The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary |
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| Authors: | Gábor Papp Erika Szeghy Judit Benedek |
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| Institution: | (1) Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences, POB 5, 9401 Sopron, Hungary;(2) Department of Statistics, University of West-Hungary, Sopron, Hungary |
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| Abstract: | In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding
average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as
many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources.
This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary,
where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling
line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is
investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results
show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if
the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the
normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10−3mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which
is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated
along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line. |
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| Keywords: | Potential difference Levelling Measured gravity Synthetical gravity DTM Inclination of level surfaces |
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