Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation

Tenzer, Róbert; Hirt, Christian; Novák, Pavel; Pitoňák, Martin; Šprlák, Michal

doi:10.1007/s00190-015-0858-5

Cited by 25 publications

(8 citation statements)

References 31 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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“…The calculation of forward models can be performed in spatial or spectral domain which have different pros and cons. The reader is referred to literature for different stateof-the-art examples (e.g., Grombein et al 2016;Root et al 2016;Tenzer et al 2016). Topographic gravity field models are used: (a) to enhance the representation of the high frequency components of the gravity field (reducing omission error), (b) to compute the topographic attraction which is then removed from gravity measurements helping to investigate the residual signal, and (c) to interpolate and predict gravity values in regions that have sparse or no gravity measurements.…”

Section: Introductionmentioning

confidence: 99%

Topographic Gravity Field Modelling for Improving High-Resolution Global Gravity Field Models

Ince

Förste

Abrykosov

et al. 2022

International Association of Geodesy Symposia

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The global gravitational potential generated by the attraction of the Earth’s topographic masses has been computed in spectral domain. The mass-source information is provided by the 1 arcmin resolution Earth2014 relief model and four averaged density values for rock, ocean, lake, and ice areas. The topography and bathymetry are split into confocal ellipsoidal shells of a defined thickness. Based on the provided mass-source information, the gravitational potential is expanded for each shell and then summed up to represent the complete gravitational potential of the topography (and bathymetry). In this contribution, we present the impact of different shell thicknesses to the model accuracy and computation time. Moreover, we expanded our topographic gravity field model up to spherical harmonic degree and order 5,494. Such short scale mass information represented by the topography can be used to complement high-resolution combined static gravity field models for the very high-frequency components of the gravity field. As an example, we enhanced (augmented) EIGEN-6C4 model with the high frequency components retrieved from the topographic model. The deflections of vertical values computed from the augmented model are compared w.r.t. ground truth observations in Germany, Southern Colorado and Iowa (USA) which suggest as expected a considerable improvement over rugged mountainous regions and comparable residuals in areas of moderate topography.

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“…Gravity forward modelling can be realized in spatial or in spectral domain. Different examples can be found in the literature as presented by Grombein et al (2016), Hirt and Rexer (2015); Hirt et al (2016a), Rexer et al (2016), Root et al (2016), Tenzer et al (2012Tenzer et al ( , 2015Tenzer et al ( , 2016, Tenzer and Chen (2019) and Wang and Yang (2013) among many others. For accurate spatial domain gravity forward modelling, related Newtonian integration should consider all the mass sources over the whole Earth.…”

Section: Introductionmentioning

confidence: 99%

Forward Gravity Modelling to Augment High-Resolution Combined Gravity Field Models

et al. 2020

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During the last few years, the determination of high-resolution global gravity field has gained momentum due to high-accuracy satellite-derived observations and development of forward gravity modelling. Forward modelling computes the global gravitational field from mass distribution sources instead of actual gravity measurements and helps improving and complementing the medium to high-frequency components of the global gravity field models. In this study, we approximate the global gravity potential of the Earth's upper crust based on ellipsoidal approximation and a mass layer concept. Such an approach has an advantage of spectral methods and also avoids possible instabilities due to the use of a sequence of thin ellipsoidal shells. Lateral density within these volumetric shells bounded by confocal lower and upper shell ellipsoids is used in the computation of the ellipsoidal harmonic coefficients which are then transformed into spherical harmonic coefficients on the Earth's surface in the final step. The main outcome of this research is a spectral representation of the gravitatioal potential of the Earth's upper crust, computed up to degree and order 3660 in terms of spherical harmonic coefficients (ROLI_EllApprox_SphN_3660). We evaluate our methodology by comparing this model with other similar forward models in the literature which show sub-cm agreement in terms of geoid undulations. Finally, EIGEN-6C4 is augmented by ROLI_EllApprox_SphN_3660 and the gravity field functionals computed from the expanded model which has about 5 km half-wavelength spatial resolution are compared w.r.t. ground-truth data in different regions worldwide. Our investigations show that the contribution of the topographic model increases the agreement up to ~ 20% in the gravity value comparisons.

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Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation

Cited by 25 publications

References 31 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

Topographic Gravity Field Modelling for Improving High-Resolution Global Gravity Field Models

Forward Gravity Modelling to Augment High-Resolution Combined Gravity Field Models

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