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物探与化探  2020, Vol. 44 Issue (1): 132-140    DOI: 10.11720/wtyht.2020.2256
     方法研究·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
基于非结构化网格的重力梯度张量反演
黄天统, 彭新发, 朱自强
核工业二三〇研究所,湖南 长沙 410007
Inversion of gravity gradient tensor based on unstructured grids
Tian-Tong HUANG, Xin-Fa PENG, Zi-Qiang ZHU
Changsha Uranium Geology Research Institute, Changsha 410007,China
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摘要 

由于重力梯度张量是重力位的二阶导数,与传统的重力测量相比,重力梯度张量具有更高的分辨率,并且重力梯度张量具有5个相互独立的分量,包含了更多的地下空间信息和密度信息,因此将重力梯度张量数据应用到反演中可以得到较好的反演结果。非结构化网格具有很强的几何适应性,能够较好地拟合复杂异常体的边界,通过非结构化网格对反演目标区域进行离散,可以降低剖分误差,从而提高计算精度。为了降低反演过程中的多解性问题,将地球物理反问题的广义正则化目标函数应用于基于非结构化网格的三维重力梯度张量反演中,推导了相关公式,实现了各分量的独立反演,并阐述了深度加权函数在反演过程中的作用。为了充分利用重力梯度张量各分量所携带的密度、空间信息,将5个独立的分量进行了联合反演,反演结果表明,基于非结构化网格的三维重力梯度张量反演能够较好地反映地下异常源的物性分布和赋存位置。通过与长方体网格反演结果对比,本反演方法突出了非结构化网格反演的优越性;最后,通过较复杂组合模型的计算证实了方法的实用性。

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黄天统
彭新发
朱自强
关键词 非结构化网格重力梯度张量反演    
Abstract

Gravity gradient tensor is the second derivatives of gravitational field. Compared with the traditional gravitational exploration, gravity gradient tensor can reach a better resolution. Gravity gradient tensor has 5 independent components, so they can contain more geological information. Therefore, gravity gradient tensor can be used to recover the causative bodies in the subsurface with high accuracy. Due to strong adaptability and flexibility of the unstructured grid, it can smoothly approximate the irregular and complex boundaries of anomalous source. Compared with the structured grid, the unstructured grid can provide researchers with more accurate discretization and calculation with less computation time. In order to reduce the ambiguity of the inversion, the authors chose to jointly and simultaneously invert all gravity gradient components based on tetrahedron grids with the help of the so called generalized objective function which is widely used in geophysical inverse problems. The authors applied the algorithm to each gravity tensor component at the beginning to ensure that the depth weighting function makes a difference in the inversion. It turns out that the depth weighting function works well. To explore all components of the gravity gradient tensor as much as possible, the authors described the joint-inversion in detail in this paper. The inversion results show that 3D inversion of gravity gradient tensor based on unstructured grids can obtain the position of causative bodies in the subsurface and the density distribution. Based on a comparison with rectangular grid inversion results, the authors highlighted the advantages of unstructured grid inversion. And the practicability of the method was verified through two synthetic models.

Key wordsunstructured grids    gravity gradient tensor    inversion
收稿日期: 2018-06-28      出版日期: 2020-03-03
:  P631  
作者简介: 黄天统(1991-),男,硕士,工程师,主要从事重磁勘探及重磁正反演工作。Email: 735084175@qq.com
引用本文:   
黄天统, 彭新发, 朱自强. 基于非结构化网格的重力梯度张量反演[J]. 物探与化探, 2020, 44(1): 132-140.
Tian-Tong HUANG, Xin-Fa PENG, Zi-Qiang ZHU. Inversion of gravity gradient tensor based on unstructured grids. Geophysical and Geochemical Exploration, 2020, 44(1): 132-140.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2020.2256      或      https://www.wutanyuhuatan.com/CN/Y2020/V44/I1/132
重力梯度张量 kx ky kz lx ly lz
Vxx 1 0 0 1 0 0
Vyy 0 1 0 0 1 0
Vzz 0 0 1 0 0 1
Vxy 1 0 0 0 1 0
Vyz 0 1 0 0 0 1
Vxz 0 0 1 1 0 0
Table 1  方向余弦的取值与重力梯度张量各分量的关系
Fig.1  面坐标系统旋转示意
Fig.2  边坐标系统旋转示意
Fig.3  单个长方体模型非结构化网格剖分示意
Fig.4  单个长方体模型重力梯度张量正演结果
Fig.5  单个长方体模型单分量反演结果
Fig.6  单个长方体模型多分量联合反演结果
Fig.7  Y型岩脉模型非结构化网格剖分示意
Fig.8  Y型岩脉模型多分量联合反演结果
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