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首页> 外文期刊>Surveys in Geophysics: An International Review Journal of Geophysics and Planetary Sciences >Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction
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Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction

机译：在垂直方向上使用具有可变密度的Tesseroids的重力场建模

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摘要

We present an accurate method for the calculation of gravitational potential (GP), vector (GV), and gradient tensor (GGT) of a tesseroid, considering a density model in the form of a polynomial up to cubic order along the vertical direction. The method solves volume integral equations for the gravitational effects due to a tesseroid by the Gauss-Legendre quadrature rule. A two-dimensional adaptive subdivision technique, which automatically divides the tesseroids near the computation point into smaller elements, is applied to improve the computational accuracy. For those tesseroids having small vertical dimensions, an extension technique is additionally utilized to ensure acceptable accuracy, in particular for the evaluation of GV and GGT. Numerical experiments based on spherical shell models, for which analytical solutions exist, are implemented to test the accuracy of the method. The results demonstrate that the new method is capable of computing the gravitational effects of the tesseroids with various horizontal and vertical dimensions as well as density models, while the evaluation point can be on the surface of, near the surface of, outside the tesseroid, or even inside it (only suited for GP and GV). Thus, the method is attractive for many geodetic and geophysical applications on regional and global scales, including the computation of atmospheric effects for terrestrial and satellite usage. Finally, we apply this method for computing the topographic effects in the Himalaya region based on a given digital terrain model and the global atmospheric effects on the Earth's surface by using three polynomial density models which are derived from the US Standard Atmosphere 1976.
机译：我们提出了一种准确的方法，用于计算Tesseroid的重力电位（GP），载体（GV）和梯度张量（GGT），考虑到沿垂直方向的多项式的形式的密度模型。该方法通过高斯传奇正交规则来解决由于TESSeroid引起的引力效应的卷积分方程。应用二维自适应细分技术，它自动将晶圆定位靠近计算点附近的TESSeroids分成较小的元件，以提高计算精度。对于具有小垂直尺寸的晶圆，另外用于确保可接受的精度，特别是用于评估GV和GGT的延伸技术。基于球面壳模型的数值实验，实施了分析解决方案，以测试方法的准确性。结果表明，新方法能够计算与各种水平和垂直尺寸以及密度模型的晶圆件的重力效应，而评估点可以在邻近甲状腺外壳附近的表面上，或者即使在它内部（仅适用于GP和GV）。因此，该方法对区域和全球尺度的许多大地测量和地球物理应用具有吸引力，包括计算陆地和卫星使用的大气效应。最后，我们通过使用来自美国标准气氛1976的三种多项式密度模型来应用该方法，用于基于给定的数字地形模型和地球表面上的全球大气效应来计算喜马拉雅地区的地形效果。

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