吉林大学学报(地球科学版) ›› 2021, Vol. 51 ›› Issue (1): 277-285.doi: 10.13278/j.cnki.jjuese.20190183

• 地球探测与信息技术 • 上一篇    

起伏地表下的复杂三维地质模型建立与重力异常计算

贾卓, 刘四新, 赵雪然, 鹿琪, 李宏卿, 王元新   

  1. 吉林大学地球探测科学与技术学院, 长春 130026
  • 收稿日期:2019-09-09 发布日期:2021-02-02
  • 通讯作者: 刘四新(1966-),男,教授,博士生导师,主要从事探地雷达、钻孔雷达及电磁波测井等方法理论和应用方面的研究,E-mail:liusixin@jlu.edu.cn E-mail:liusixin@jlu.edu.cn
  • 作者简介:贾卓(1988-),男,博士研究生,主要从事深部矿产资源指标体系建立与信息提取方面的研究,E-mail:jia-zhuo16@mails.jlu.edu.cn
  • 基金资助:
    国家重点研发计划项目（2016YFC0600505）

Complex 3D Model Establishment Under Undulating Surface and Gravity Anomaly Calculation

Jia Zhuo, Liu Sixin, Zhao Xueran, Lu Qi, Li Hongqing, Wang Yuanxin   

  1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
  • Received:2019-09-09 Published:2021-02-02
  • Supported by:
    Supported by the National Key Research and Development Program of China (2016YFC0600505)

PDF (PC)

208

摘要： 由于地质体和矿体的形态非常复杂，使用长方体网格离散建立正演模型时可能和真实情况有很大差别，因此计算结果可靠性差。本文提出一种基于约束Delaunay网格剖分的方法对地质体进行离散并进行重力建模，在模型边界等复杂区域使用网格自适应加密技术，将三维地质体离散为有限个四面体；并详细推导出针对四面体网格的重力正演公式，实现了基于约束Delaunay网格剖分技术的三维重力数值模拟；最后，针对一个合成数据模型，将计算解与解析解对比。结果表明，细化网格的模拟结果比粗糙网格更好，满足数值模拟的精度要求。将该方法应用到金川矿区实际地质体建模中，根据局部需要，建立各处网格密度不均匀的三维模型，并计算该模型的地表重力场，而后对比模拟数据与实测数据，结果表明Delaunay网格建模方法具有很强的适用性，能够模拟复杂的地质体重力异常。

关键词: Delaunay网格, 四面体, 三维地质体模型, 重力正演, 金川矿区

Abstract: Because of the complicated shape of the actual geological bodies, it may be quite different from the real situation when using the cuboid grid to establish the forward model, and the reliability of the calculation results is poor. In this paper, a constrained Delaunay meshing method is proposed to discretize the geological bodies and perform gravity modeling. The grid adaptive cryptography is used in the complex region such as a model boundary to discretize a three-dimensional geological body into a finite tetrahedron;then, the gravity forward formula of the tetrahedral mesh is derived in detail;and finally,the three-dimensional gravity numerical simulation based on the constrained Delaunay meshing technique is realized. For a composite data model, the calculated solution is compared to the analytical solution. And the simulation results of fine mesh are better than that of coarse mesh, and meet the accuracy requirements of numerical simulation. The method was applied to the actual geological body modeling in Jinchuan mining area. According to the local needs, a three-dimensional model with uneven mesh density was built, the surface gravity field of the model was calculated, and the simulation data was compared with the measured data. The results show that the unstructured mesh modeling method is strongly applicable and can simulate the gravity anomalies of complex geological bodies.

Key words: Delaunay grid, tetrahedron, 3D geological model, gravity forward, Jinchuan mining area

中图分类号: 

