Journal of Jilin University(Earth Science Edition) ›› 2015, Vol. 45 ›› Issue (4): 1217-1226.doi: 10.13278/j.cnki.jjuese.201504301

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Forward Calculation of Three Dimensional Gravity Vector Using Finite Element Method

Jiang Fuyu1, Xie Leilei1, Chang Wenkai1, Huang Yan2, Zhang Zuohong2   

  1. 1. School of Earth Sciences and Engineering, Hohai University, Nanjing 210098, China;
    2. Geology Exploration Technology Institute of Jiangsu Province, Nanjing 210048, China
  • Received:2014-10-30 Published:2015-07-26

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Abstract:

Variational problem of three dimensional gravity vector was deduced to meet the boundary value based on Poisson equation and the third boundary condition, and the solution of variational problem is further implemented by using the finite element method. The results of the cubic model test show that the proposed new coefficient matrix storage strategy is more effective to save storage space than a traditional approach; this, in turn, makes it possible to quickly solve liner equations by using the preconditioned conjugate gradient technology. The calculation precision of the gravity vector is closely related to the boundary length and unit grid; while the computational efficiency mainly depends on the total number of nodes and the algorithm used in solving a large sparse system of linear equation. In general, when the length of unit grid is less than 1/10 of the body length, and the boundary length is greater than 7.5 times of the length of the source, a desired result can be achieved.

Key words: variational problem, gravity vector, finite element method, data storage, calculation precision, three dimensional body

CLC Number: 

  • P631.1

[1] 曾华霖. 重力场与重力勘探[M]. 北京: 地质出版社, 2005. Zeng Hualin. Gravity Field and Gravity Exploration[M]. Beijing: Geological Publishing House, 2005.

[2] 李姗姗, 吴晓平, 吴星. 重力矢量及张量信息在地球重力场中的应用[J]. 测绘学院学报, 2005, 22(2): 94-96. Li Shanshan, Wu Xiaoping, Wu Xing. Applications of Gravity Vector and Tensor in the Gravity Field[J]. Journal of Institute of Surveying and Mapping, 2005, 22(2): 94-96.

[3] Nagy D. The Gravitational Attraction of a Right Rectangular Prism[J]. Geophysics, 1966, 31(2): 362-371.

[4] Talwani M. Computer Usage in the Computation of Gravity Anomalies[J]. Methods in Computational Physics, 1973, 13(1): 343-389.

[5] Kwok Y K. Singularities in Gravity Computation for Vertical Cylinders and Prisms[J]. Geophysical Journal International, 1991, 104(1): 1-10.

[6] Kwok Y K. Gravity Gradient Tensors Due to a Polyhedron with Polygonal Facets[J]. Geophysical Prospecting, 1991, 39(3): 435-443.

[7] Okabe M. Analytical Expressions for Gravity Anomalies Due to Homogeneous Polyhedral Bodies and Translations into Magnetic Anomalies[J].Geophysics, 1979, 44(4): 730-741.

[8] Holstein H, Ketteridge B. Gravimetric Analysis of Uniform Polyhedral[J]. Geophysics, 1996, 61(2): 357-364.

[9] Commer M. Three-Dimensional Gravity Modelling and Focusing Inversion Using Rectangular Meshes[J]. Geophysical Prospecting, 2011, 59(5): 966-979.

[10] Li X, Chouteau M. Three-Dimensional Gravity Mo-deling in All Space[J]. Surveys in Geophysics, 1998, 19(4): 339-368.

[11] 蒋甫玉, 高丽坤, 黄麟云. 油气模型的重力梯度张量研究[J]. 吉林大学学报: 地球科学版, 2011, 41(2): 545-551. Jiang Fuyu, Gao Likun, Huang Linyun. Study on Gravity Gradient Tensor of the Oil-Gas Model[J]. Journal of Jilin University: Earth Science Edition, 2011, 41(2): 545-551.

[12] 骆遥, 姚长利. 复杂形体重力场、梯度及磁场计算方法[J]. 地球科学: 中国地质大学学报, 2007, 32(4): 517-522. Luo Yao, Yao Changli. Forward Method for Gravity, Gravity Gradient and Magnetic Anomalies of Complex Body[J]. Earth Science: Journal of China University of Geosciences, 2007, 32(4): 517-522.

[13] 陈召曦, 孟小红, 郭良辉, 等. 基于GPU并行的重力、重力梯度三维正演快速计算及反演策略[J]. 地球物理学报, 2012, 55(12): 4069-4077. Chen Zhaoxi, Meng Xiaohong, Guo Lianghui, et al. Three Dimensional Fast Forward Modeling and the Inversion Strategy for Large Scale Gravity and Gravimetry Data Based on GPU[J]. Chinese Journal of Geophysics, 2012, 55(12): 4069-4077.

[14] Dave A M, Matthew G K. Optimal, Scalable Forward Models for Computing Gravity Anomalies[J]. Geophysical Journal International, 2011, 187(1): 161-177.

[15] Cai Yongen, Wang Chiyun. Fast Finite-Element Cal-culation of Gravity Anomaly in Complex Geolo-gical Regions[J]. Geophysical Journal International, 2005, 162(3): 696-708.

[16] Cruz F A, Knepley M G, Barba L A. PetFMM: A Dynamically Load-Balancing Parallel Fast Multipole Library[J]. International Journal for Numerical Methods in Engineering, 2010, 85(4): 403-428.

[17] Farquharson C G,Mosher C R W.Three-Dimensional Modelling of Gravity Data Using Finite Differences[J]. Journal of Applied Geophysics, 2009, 68(3): 417-422.

[18] 朱自强, 曾思红, 鲁光银, 等. 二度体的重力张量有限元正演模拟[J]. 物探与化探, 2010, 34(5): 668-672. Zhu Ziqiang, Zeng Sihong, Lu Guangyin, et al. Finite Element Forward and Simulation of the Two Dimensional Gravity Gradient Tensor[J]. Geophysical and Geochemical Exploration, 2010, 34(5): 668-672.

[19] 徐世浙. 地球物理中的有限单元法[M]. 北京: 科学出版社, 1994. Xu Shizhe. Finite Element Method in Geophysics[M]. Beijing: Science Press, 1994.

[20] 张力. 坑道直流聚焦超前探测有限元数值模拟研究[D]. 长沙:中南大学, 2011. Zhang Li. Research on Numerical Simulation for DC Focusing Advanced Detection in Tunnel with Finite Element Method[D]. Changsha: Central South University, 2011.

[21] 吴小平, 徐果明. 不完全Cholesky共轭梯度法及其在地电场计算中的应用[J]. 石油地球物理勘探, 1998, 33(1): 89-94. Wu Xiaoping, Xu Guoming. Incomplete Cholesky Conjugate Gradient Method and Its Application in Geoelectric Field Computation[J]. OGP, 1998, 33(1): 89-94.

[22] 吴小平, 徐果明, 李时灿. 利用不完全Cholesky共轭梯度法求解点源三维地电场[J]. 地球物理学报, 1998, 41(6): 848-855. Wu Xiaoping, Xu Guoming, Li Shican. The Calculation of Three-Dimensional Geoelectric Field of Point Source by Incomplete Cholesky Conjugate Gradient Method[J]. Chinese Joural of Geophysics, 1998, 41(6): 848-855.

[23] Nagy D, Papp G, Beneded J. The Gravitational Potential and Its Derivatives for the Prism[J]. Journal of Geodesy, 2000, 74: 552-560.
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