| 利用重力梯度张量等位面曲率的地质体定位 |
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| 引用本文： | 胡双贵, 李广, 汤井田, 侯振隆, 张林成. 2024. 利用重力梯度张量等位面曲率的地质体定位. 地球物理学报, 67(4): 1641-1655, doi: 10.6038/cjg2023Q0221 |
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| 作者姓名： | 胡双贵 李广 汤井田 侯振隆 张林成 |
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| 作者单位： | 1. 中国矿业大学资源与地球科学学院, 江苏徐州 221008; 2. 东华理工大学南昌市地质灾害智能感知技术与仪器重点实验室, 南昌 330013; 3. 有色金属成矿预测与地质环境监测教育部重点实验室(中南大学), 长沙 410083; 4. 东北大学资源与土木工程学院, 沈阳 110819; 5. 湖南城市学院信息与电子工程学院, 湖南益阳 413002 |
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| 基金项目： | 国家自然科学基金(42004120), 有色金属成矿预测与地质环境监测教育部重点实验室开放基金(2021YSJS02), 湖南省自然科学青年基金(2021JJ40024)和益阳市应用基础研究与软科学研究计划(益财教指108号)联合资助 |
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| 摘 要： | 针对重力梯度张量曲率的研究, 前人的工作主要集中在重力张量曲率的解释及边缘检测中, 几乎没有涉及到地下密度异常体的定位.本文结合重力矢量和重力梯度张量提出了一套基于重力梯度张量等位面曲率的地下密度异常体位置估计策略.首先, 从重力梯度张量等位面曲率的基本定义出发, 计算重力梯度张量等位面曲率.然后, 通过寻找球面或圆形等位面的重力梯度张量曲率, 提出了利用最大主曲率定位地下密度异常体位置的源参数估计方法, 并详细推导了估计3D球体(质点)和2D水平线源位置信息的解析表达式.再者, 针对噪声和多源存在的情况, 提出了一套利用重力梯度张量等位面曲率获得密度异常体位置信息的稳健估计流程, 并利用模糊C均值聚类算法进一步确定地下密度异常体的中心位置.最后, 通过理论模型测试和文顿盐丘实测航空重力梯度数据测试, 验证了本文算法的可行性和可靠性.结果表明: 在满足曲率半径定义条件的情况下, 本文所提出的源参数估计方法可以定位单个或多个地下3D和2D密度异常体的空间位置, 具有较好的稳健性和抗噪能力.该方法拓展了重力梯度张量曲率的应用范围, 可为重力梯度张量的三维反演工作提供先验的空间位置信息.
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| 关 键 词： | 重力梯度张量 等位面曲率 源参数估计 模糊C均值聚类算法 |
| 收稿时间： | 2022-04-03 |
| 修稿时间： | 2023-05-12 |
Localization of geologic bodies using the curvature of the equipotential surface in gravity gradiometry |
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| HU ShuangGui, LI Guang, TANG JingTian, HOU ZhenLong, ZHANG LinCheng. 2024. Localization of geologic bodies using the curvature of the equipotential surface in gravity gradiometry. Chinese Journal of Geophysics (in Chinese), 67(4): 1641-1655, doi: 10.6038/cjg2023Q0221 |
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| Authors: | HU ShuangGui LI Guang TANG JingTian HOU ZhenLong ZHANG LinCheng |
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| Affiliation: | 1. School of Resources and Geosciences, China University of Mining and Technology, Xuzhou Jiangsu 221008, China; 2. Nanchang Key Laboratory of Intelligent Sensing Technology and Instruments for Geological Hazards, East China University of Technology, Nanchang 330013, China; 3. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University), Ministry of Education, Changsha 410083, China; 4. School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China; 5. College of Information and Electronic Engineering, Hunan City University, Yiyang Hunan 413002, China |
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| Abstract: | For the study of the curvature of gravity gradient tensor, previous work mainly focuses on their interpretation and edge detection, and rarely involves utilizing it for source parameter estimation. With the previous work, this paper proposed a source parameter estimation strategy using the curvature of the equipotential surface in gravity gradiometry. According to the fundamentals of the curvature of the equipotential surface in gravity gradiometry, the analytical formulas for estimating the source parameters of 3D causative bodies and 2D material lines are deduced in detail. We expand it to general density sources by finding curvatures corresponding to spheres or circular equipotential surfaces. Then, for noise and interference sources, a robust source parameter estimation process with gravity gradient tensor curvature and fuzzy C-means clustering algorithm is proposed. Tests using synthetic gravity and its gradient tensor data, the real gravity gradient tensor data collected from Vinton dome in the Gulf of Mexico are performed to verify our new proposed algorithm. Results show that the source parameter estimation method based on the curvature of the equipotential surface in gravity gradiometry can be applied to locate 3D and 2D causative bodies with strong anti-noise ability. It expands the application scope of the curvature of the gravity gradient tensor and can provide a priori spatial position information for the three-dimensional inversion of the gravity gradient tensor. |
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| Keywords: | Gravity gradient tensor Curvature of the equipotential surface Source parameter estimation Fuzzy C-means clustering algorithm |
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