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A practical software package for computing gravimetric geoid by the least squares modification of Hotine’s formula


Today’s geodetic community starts to model an accurate gravimetric geoid within a 5 mm level, which entirely meets the demands of all technical and geoscientific studies. In this context, a wide range of geoid modelling methods have been published through the years, each of them has its own philosophy. Recently, a new geoid modelling technique has been developed by using the least squares modification of Hotine’s formula (LSMH), which gives more reasonable results than other methods. However, a practical and compact software package is not publicly accessible for researchers in this method. Thus, a scientific software package named “LSMHSOFT” is developed by C programming language and made available for public use in this study. Subsequently, the software is employed for the composition of gravimetric geoid in the Auvergne test-bed, verifying it by GNSS (Global Navigation Satellite Systems)-levelling data. Numerical results indicate that LSMHSOFT is a powerful tool for modelling gravimetric geoid by the least squares modification of Hotine’s formula and its additive corrections.

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Code Availability

The present software is developed in C programming language, which is freely available under the license of GNU public. Interested readers can find the software together with experimental data from github/aabbak/LSMHSOFT. Inquiries and bug reports about the software are cordially welcome to the authors.


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The authors thank to Prof. Dr. Lars E. Sjöberg at Geodesy Division of Royal Institute of Technology in Sweden for his beneficial discussion during the compilation of the manuscript. The second author is partly supported by the Estonian Research Council Grant PRG330. Two anonymous reviewers are cordially acknowledged for their constructive suggestions on the manuscript.

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Correspondence to Ramazan Alpay Abbak.

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Communicated by: H. Babaie

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Abbak, R.A., Ellmann, A. & Ustun, A. A practical software package for computing gravimetric geoid by the least squares modification of Hotine’s formula. Earth Sci Inform (2021).

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  • Auvergne test-bed
  • Hotine’s integral
  • Rugged topography
  • Point-wise integration