  • P631
[1] Juan G A. 3D Forward and Inverse Modeling of Total-Field Magnetic Anomalies Caused by a Uniformly Magnetized Layer Defined by a Linear Combination of 2D GaussianFunctions[J]. Geophysics, 2007, 73(1):11.
[2] Bhattacharyya B K. A Generalized Multibody Model for Inversion of Magnetic Anomalies[J]. Geophysics, 1980, 45(2):255-270.
[3] Gunn P J. Quantitative Methods for Interpreting Aeromagnetic Data:A Subjective Review[J]. AGSO Journal of Australian Geology & Geophysics, 1997, 17(2):105-113.
[4] Nettleton L L. Gravity and Magnetic Calculations[J]. Geophysics, 1942, 7(3):293.
[5] Caratori T F, Cocchi L, Carmisciano C. Rapid 3-D Forward Model of Potential Fields with Application to the Palinuro Seamount Magnetic Anomaly (Southern Tyrrhenian Sea, Italy)[J]. Journal of Geophysical Research, 2009, 114(B2):B02103.
[6] Hamilton D E, Jones T A. Computer Modeling of Geologic Surfaces and Volumes[C]//AAPG Computer Applications in Geology. Tulsa:[s.n.], 1992:297.
[7] Christian J T. 3D Geoscience Modeling:Computer Techniques for Geological Characterization[M]. Berlin:Berlin Springer-Verlag, 1996.
[8] Jessell M. Three-Dimensional Geological Modelling of Potential-Field Data[J]. Computers & Geosciences, 2001, 27(4):455-465.
[9] Reinhard P, John W H. Computer Graphics in Geology[J]. Lecture Notes in Earth Sciences, 1992, 41(4):613-614.
[10] Talwani M. Computation with the Help of a Digital Computer of Magnetic Anomalies Caused by Bodies of Arbitrary Shape[J]. Geophysics, 1965, 30(5):797.
[11] Plouff D. Gravity and Magnetic Fields of Polygonal Prisms and Applications to Magnetic Terrain Corrections[J]. Geophysics, 1976, 41:727-741.
[12] Pignatelli A, Nicolosi I,Carluccio R, et al. Graphical Interactive Generation of Gravity and Magnetic Fields[J]. Computers & Geosciences, 2011, 37(4):567-572.
[13] Tontini C. Rapid Interactive Modeling of 3D Magnetic Anomalies[J]. Computers & Geosciences, 2012, 48:308-315.
[14] Blakely R J. Potential Theory in Gravity and Magnetic Applications[M]. London:Cambridge University Press, 1995.
[15] Shin Y H, Choi K S, Xu H. Three-Dimensional Forward and Inverse Models for Gravity Fields Based on the Fast Fourier Transform[J]. Computers & Geosciences, 2006, 32(6):727-738.
[16] 张岭, 郝天珧. 基于Delaunay剖分的二维非规则重力建模及重力计算[J].地球物理学报,2006, 49(3):877-884. Zhang Ling, Hao Tianyao. 2-D Irregular Gravity Modeling and Computation of Gravity Based on Delaunay Triangulation[J]. Chinese Journal of Geophysics, 2006, 49(3):877-884.
[17] Barnett C T. Theoretical Modeling of the Magnetic and Gravitational Fields of an Arbitrary Shaped Three-Dimensional Body[J]. Geophysics, 1976, 41:1353-1364.
[18] Okabe M. Analytical Expressions for Gravity Anomalies Due to Homogeneous Polyhedral Bodies and Translations into Magnetic Anomalies[J]. Geophysics, 1979, 44(4):730-741.
[19] Pohanka V. Optimum Expression for Computation of the Gravity Field of Homogeneous Polyhedral Body[J]. Geophysical Prospecting, 1988, 36(7):733-751.
[20] Liu S, Hu X, Xi Y, et al. 2D Inverse Modeling for Potential Fields on Rugged Observation Surface Using Constrained Delaunay Triangulation[J]. Computers & Geosciences, 2015, 76:18-30.
[21] Luo Yao,Yao Changli. Forward Modeling of Gravity, Gravity Gradients, and Magnetic Anomalies Due to Complex Bodies[J]. Journal of China University of Geosciences, 2007, 18(3):280-286.
[22] Roy K K. Potential Theory in Applied Geophysics[M]. Calcutta:Springer Science & Business Media, 2007.
[23] 刘海飞, 柳建新, 郭荣文,等.起伏地形三维激电连续介质模型快速反演[J]. 吉林大学学报(地球科学版), 2011,41(4):1212-1218. Liu Haifei, Liu Jianxin, Guo Rongwen, et al. Efficient Inversion of 3D IP Data for Continuous Model with Complex Geometry[J]. Journal of Jilin University (Earth Science Edition), 2011, 41(4):1212-1218.
[24] 林家勇, 汤井田, 丁茂斌, 等. 复杂地形条件下激发极化有限单元法三维数值模拟[J]. 吉林大学学报(地球科学版), 2010, 40(5):1183-1187. Lin Jiayong, Tang Jingtian, Ding Maobin, et al. Three-Dimension Numerical Simulation of Induced Polarization & Finite Element Method Under Complicated Terrain[J]. Journal of Jilin University (Earth Science Edition), 2010, 40(5):1183-1187.
[25] 李振海, 罗志才, 钟波. 基于3D Delaunay剖分算法的重力建模与分析[J]. 地球物理学报, 2012, 55(7):2259-2267. Li Zhenhai, Luo Zhicai, Zhong Bo. Gravity Modeling and Analyzing Based on 3D Delaunay Triangulation Algorithm[J]. Chinese Journal of Geophysics, 2012, 55(7):2259-2267.
[26] 郑耀, 陈建军. 非结构网格生成:理论、算法和应用[M]. 北京:科学出版社, 2016. Zheng Yao,Chen Jianjun. Unstructured Mesh Generation:Theories, Algorithms and Applications[M].Beijing:Science Press, 2016.
[27] Tang Z. Main Genetic Types of Ni Ore Deposits in China and Their Relations to Paleo-Plate Tectonics[J]. Geochemistry, 1984, 3(2):102-114.
[28] 段俊, 钱壮志, 焦建刚, 等. 甘肃龙首山岩带西井镁铁质岩体成因及其构造意义[J]. 吉林大学学报(地球科学版), 2015(3):832-846. Duan Jun, Qian Zhuangzhi, Jiao Jiangang, et al. Genesis of Xijing Intrusion from Longshoushan Terrane and the Tectonic Significance[J]. Journal of Jilin University (Earth Science Edition), 2015, 45(3):832-846.
[1] 林家勇, 汤井田, 丁茂斌, 杨晓弘, 杨树云. 复杂地形条件下激发极化有限单元法三维数值模拟[J]. J4, 2010, 40(5): 1183-1187.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 《吉林大学学报(地球科学版)》编辑部
地址：长春市西民主大街938号(130026)　电话：+86-431-88502374；13756165364　E-mail: xuebao1956@jlu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发