Comparison of different methods for estimating the geoid-to-quasi-geoid separation

Foroughi, Ismael; Tenzer, Róbert

doi:10.1093/gji/ggx221

Cited by 22 publications

(12 citation statements)

References 24 publications

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“…A more refined method of computing the disturbing potential on the geoid that takes into consideration a variable topographic density distribution was developed by Reference [15] and later applied by References [6,7].…”

Section: Methodsmentioning

confidence: 99%

“…Ascertaining that the topographic density could not be determined accurately, Molodensky [3] introduced the concept of the quasigeoid surface, which serves as a practical height reference surface to define the normal heights without adopting any hypothesis about the topographical density distribution. The differences between the geoid and the quasigeoid (i.e., the geoid-to-quasigeoid separation) were found to be typically within a few centimeters, with maxima in mountainous regions reaching a few meters [4][5][6][7], while completely negligible offshore [8]. In planetary studies, geometric heights are widely used instead of physical heights.…”

Section: Introductionmentioning

confidence: 99%

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On the Applicability of Molodensky’s Concept of Heights in Planetary Sciences

Tenzer

Foroughi

2018

Geosciences

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Geometric heights, defined with respect to a geometric reference surface, are the most commonly used in planetary studies, but the use of physical heights defined with respect to an equipotential surface (typically the geoid) has been also acknowledged for specific studies (such as gravity-driven mass movements). In terrestrial studies, the geoid is defined as an equipotential surface that best fits the mean sea surface and extends under continents. Since gravimetric geoid modelling under continents is limited by the knowledge of a topographic density distribution, alternative concepts have been proposed. Molodensky introduced the quasigeoid as a height reference surface that could be determined from observed gravity without adopting any hypothesis about the topographic density. This concept is widely used in geodetic applications because differences between the geoid and the quasigeoid are mostly up to a few centimeters, except for mountainous regions. Here we discuss the possible applicability of Molodensky's concept in planetary studies. The motivation behind this is rationalized by two factors. Firstly, knowledge of the crustal densities of planetary bodies is insufficient. Secondly, large parts of planetary surfaces have negative heights, implying that density information is not required. Taking into consideration the various theoretical and practical aspects discussed in this article, we believe that the choice between the geoid and the quasigeoid is not strictly limited because both options have advantages and disadvantages. We also demonstrate differences between the geoid and the quasigeoid on Mercury, Venus, Mars and Moon, showing that they are larger than on Earth.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Applicability of Molodensky’s Concept of Heights in Planetary Sciences

Tenzer

Foroughi

2018

Geosciences

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“…Each of the terms in Eq. 17is translated to the height correction and defined as follows (Tenzer et al (2005), Santos et al (2006) and Foroughi and Tenzer (2017)).…”

Section: Rigorous Determination Of Orthometric Heightsmentioning

confidence: 99%

“…This option removes the effect of topography, thus providing the no-topography gravity anomaly (geoid). For this the Equation 22 was used, obtained in Tenzer et al (2015) and Foroughi and Tenzer (2017). To calculate the effect of topography (topographic surface, ice, lakes, sediments and earth crust) the spherical harmonic coefficients are used.…”

Section: Rigorous Determination Of Orthometric Heightsmentioning

confidence: 99%

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A New Perspective for Physical Heights in Brazil

et al. 2019

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The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights.

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Assessing Molodensky’s Heights: A Rebuttal

Kingdon¹,

Vaníček²,

Santos³

et al. 2022

International Association of Geodesy Symposia

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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.

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Comparison of different methods for estimating the geoid-to-quasi-geoid separation

Cited by 22 publications

References 24 publications

On the Applicability of Molodensky’s Concept of Heights in Planetary Sciences

On the Applicability of Molodensky’s Concept of Heights in Planetary Sciences

A New Perspective for Physical Heights in Brazil

Assessing Molodensky’s Heights: A Rebuttal

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