基于三棱柱单元的青藏高原重力场地形效应计算
Calculation of Gravity Topographic Effect of Qinghai-Tibet Plateau Based on Triangular Prism Elements
DOI: 10.12677/AG.2022.124051, PDF,   
作者: 岳国璇：中南大学地球科学与信息物理学院，湖南 长沙
关键词: 青藏高原；重力场；地形效应；网格建模；The Qinghai-Tibet Plateau； Gravity Field； Topographic Effect； Mesh Modeling
摘要: 地球是一个梨形的不规则椭球体，其表面起伏的地形产生的重力场地形效应对地球物理勘探布格重力异常校正、大地测量学地形校正和确定大地水准面起伏都具有十分重要的意义。青藏高原是全球地质情况最复杂、地形变化最大的区域之一，其产生的地形效应是我国重力勘探普查、反演解释的研究热点。为了计算该地区的重力场地形效应，对该区域进行基础网格建模是最重要的步骤，其次还需进行高精度正演计算。本文提出了一种基于不规则三棱柱单元的带曲率大规模区域网格构建方法，并使用重力场闭合解析公式对其进行了正演计算，我们的结果与前人研究高度一致，证明了建模方法的正确性，同时该方法也可以被用于任意复杂的陆地区域建模，因此也具有应用指导意义。
Abstract: The earth is a pear-shaped irregular ellipsoid, and the topographic effect of the gravity field pro-duced by the undulating topography on its surface is of great significance to the correction of the Bouguer gravity anomaly in geophysical exploration, the topographic correction of geodesy and the determination of geoid fluctuations. The Qinghai-Tibet Plateau is one of the regions with the most complex geological conditions and the largest topographic changes in the world. The topo-graphic effect produced by this area is a research hotspot of gravity exploration census and inversion geological interpretation. In order to calculate the topographic effect of the gravity field the Qinghai-Tibet Plateau, the basic mesh construction of the area is the most important step, followed by high-precision forward calculation. In this paper, a method for constructing a large-scale regional grid with curvature based on irregular triangular prism elements is proposed, and the forward calculation is carried out using the closed analytical formula of the gravity field. The method which is verified correctly can also be used for arbitrarily complex land area modeling, so it also has the guiding significance.
文章引用：岳国璇. 基于三棱柱单元的青藏高原重力场地形效应计算[J]. 地球科学前沿, 2022, 12(4): 505-514. https://doi.org/10.12677/AG.2022.124051

参考文献

[1] Nabighian, M.N., Grauch, V.J.S., Hansen, R.O., LaFehr, T.R., Li, Y., Peirce, J.W., et al. (2005) 75th Anniversary: The Historical Development of the Magnetic Method in Exploration. Geophysics, 70, 33ND-61ND. [Google Scholar] [CrossRef] 
[2] 殷长春, 孙思源, 高秀鹤, 刘云鹤, 陈辉. 基于局部相关性约束的三维大地电磁数据和重力数据的联合反演[J]. 地球物理学报, 2018, 61(1): 358-367.
[3] Reigber, C., Lühr, H. and Schwintzer, P. (2002) CHAMP Mission Status. Advances in Space Research, 30, 129-134. [Google Scholar] [CrossRef] 
[4] Tapley, B.D., Bettadpur, S., Ries, J.C., Thompson, P.F. and Watkins, M.M. (2004) GRACE Measurements of Mass Variability in the Earth System. Science, 305, 503-505. [Google Scholar] [CrossRef] [PubMed]
[5] Drinkwater, M.R., Floberghagen, R., Haagmans, R., Muzi, D. and Popescu, A. (2003) VII: Closing Session: GOCE: ESA’s First Earth Explorer Core Mission. Space Science Reviews, 108, 419-432. [Google Scholar] [CrossRef] 
[6] Floberghagen, R., Fehringer, M., Lamarre, D., Muzi, D., Frommknecht, B., Steiger, C., et al. (2011) Mission Design, Operation and Exploitation of the Gravity Field and Steady-State Ocean Circulation Explorer Mission. Journal of Geodesy, 85, 749-758. [Google Scholar] [CrossRef] 
[7] 张壹. 基于球面三角剖分的重力场正反演技术研究[D]: [博士学位论文]. 武汉: 中国地质大学(武汉), 2019.
