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Regional geoid computation by least squares modified Hotine’s formula with additive corrections

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Abstract

Geoid and quasigeoid modelling from gravity anomalies by the method of least squares modification of Stokes’s formula with additive corrections is adapted for the usage with gravity disturbances and Hotine’s formula. The biased, unbiased and optimum versions of least squares modification are considered. Equations are presented for the four additive corrections that account for the combined (direct plus indirect) effect of downward continuation (DWC), topographic, atmospheric and ellipsoidal corrections in geoid or quasigeoid modelling. The geoid or quasigeoid modelling scheme by the least squares modified Hotine formula is numerically verified, analysed and compared to the Stokes counterpart in a heterogeneous study area. The resulting geoid models and the additive corrections computed both for use with Stokes’s or Hotine’s formula differ most in high topography areas. Over the study area (reaching almost 2 km in altitude), the approximate geoid models (before the additive corrections) differ by 7 mm on average with a 3 mm standard deviation (SD) and a maximum of 1.3 cm. The additive corrections, out of which only the DWC correction has a numerically significant difference, improve the agreement between respective geoid or quasigeoid models to an average difference of 5 mm with a 1 mm SD and a maximum of 8 mm.

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Acknowledgements

The Nordic Geodetic Commission (NKG) is thanked for making this study possible. Authors from Tallinn University of Technology have been co-financed by a Connecting Europe Facility (CEF) project “FAMOS (Finalising Surveys for the Baltic Motorways of the Sea) Odin” (VEU16013). The figures have been generated using GMT (Wessel et al. 2013). Three anonymous reviewers and the editor are thanked for their constructive comments on the manuscript.

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  1. Tallinn University of Technology, Tallinn, Estonia

    Silja Märdla & Artu Ellmann

  2. Lantmäteriet, The Swedish Mapping, Cadastral and Land Registration Authority, Gävle, Sweden

    Jonas Ågren

  3. KTH, Royal Institute of Technology, Stockholm, Sweden

    Lars E. Sjöberg

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  1. Silja Märdla
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Märdla, S., Ellmann, A., Ågren, J. et al. Regional geoid computation by least squares modified Hotine’s formula with additive corrections. J Geod 92, 253–270 (2018). https://doi.org/10.1007/s00190-017-1061-7

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