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


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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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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Correspondence to Sajjad Sajjadi.

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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).

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  • downward continuation
  • Stokes integral
  • Poisson formula