测高重力异常中央区奇异积分数值求积公式

doi:10.11947/j.AGCS.2021.20200564

测绘学报 ›› 2021, Vol. 50 ›› Issue (10): 1308-1319.doi: 10.11947/j.AGCS.2021.20200564

测高重力异常中央区奇异积分数值求积公式

宗敬文¹, 李厚朴¹, 纪兵¹, 欧阳永忠²

1. 海军工程大学导航工程教研室, 湖北武汉 430033;
2. 自然资源部海洋环境探测技术与应用重点实验室, 广东广州 510300

收稿日期:2020-12-01 修回日期:2021-06-15 发布日期:2021-11-09
通讯作者: 李厚朴 E-mail:lihoupu1985@126.com
作者简介:宗敬文(1995-),男,博士生,研究方向为物理大地测量。E-mail:zjw19950613@163.com
基金资助:
国家自然科学基金（41774021；41874091；41631072）；湖北省杰出青年科学基金（2019CFA086）

Some numerical quadrature for singular integral of the altimetry gravity in the innermost area

ZONG Jingwen¹, LI Houpu¹, JI Bing¹, OUYANG Yongzhong²

1. Department of Navigation, Naval University of Engineering, Wuhan 430033, China;
2. Key Laboratory of Marine Environmental Survey Technology and Application, Ministry of Natural Resources, Guangzhou 510300, China

Received:2020-12-01 Revised:2021-06-15 Published:2021-11-09
Supported by:
The National Natural Science Foundation of China (Nos. 41774021;41874091;41631072);The Hubei Province Science Fund for Distinguished Young Scholars(No. 2019CFA086)

摘要/Abstract

摘要： 为简化逆Stokes法和逆Vening-Meinesz法反演中央区重力异常计算过程，提高计算效率，本文采用数值求积公式，分别利用Simpson公式和Cotes公式对逆Stokes法和逆Vening-Meinesz法中的奇异积分问题进行了新的研究，系统地推导出了中央区重力异常普适数值积分计算公式。在大地水准面高和垂线偏差理论模型下的分析表明，此公式可直接利用格网节点处的大地水准面高和垂线偏差计算重力异常值，形式简单，计算效率高，计算精度与解析法计算结果精度相当，可以满足实际应用。研究结果可为高精度卫星测高反演重力异常提供基础理论依据。

关键词: 卫星测高, 逆Stokes公式, 逆Vening-Meinesz公式, 非奇异变换, 数值求积公式

Abstract: In order to simplify the calculation process and improve the calculation efficiency of inverse Stokes formula method and the inverse Vening-Meinesz formula method to invert the gravity anomaly, the numerical quadrature method is adopted. A new study on the investigation of singular integral of inverse Stokes formula and inverse Vening-Meinesz formula based on Simpson formula and Cotes formula is done and the formula of gravity anomaly in innermost area are derived systematically. The analysis based on the theoretical model of geoidal height and vertical deflections shows that the formula can directly use the geoid height and vertical deviation at the grid node to calculate the gravity anomaly which have simple form, high precision and high calculation efficiency.These research results can provide theoretical basis for high-precision satellite altimetry inversion of gravity anomalies.

Key words: satellite altimetry, inverse Stokes formula, inverse Vening-Meinesz formula, non-singular transformation, numerical quadrature formula

中图分类号:

P228.3

宗敬文, 李厚朴, 纪兵, 欧阳永忠. 测高重力异常中央区奇异积分数值求积公式[J]. 测绘学报, 2021, 50(10): 1308-1319.

ZONG Jingwen, LI Houpu, JI Bing, OUYANG Yongzhong. Some numerical quadrature for singular integral of the altimetry gravity in the innermost area[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(10): 1308-1319.

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测高重力异常中央区奇异积分数值求积公式

Some numerical quadrature for singular integral of the altimetry gravity in the innermost area

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