﻿ 利用全张量重力梯度异常探测月球地下隐伏地质结构及其解释
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 大地测量与地球动力学  2023, Vol. 43 Issue (4): 409-413, 440  DOI: 10.14075/j.jgg.2023.04.014

### 引用本文

YE Zhourun, LIANG Xinghui, LIU Jinzhao, et al. Exploration and Interpretation of Lunar Underground Concealed Structures Using Full Gravity Gradients Anomaly[J]. Journal of Geodesy and Geodynamics, 2023, 43(4): 409-413, 440.

### Foundation support

National Natural Science Foundation of China, No.41904010;Natural Science Foundation of Anhui Province, No.2008085MD115;Open Fund of State Key Laboratory of Geodesy and Earth's Dynamics, Innovation Academy for Precision Measurement Science and Technology, CAS, No.SKLGED2022-1-4; Fundamental Research Funds for the Central Universities, No.JZ2021HGTB0107.

### Corresponding author

LIANG Xinghui, PhD, associate researcher, majors in physical geodesy, E-mail: lxh_whigg@whigg.ac.cn.

### 第一作者简介

YE Zhourun, PhD, associate professor, majors in physical geodesy, E-mail: yezhorun329@hotmail.com.

### 文章历史

1. 合肥工业大学土木与水利工程学院，合肥市屯溪路193号，230009;
2. 中国科学院精密测量科学与技术创新研究院大地测量与地球动力学国家重点实验室，武汉市徐东大街340号，430077;
3. 中国地震局第一监测中心，天津市耐火路7号，300180

1 研究方法 1.1 月球自由空气扰动重力梯度获取

 $\begin{gathered} T(r, \theta, \lambda)=\frac{G M}{R} \sum\limits_{n=N_{\min }}^{N_{\max }} \sum\limits_{m=0}^n\left(\frac{R}{r}\right)^{n+1} \cdot \\ \left(\bar{C}_{n m} \cos (m \lambda)+\bar{S}_{n m} \sin (m \lambda)\right) \bar{P}_{n m}(\cos \theta) \end{gathered}$ (1)

 \begin{aligned} & T_{x x}=\frac{1}{r^2}\left(T_{\theta \theta}+r T_r\right) \\ & T_{x y}=T_{y x}=\frac{1}{r^2 \sin \theta}\left(T_{\lambda \theta}-\frac{\cos \theta}{\sin \theta} T_\lambda\right) \\ & T_{x z}=T_{z x}=\frac{1}{r}\left(\frac{1}{r} T_\theta-T_{r \theta}\right) \\ & T_{y y}=\frac{1}{r^2 \sin ^2 \theta}\left(T_{\lambda\lambda}+r \sin ^2 \theta T_r+\right. \\ &\left.\cos \theta \sin \theta T_\theta\right) \\ & T_{y z}=T_{z y}=\frac{1}{r \sin \theta}\left(T_{\lambda r}-\frac{1}{r} T_\lambda\right) \\ & T_{z z}=T_{r r} \end{aligned} (2)

1.2 地形高程获取

 $\begin{gathered} H(\theta, \lambda)=\sum\limits_{n=0}^{N_{\max }^{\mathrm{DTM}}} \sum\limits_{m=0}^n\left(\overline{\mathrm{HC}}_{n m} \cos (m \lambda)+\right. \\ \left.\overline{\mathrm{HS}}_{n m} \sin (m \lambda)\right) \bar{P}_{n m}(\cos \theta) \end{gathered}$ (3)

1.3 基于有限功率地形法的地形重力梯度改正

 $C_{m m}^\beta=\left\{\begin{array}{l} \bar{C}_{n m} \\ \bar{S}_{n m} \end{array}\right\}=\frac{3}{2 n+1} \frac{1}{\bar{\rho}}\left(\frac{H_{n m}^1}{R}+\frac{(n+2) H_{n m}^2}{2 R^2}+\right. \\ \quad\quad\quad\quad\quad \left.\frac{(n+2)(n+1) H_{n m}^3}{6 R^3}\right)$ (4)

 $\begin{gathered} H_{n m}^i=\frac{1}{4 \pi} \int_{\lambda_1=0}^{\lambda_2=2 \pi} \int_{\theta_1=0}^{\theta_2=\pi}\left(h_2^i-h_1^i\right) \cdot \\ \rho\left(r^{\prime}, \theta^{\prime}, \lambda^{\prime}\right) Y_{m m}^\beta\left(r^{\prime}, \theta^{\prime}, \lambda^{\prime}\right) \sin \theta^{\prime} \mathrm{d} \theta^{\prime} \mathrm{d} \lambda^{\prime} \end{gathered}$ (5)
 $Y_{n m}^\beta(\theta, \lambda)=\bar{P}_{m m}(\cos \theta)\left\{\begin{array}{l} \cos m \lambda, \beta=0 \\ \sin m \lambda, \beta=1 \end{array}\right.$ (6)

 图 1 地形起伏示意图 Fig. 1 Schematic view of topography
2 实验计算和讨论

 图 2 原始扰动重力梯度 Fig. 2 Original disturbing gravity gradient

 图 3 月球地形起伏 Fig. 3 Lunar topographic relief

 图 4 地形校正后重力梯度异常 Fig. 4 Gravity gradient anomaly after terrain correction

3 结语

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Exploration and Interpretation of Lunar Underground Concealed Structures Using Full Gravity Gradients Anomaly
YE Zhourun1,2     LIANG Xinghui2     LIU Jinzhao3     LIU Lintao2
1. College of Civil Engineering, Hefei University of Technology, 193 Tunxi Road, Hefei 230009, China;
2. State Key Laboratory of Geodesy and Earth's Dynamics, Innovation Academy for Precision Measurement Science and Technology, CAS, 340 Xudong Street, Wuhan 430077, China;
3. The First Monitoring and Application Center, CEA, 7 Naihuo Road, Tianjin 300180, China
Abstract: We apply the finite power terrain correction method(i.e., the Tesseroid forward modelling in harmonic spectral domain) to the gravity gradient calculation in terms of lunar topography. Using gravity data from the Gravity Recovery and Interior Laboratory(GRAIL) mission and terrain information recovered from the Moontopo720 model, we calculate the total gravity tensors anomaly after terrain correction at the height of GRAIL satellite. By taking advantage of the multi-component characteristics of gravity gradient and the relevant experimental results, we estimate the spatial horizontal range distributions of underground mascons through the horizontal gradient anomaly. Using the total gravity gradient anomaly maps, we preliminarily verify the distributions of main fault structures caused by tidal gravity.
Key words: Moon; gravity gradient; terrain correction; Tesseroid model