pp 1-7 | Cite as

Quality and Distribution of Terrestrial Gravity Data for Precise Regional Geoid Modeling: A Generalized Setup

  • Christian GerlachEmail author
  • Vegard Ophaug
  • Ove Christian Dahl Omang
  • Martina Idžanović
Part of the International Association of Geodesy Symposia book series


Based on the success of the satellite mission GOCE in providing information on the global gravity field with high quality and spectral resolution, the realization of the 1 cm-geoid is at reach, leading to an increased interest in regional geoid modeling. It is therefore necessary to review theoretical and numerical aspects of regional geoid modeling, including availability of adequate data. In this study, we deal with the latter aspect, specifically the representation error implied by the available gravity data.

We use least-squares collocation to derive formal errors of block mean gravity anomalies and geoid heights for given distributions of scattered gravity stations. By comparison with independent error measures, we validate a generalized procedure in which we do not base the solution on an empirical covariance function of a specific test area, but rather use band-pass filtered global functions. This implies that the procedure is applicable beyond our specific test-bed and can be used to give general error measures, e.g., for network design in poorly surveyed regions.

The computations are carried out in a medium size test area along the Norwegian coast, where the national gravity basis network had been densified in recent years. This allows to show the gain in geoid accuracy that can be expected from adding the new gravity data. We show that the signal variance of the regional gravity field corresponds well with the one derived from the global covariance function, thus validating our generalized procedure. In previous studies, the accuracy of gravity anomalies and geoid heights in Norway were estimated to be (on average) around 2 mGal and 3 cm, respectively. We find good agreement of the formal gravity anomaly error with the empirical measure. By adding the new data, the gravity anomaly error can be reduced to almost 1 mGal. The formal geoid error can be reduced from around 1.7 to 1.3 cm (on average). The discrepancy between the formal error and the empirical measure of 3 cm is probably due to contributions from GNSS and leveling errors, which are not considered in our formal estimate. The results presented here show larger errors over ocean areas, because the computations are restricted to land data. Available airborne and marine gravity will be considered in the future.


Geoid stepwise collocation Wenzel modification 



The study is part of the GOCODYN project, funded by the Norwegian Research Council under project number 231017.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Christian Gerlach
    • 1
    Email author
  • Vegard Ophaug
    • 2
  • Ove Christian Dahl Omang
    • 4
  • Martina Idžanović
    • 3
  1. 1.Bavarian Academy of Sciences and HumanitiesGeodesy and GlaciologyMunichGermany
  2. 2.Faculty of Science and Technology (RealTek)Norwegian University of Life Sciences (NMBU)ÅsNorway
  3. 3.Faculty of Science and Technology (RealTek)Norwegian University of Life Sciences (NMBU)ÅsNorway
  4. 4.Geodetic InstituteNorwegian Mapping AuthorityHønefossNorway

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