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The Iranian height datum offset from the GBVP solution and spirit-leveling/gravimetry data

  • Amir EbadiEmail author
  • Alireza A. Ardalan
  • Roohollah Karimi
Original Article

Abstract

The gravity potential of the zero point of the Iranian height datum (IRHD) is determined as well as the IRHD offset from a global geoid. For this purpose, the geodetic boundary value problem (GBVP) solution based on the remove–compute–restore (RCR) technique is used. In the RCR technique, a global geopotential model (GGM) is required as a reference to remove and restore the long wavelengths of the gravity field. Since the GGMs do not have adequate accuracy over Iran, the IRHD offset is not precisely estimated by the GBVP solution. In this study, aiming to improve the latter, a combination solution based on the GBVP approach and spirit-leveling/gravimetry (LG) data, called the GBVP_LG solution, is proposed. To obtain the GBVP_LG solution, gravity potential obtained from the GBVP solution and the gravity potential differences derived from the LG data are used as two types of observations in a least-squares adjustment. The proper relative weight matrices are determined using the variance component estimation method. To evaluate the proposed method, the gravity potential differences between the start and end points of several check-lines in the leveling network derived from the GBVP and GBVP_LG solutions are compared with those of the LG data. The results show that the dependency of the GBVP_LG solution on the reference model used is much less than that of the GBVP solution. In addition, the results indicate that the GBVP_LG solution has a 42% improvement with respect to the GBVP solution in terms of root-mean-square error. As a result of the GBVP_LG solution, the gravity potential of the IRHD zero point is estimated equal to \( W_{0}^{\text{IRHD}} = 62,636,855.89 \pm 0.16\,{\text{m}}^{2} / {\text{s}}^{2} \). Therefore, the IRHD offset with respect to the geoid defined by \( W_{0} = 62,636,853.4\,{\text{m}}^{2} / {\text{s}}^{2} \) is obtained equal to \( - \,25.4 \pm 1.6\,{\text{cm}} \), which means that the IRHD is 25.4 cm below the geoid.

Keywords

Geodetic boundary value problem Spirit-leveling/gravimetry data Height system unification Iranian height datum offset Remove–compute–restore technique Variance component estimation 

Notes

Acknowledgements

We would like to thank the National Cartographic Center (NCC) of Iran for providing the data and supporting this study under contract No. 4142. We would also like to thank the editor-in-chief, Prof. J. Kusche, and the responsible editor, Prof. I.N. Tziavos, for taking the time and handling our manuscript. We are very grateful to three anonymous reviewers for very constructive and valuable comments, which helped us to improve the manuscript.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Amir Ebadi
    • 1
    Email author
  • Alireza A. Ardalan
    • 1
  • Roohollah Karimi
    • 2
  1. 1.School of Surveying and Geospatial Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.Department of Geodesy and Surveying EngineeringTafresh UniversityTafreshIran

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