Application of the one-step integration method for determination of the regional gravimetric geoid

This paper is written as a progression of the ongoing discussion in geodesy about the merits of the Molodensky height system versus the classical height system. It is a rebuttal of a publication in the Proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy by Victor Popadyev titled “On the Advantage of Normal Heights: Once More on the Shape of Quasigeoid.” Even though Popadyev’s paper was not presented at the symposium it was published in the proceedings regardless. It purports to address a presentation from the symposium titled “The shape of the quasigeoid”, that applied a set of criteria to judge the suitability of the quasigeoid as a vertical reference surface, ultimately finding it inferior due to its edges and folds. The proceedings paper acknowledges these irregularities in the quasigeoid, but instead argues that the Molodensky system, apart from any vertical reference surface, should be evaluated on two different and more favorable criteria, and finds it superior on that basis. Herein, we continue the ongoing discussion by clarifying some of the misunderstandings in the Popadyev paper and explaining that even on the favourable criteria proposed the Molodensky system holds no advantages over the classical system.

Assessing Molodensky’s Heights: A Rebuttal

Kingdon¹,

Vaníček²,

Santos³

et al. 2022

The Uncertainties of the Topographical Density Variations in View of a Sub-Centimetre Geoid

Foroughi¹,

Goli²,

Pagiatakis³

et al. 2023

We estimate the uncertainty of the modelled geoid heights based on the standard deviations of the topographic mass density variation. We model the geoid using the one-step integration method considering mass density variations along with their associated error estimates to calculate the direct and indirect topographic density effects on the geoid heights in the Helmert space. We employ the UNB_TopoDensT_2v01 global lateral density model and its standard deviations and test our algorithms in the Auvergne test area, in central France. Our results show that the topographic mass density variations are currently known well enough to model the geoid with sub-centimetre internal error in topographically mild regions such as Auvergne.

Optimizing Airborne Flight Line Spacing for Geoid Determination with Full Gravity Vectors

Foroughi,

Goli,

Ferguson

et al. 2024

The horizontal components of the airborne gravity vector are equivalent to the deflection of the vertical at the flight level and contain signals of the slope of Earth’s gravity field. We test the contribution of such components in finding the optimum flight line spacing for geoid modelling. We use the one-step integration method and create a system of linear equations containing the three components of the airborne gravity vector as observations and solve the geodetic boundary value problem on the reference ellipsoid as an overdetermined weighted least-squares problem. We test our methodology in the Colorado region in the USA given that it is one of the most challenging areas for geoid modelling. We show that by incorporating the horizontal components at the flight level, one can increase the flight line spacing by almost 40%, thereby significantly reducing the cost of airborne surveys while maintaining the same accuracy in the estimated geoid heights as when the scalar value of gravity is used.