利用垂直重力梯度异常反演海底地形的解析方法

doi:10.11947/j.AGCS.2022.20200578

测绘学报 ›› 2022, Vol. 51 ›› Issue (1): 53-62.doi: 10.11947/j.AGCS.2022.20200578

利用垂直重力梯度异常反演海底地形的解析方法

徐焕^1,2, 于锦海^1,2, 安邦^1,2, 万晓云³

1. 中国科学院计算地球动力学重点实验室, 北京 100049;
2. 中国科学院大学地球与行星科学学院, 北京 100049;
3. 中国地质大学(北京)土地科学与技术学院, 北京 100083

收稿日期:2020-12-01 修回日期:2021-11-08 发布日期:2022-02-15
通讯作者: 于锦海 E-mail:yujinhai@ucas.edu.cn
作者简介:徐焕(1993-),男,博士生,主要从事海底地形反演。E-mail:xuhuan16@mails.ucas.ac.cn
基金资助:
国家重点研发计划（2016YFB0501702）；国家自然科学基金（41774089；41674026）

An analytical method for bathymetry inversion using vertical gravity gradient anomaly

XU Huan^1,2, YU Jinhai^1,2, AN Bang^1,2, WAN Xiaoyun³

1. Key Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing 100049, China;
2. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. School of Land Science and Technology, China University of Geosciences (Beijing), Beijing 100083, China

Received:2020-12-01 Revised:2021-11-08 Published:2022-02-15
Supported by:
The National Key Research and Development Program of China (No. 2016YFB0501702);The National Natural Science Foundation of China (Nos. 41774089; 41674026)

摘要/Abstract

摘要： 目前，基于重力数据反演海底地形方法的主要原理是利用测深数据拟合出海底地形与重力（或重力梯度）数据之间的线性关系，这会导致对不同的海底地形会有不同的线性关系。为了克服这种不确定性的制约，本文基于长方体海山产生的垂直重力梯度的表达式，通过将研究海域进行格网化，建立了垂直重力梯度（vertical gravity gradient，VGG）与海深之间的函数关系，即关于海深的观测方程组，在此基础上，通过模拟计算，验证了观测方程组的解不仅唯一可解，而且具有较好的抗误差干扰性质。由于观测方程组受到研究海域外海山的影响（分为边界效应、远区影响），因此，需要相应的数学方法来处理这些影响。本文将研究海域进行扩充得到扩展区域，然后在扩展海域上研究观测方程组，此时为了避免观测方程组出现奇异性，引入了正则化方法对扩展后的观测方程组进行求解，并从中截取研究海域上的海深。模拟试验表明，使用正则化方法后，边界效应对反演海深的均方根误差为0.48 m。最后，对南中国海真实海底地形进行了反演计算，将反演的海深与研究海域内的289个船测数据点进行对比，反演结果的均方根误差达到109 m。

关键词: 海底地形, 垂直重力梯度, 边界效应, 远区影响, 正则化

Abstract: At present, the main principle of the seafloor topography inversion method is to fit the most appropriate linear relationship between topography and gravity or gravity gradient. However, different topography will have different linear relationships. In order to overcome the constraint of uncertainty, this paper firstly derives the expression of vertical gravity gradient generated by cubic prism. Then, by gridding the research sea area, a functional relationship between vertical gravity gradient (VGG) and sea depth is established, i.e. the observation equations of sea depth. On the basis of which, it is that the observation equations have strong anti-error interference properties through simulation calculation. Because the observation equations are affected by the seamounts outside the study area (divided into boundary effects and far area effects), it is necessary to propose corresponding mathematical methods to deal with these effects. This paper proposes to expand the research sea area to obtain an expanded area, and then study the observation equations on the expanded sea. At this time, in order to avoid the singularity of the observation equations, a regularization method is introduced to solve the expanded observation equations and cut out the sea depth in the study area. Simulation experiments show that after using the regularization method, the root-mean-square error of the inverted sea depth is only 0.48 m. Finally, this paper inverts an actual seafloor topography of the South China Sea, and the results are compared with the 289 ship sounding data. The root-mean-square error of the inversion results can reach 109 m.

Key words: seafloor topography, vertical gravity gradient, boundary effect, far area effects, regularization

中图分类号:

P228

徐焕, 于锦海, 安邦, 万晓云. 利用垂直重力梯度异常反演海底地形的解析方法[J]. 测绘学报, 2022, 51(1): 53-62.

XU Huan, YU Jinhai, AN Bang, WAN Xiaoyun. An analytical method for bathymetry inversion using vertical gravity gradient anomaly[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(1): 53-62.

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利用垂直重力梯度异常反演海底地形的解析方法

An analytical method for bathymetry inversion using vertical gravity gradient anomaly

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