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/quasige
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Z. Fasˇkova´, R. Cˇunderlı´k, K. Mikula, and R. Tenzer
Abstract
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. Keywords
Boundary value problem with mixed boundary conditions Finite element method Finite volume method Inconsistencies of local vertical datums
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Z. Fasˇkova´ (*) R. Cˇunderlı´k K. Mikula Department of Mathematics and Descriptive Geometry, The Slovak University of Technology, Faculty of Civil Engineering, Radlinske´ho 11, Bratislava 813 68, Slovakia e-mail: [email protected]; [email protected]; [email protected] R. Tenzer National School of Surveying, University of Otago, 310 Castle Street, Dunedin, New Zealand e-mail: [email protected]
Introduction
The unification of local vertical datums (LVDs) and the realization of the World Height System (WHS) are very important tasks of recent geodesy. They are usually performed on a basis of global geopotential models (GGMs); cf. Bursˇa et al. (1999, 2004, 2007), Sa´nchez (2005). The low frequency part of GGMs is very precisely obtained from satellite missions. It is fully independent from LVDs but it has insufficient resolution for a unification of LVDs, especially in small regions. The high frequency part
Z. Altamimi and X. Collilieux (eds.), Reference Frames for Applications in Geosciences, International Association of Geodesy Symposia 138, DOI 10.1007/978-3-642-32998-2_30, # Springer-Verlag Berlin Heidelberg 2013
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Z. Fasˇkova´ et al.
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