Corrections to: “Accurate computation of gravitational field of a tesseroid” by Fukushima (2018) in J. Geod. 92(12):1371–1386

Abstract

An accurate method with conditional split, double exponential quadrature rule, and numerical differentiation has been proposed in the paper “Accurate computation of gravitational field of a tesseroid” (Fukushima in J Geod 92(12):1371–1386, https://doi.org/10.1007/s00190-018-1126-2, 2018) to compute the gravitational field (i.e. gravitational potential, gravitational acceleration vector, and gravity gradient tensor) of a tesseroid. This study presents the corrections for some formulas in the main paper and electronic supplementary material of Fukushima (J Geod 92(12):1371–1386, https://doi.org/10.1007/s00190-018-1126-2, 2018). Moreover, the FORTRAN subroutines gtess (or qgtess) and ggtess (or qggtess) in the original codes xtess.txt (or xqtess.txt) in double (or quadrature) precision provided by Fukushima (J Geod 92(12):1371–1386, https://doi.org/10.1007/s00190-018-1126-2, 2018) are revised. The revised parts have impacts on the calculation of these components of the gravitational acceleration vector (g_{varPhi } and g_{varLambda }) and gravity gradient tensor (varGamma _{varPhi varPhi }, varGamma _{varPhi varLambda }, varGamma _{varPhi H}, varGamma _{varLambda varLambda }, varGamma _{varLambda H}, and varGamma _{H H}). The revised FORTRAN codes xtess.f90 and xqtess.f90 in double and quadrature precision are presented at the GitHub website https://github.com/xiaoledeng/xtess-xqtess. These revised FORTRAN codes can accurately compute the gravitational field of a tesseroid in double and quadrature precision no matter the computation point is located outside, near the surface of, on the surface of, or inside the tesseroid. They can be applied to calculate the gravitational field of the different layers (e.g. atmosphere, topography, crust, and mantle) of the Earth or other celestial bodies, which helps investigate the various geoscience applications, e.g. geoid determination in geodesy and gravity interpretation in geophysics.