A comparison of different mass elements for use in gravity gradiometry |
| |
Authors: | F Wild-Pfeiffer |
| |
Institution: | (1) Institute of Navigation, University of Stuttgart, Breitscheidstr. 2, 70174 Stuttgart, Germany |
| |
Abstract: | Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist
in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour
of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic
reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different
mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed
and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential,
the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different
mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap
and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the
tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements
is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the
most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect
is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The
order of magnitude in the radial-radial component is about ± 8 E.U.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. |
| |
Keywords: | Topographic reductions Isostatic reductions Mass elements (tesseroid prism point mass mass layer mass line) Satellite gravity gradiometry |
本文献已被 SpringerLink 等数据库收录! |
|