The stability criterion for downward continuation of surface gravity data with various spatial resolutions over Ireland

Sajjadi, Sajjad; Martinec, Zdeněk; Prendergast, Patrick; Hagedoorn, Jan; Šachl, Libor

doi:10.1007/s11200-020-0769-7

Published: 04 September 2021

The stability criterion for downward continuation of surface gravity data with various spatial resolutions over Ireland

Sajjad Sajjadi^1,2,
Zdeněk Martinec^2,3,
Patrick Prendergast⁴,
Jan Hagedoorn⁵ &
Libor Šachl³

Studia Geophysica et Geodaetica volume 65, pages 219–234 (2021)Cite this article

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Abstract

The differences between local and reference geopotential values are the fundamental quantities of interest in the geodetic boundary value problem approach for connecting independent height reference frames. The local gravity potential values are usually derived from gravimetric and geometric geoid undulations. In determining the short-wavelength components of the gravimetric geoid, a harmonic or analytical downward continuation of the external harmonic functions of gravity to the geoid is necessary. This study analyses the stability of the Poisson downward continuation technique with respect to varying the spatial resolution of surface gravity data in Ireland in order to estimate an effective grid resolution on this reduction. Results of the study show that the minimum range of 500-m resolution provides an unconditionally stable solution to downward continuation without the need for regularisation of the computation algorithm. In this case, downward continued data contribute from −13 to 12 mm to geoid heights and from −0.128 to 0.118 m²s⁻² to local gravity potential value at Malin-Head tide gauge station in Ireland.

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Acknowledgments

This work has been carried out within the framework of Sajad Sajjadi’s Ph.D. research in Dublin Institute for Advanced Studies, Geophysics Section under the supervision of Professor Zdeněk Martinec and financed by Limerick Institute of Technology. The first author appreciates these supports. The authors would like to thank Dr. Nic Wilson (UCC) and Dr. Pat Gill (LIT) for the comments that have helped improve the manuscript.

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Authors and Affiliations

Faculty of Applied Science, Engineering and Technology, Limerick Institute of Technology, Limerick, Ireland
Sajjad Sajjadi
School of Cosmic Physics, Geophysics Section, Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2, Ireland
Sajjad Sajjadi & Zdeněk Martinec
Department of Geophysics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 18000, Prague 8, Czech Republic
Zdeněk Martinec & Libor Šachl
Property Boundaries Ireland Ltd - Chartered Surveyors, 12 Castleknock Manor, Castleknock, Dublin, Ireland
Patrick Prendergast
Research and Publication Support, University of Potsdam, Building 18 - IKMZ, Karl-Liebknecht-Str. 24-25, 14476, Potsdam, Germany
Jan Hagedoorn

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Sajjad Sajjadi
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Zdeněk Martinec
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Patrick Prendergast
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Jan Hagedoorn
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Libor Šachl
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Sajjadi, S., Martinec, Z., Prendergast, P. et al. The stability criterion for downward continuation of surface gravity data with various spatial resolutions over Ireland. Stud Geophys Geod 65, 219–234 (2021). https://doi.org/10.1007/s11200-020-0769-7

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Received: 28 October 2020
Revised: 04 May 2021
Accepted: 01 July 2021
Published: 04 September 2021
Issue Date: October 2021
DOI: https://doi.org/10.1007/s11200-020-0769-7

Keywords

downward continuation
Stokes integral
Poisson formula