大值 最小值 平均值 RMS < RMS < 2×RMS < 3×RMS 0.5° 区域1 46 081 0.193 -0.186 0.000 75 0.049 32 492 43 540 45 905 区域2 13 0.017 -0.064 -0.009 43 0.023 11 12 13 区域3 106 0.126 -0.127 -0.002 52 0.053 68 104 106 区域4 1898 0.157 -0.153 0.005 57 0.050 1291 1808 1895 区域5 44 0.119 -0.155 0.007 93 0.063 28 43 44 区域6 1335 0.151 -0.140 -0.002 10 0.048 905 1276 1333 1° 区域1 147 926 0.193 -0.193 0.000 5 0.053 102 121 140 484 147 632 区域2 31 0.080 -0.141 -0.011 2 0.049 25 29 31 区域3 263 0.145 -0.175 -0.000 3 0.064 175 252 263 区域4 3851 0.179 -0.168 0.005 5 0.052 2628 3665 3844 区域5 128 0.137 -0.155 0.007 5 0.065 84 125 128 区域6 4434 0.177 -0.162 -0.000 2 0.052 3015 4240 4427 2° 区域1 439 026 0.194 -0.196 -0.000 06 0.054 299 623 418 211 438 343 区域2 95 0.161 -0.183 0.003 5 0.067 68 87 95 区域3 805 0.162 -0.178 0.002 0 0.065 543 772 805 区域4 7983 0.180 -0.171 0.004 2 0.056 5409 7624 7978 区域5 418 0.174 -0.184 0.012 6 0.072 279 403 418 区域6 13 876 0.186 -0.169 0.001 7 0.055 9301 13 318 13 865

 图 20 相对高程异常差大小统计 Fig. 20 The statistic of differences of relative height anomaly

3 结论

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http://dx.doi.org/10.11947/j.AGCS.2018.20170076

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文章信息

XING Zhibin, LI Shanshan

The 3D Gravity Vectors Method in China Land and Ocean Quasi-geoid Determination

Acta Geodaetica et Cartographica Sinica, 2018, 47(5): 575-583
http://dx.doi.org/10.11947/j.AGCS.2018.20170076