Global gravity modelling is one of the most important issues in geophysics and geodesy. Because a tesseroid model comprises the curvature of the Earth, the computation methods for the gravitational potential of tesseroids and its first-order derivatives in spherical coordinates are attracting great attention in recent years. In this paper we deal with the numerical evaluation of the radial component of the gravitational attraction generated by tesseroid masses at satellite height with the Gauss-Legendre quadrature (GLQ), the Taylor series expansion (TSE) and the prism approximation (PA) methods. Forward modelling of tesseroids of 1° × 1° and 5′ × 5′ are performed by three computation methods and the comparison between them are made in terms of computational efficiency and accuracy. The numerical results show that the GLQ of order 5 can provide the adequate accuracy for the gravity modelling of 1° × 1° tesseroids at satellite height. The GLQ of order 2 and TSE methods are superior to the PA approach in both computational accuracy and efficiency. The satellite height has important impact on the accuracy of the GLQ and TSE, whereas it has no effect on the PA method. In addition, we developed combined GLQ approach and combined TSE method, respectively, for global gravity modelling based on 1° × 1° and 5′ × 5′ tesseroids. Apart from the synthetic tesseroids, 1° × 1° data from the CRUST1.0 global crustal model and 5′ × 5′ rock-equivalent topographic data from the Earth2014 model are used to validate two combined methods. The numerical results show that these two combined methods can balance the computational accuracy and efficiency.

全球重力建模是地球物理学和大地测量学中最重要的问题之一。由于土卫二模型包含地球的曲率，因此土卫二及其在球坐标系中的一阶导数的引力计算方法近年来引起了极大的关注。在本文中，我们使用高斯-勒根德正交（GLQ），泰勒级数展开（TSE）和棱镜近似（PA）方法，对卫星高度上的脉状质量产生的重力引力的径向分量进行了数值评估。通过三种计算方法对1°×1°和5′×5′的类贝类动物进行正向建模，并在计算效率和准确性方面进行比较。数值结果表明，5阶GLQ可以为卫星高度1°×1°齿状拟星体的重力建模提供足够的精度。2阶GLQ和TSE方法在计算精度和效率上均优于PA方法。卫星高度对GLQ和TSE的精度有重要影响，而对PA方法则没有影响。此外，我们分别为基于1°×1°和5′×5′tesseroids的全球重力模型开发了组合GLQ方法和组合TSE方法。除了人工合成的类脉龙以外，CRUST1.0全球地壳模型的1°×1°数据和Earth2014模型的5'×5'岩石等效地形数据也用于验证两种组合方法。