Influence of Vertical Datum Inconsistencies on Gravity Field Modelling
Precise gravity field modelling is essential for a unification of local vertical datums (LVDs) and realization of the World Height System. The quality of terrestrial gravimetric measurements has substantial impact on the accuracy of detailed geoid/quasigeoid models. The precision of their positions, especially their vertical components, is of the same importance as precision of gravity itself. Therefore inconsistencies due to shifts and tilts of LVDs can distort precise solutions.
In this paper we present how inconsistencies of vertical positions of input terrestrial gravity data can influence numerical solutions obtained by the finite element method and finite volume method. Considering information from satellite missions, we solve the geodetic BVP with mixed boundary conditions (BCs) in the 3D domain above the Earth’s surface. This space domain is bounded by the Earth’s surface at the bottom, one spherical artificial boundary outside the Earth at altitude of a satellite mission and four side artificial boundaries. All numerical solutions are fixed to the satellite only geopotential model on all artificial boundaries, where the Dirichlet BCs are imposed. On the Earth surface the oblique derivative BC in the form of surface, gravity disturbances is prescribed. In our numerical experiments we compare numerical solutions with and without considering the corrections from the shifts and tilts of LVDs in the input surface gravity disturbances. We study how the corrected solutions backward-influence estimations of the shifts and tilts of LVDs. Our experiments are performed in areas of Australia, New Zealand and Great Britain.
KeywordsBoundary value problem with mixed boundary conditions Finite element method Finite volume method Inconsistencies of local vertical datums
The authors gratefully thank the providers of all data used, especially for the opportunity to access the new GPS-levelling dataset in Australia supplied by the Intergovernmental Committee on Surveying and Mapping (ICSM) members and compiled by Geoscience Australia. The work has been supported by the grants VEGA 1/0269/09, grant VEGA 1/1063/11 and the project APVV-0184-10.
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