Comparison of three methods for computing the gravitational attraction of tesseroids at satellite altitude

Abstract

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.