Efficient computation of gravitational effects and curvatures for a spherical zonal band discretized using tesseroids

Deng, Xiao-Le

2022-10-01

10.1007/s00190-022-01643-8

JOURNAL OF GEODESY   Impact Factor & Quartile

0949-7714

1432-1394

The gravity field modelling due to mass distributions of the Earth is one of the primary fields in geodesy and geophysics. Among the mass bodies, a spherical shell has become a commonly used mass body to evaluate the gravitational effects of a tesseroid due to its analytical solutions and simple formulae. However, this classic numerical strategy has the shortcoming that its computation time is longer with a finer grid size of the discretized tesseroids, and it has to be performed on a high-performance computer. In this contribution, the simpler analytical expressions for the radial gravity vector and radial- radial gravity gradient tensor of a homogeneous spherical cap and spherical zonal band are derived. Moreover, new analytical formulae of the gravitational curvatures (i.e., third-order derivatives of the gravitational potential) of a homogeneous spherical cap and spherical zonal band are also derived. The analytical consistencies between the new and old radial gravity vector and radial-radial gravity gradient tensor of a spherical cap are confirmed. The computation time and relative approximation errors between a spherical zonal band and spherical shell discretized using tesseroids are quantitatively analyzed with different grid sizes. Numerical experiments show that the computation time of a spherical zonal band discretized using tesseroids is about 180/n times less than that of a spherical shell discretized using tesseroids for the gravitational effects up to gravitational curvatures with different grid sizes both in double and quadruple precision, where n is from the grid size n degrees x n degrees. Moreover, the mean values of the relative approximation errors of the gravitational effects of a spherical zonal band discretized using tesseroids are smaller than those of a spherical shell discretized using tesseroids with the influence of the computation point's height at different grid sizes. Numerical results confirm the benefit of a spherical zonal band in comparison with a spherical shell discretized using tesseroids regarding both the computation time and errors. The numerical strategy of a spherical zonal band discretized using tesseroids can be applied instead of the commonly used numerical strategy of a spherical shell discretized using tesseroids in the numerical evaluation of a tesseroid with different numerical methods in the future research.

Gravity field modelling Gravitational curvatures Spherical cap Spherical zonal band Spherical shell Tesseroid

SCI

English

First ; Corresponding

China Postdoctoral Science Foundation[2021M691402]

Geochemistry & Geophysics ; Remote Sensing

Geochemistry & Geophysics ; Remote Sensing

WOS:000860707900005

SPRINGER

GEOSCIENCES

Web of Science

Southern Univ Sci & Technol, Dept Earth & Space Sci, Shenzhen 518055, Peoples R China

Deng, Xiao-Le. Efficient computation of gravitational effects and curvatures for a spherical zonal band discretized using tesseroids[J]. JOURNAL OF GEODESY,2022,96(10).

Deng, Xiao-Le.(2022).Efficient computation of gravitational effects and curvatures for a spherical zonal band discretized using tesseroids.JOURNAL OF GEODESY,96(10).

Deng, Xiao-Le."Efficient computation of gravitational effects and curvatures for a spherical zonal band discretized using tesseroids".JOURNAL OF GEODESY 96.10(2022).