[8] Šprlák, M., Han, S.C. and Featherstone, W.E. (2020) Spheroidal Forward Modelling of the Gravitational Fields of 1 Ceres and the Moon. Icarus, 335, Article ID: 113412. [Google Scholar] [CrossRef] 
[9] Heck, B. and Seitz, K. (2007) A Comparison of the Tesseroid, Prism and Point-Mass Approaches for Mass Reductions in Gravity Field Modelling. Journal of Geodesy, 81, 121-136. [Google Scholar] [CrossRef] 
[10] Wild-Pfeiffer, F. (2008) A Comparison of Different Mass Elements for Use in Gravity Gradiometry. Journal of Geodesy, 82, 637-653. [Google Scholar] [CrossRef] 
[11] 史庆斌, 胡双贵, 杨磊. 基于高精度卫星重力数据反演青藏高原莫霍面深度[J]. 工程地球物理学报, 2018, 15(4): 466-474.
[12] 汤井田, 杨磊, 任政勇, 胡双贵, 徐志敏. 龙门山断裂带卫星重力场特征及其发震机制[J]. 地震地质, 2019, 41(5): 1136-1154.
[13] Zhong, Y., Ren, Z., Chen, C., Chen, H., Yang, Z. and Guo, Z. (2019) A New Method for Gravity Modeling Using Tesseroids and 2D Gauss-Legendre Quadrature Rule. Journal of Applied Geophysics, 164, 53-64. [Google Scholar] [CrossRef] 
[14] Lin, M. and Denker, H. (2019) On the Computation of Gravitational Effects for Tesseroids with Constant and Linearly Varying Density. Journal of Geodesy, 93, 723-747. [Google Scholar] [CrossRef] 
[15] Lin, M., Denker, H. and Müller, J. (2020) Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction. Surveys in Geophysics, 41, 723-765. [Google Scholar] [CrossRef] 
[16] Casenave, F., Métivier, L., Pajot-Métivier, G. and Panet, I. (2016) Fast Computation of General Forward Gravitation Problems. Journal of Geodesy, 90, 655-675. [Google Scholar] [CrossRef] 
[17] Saraswati, A.T., Cattin, R., Mazzotti, S. and Cadio, C. (2019) New Analytical Solution and Associated Software for Computing Full-Tensor Gravitational Field Due to Irregularly Shaped Bodies. Journal of Geodesy, 93, 2481-2497. [Google Scholar] [CrossRef] 
[18] Ren, Z., Chen, C., Pan, K., Kalscheuer, T., Maurer, H. and Tang, J. (2017) Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts. Surveys in Geophysics, 38, 479-502. [Google Scholar] [CrossRef] 
[19] Ren, Z., Zhong, Y., Chen, C., Tang, J. and Pan, K. (2018) Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts up to Cubic Order. Geophysics, 83, G1-G13. [Google Scholar] [CrossRef] 
[20] Ren, Z., Zhong, Y., Chen, C., Tang, J., Kalscheuer, T., Maurer, H., et al. (2018) Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts. Surveys in Geophysics, 39, 901-935. [Google Scholar] [CrossRef] 
[21] Amante, C. and Eakins, B.W. (2009) ETOPO1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis. National Geophysical Data Center, National Oceanic and Atmospheric Administration, Washington DC. [Google Scholar] [CrossRef] 
[22] Geuzaine, C. and Remacle, J.F. (2009) Gmsh: A 3-D Finite Element Mesh Generator with Built-In Pre- and Post- Processing Facilities. International Journal for Numerical Methods in Engineering, 79, 1309-1331. [Google Scholar] [CrossRef] 
[23] Wang, H., Wu, P. and Wang, Z. (2006) An Approach for Spherical Harmonic Analysis of Non-Smooth Data. Computers & Geosciences, 32, 1654-1668. [Google Scholar] [CrossRef] 
[24] Blakely, R.J. (1996) Potential Theory in Gravity and Magnetic Applications. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef]