Centre de documentation
scientifique

The relation between degree-2160 spectral models of Earth’s gravitational and topographic potential : a guide on global correlation measures and their dependency on approximation effects / Christian Hirt in Journal of geodesy, vol 91 n° 10 (October 2017)  

Public [article]  inJournal of geodesy > vol 91 n° 10 (October 2017) . - pp 1179 – 1205 Titre : The relation between degree-2160 spectral models of Earth’s gravitational and topographic potential : a guide on global correlation measures and their dependency on approximation effects Type de document : Article/Communication Auteurs : Christian Hirt, Auteur ; Moritz Rexer, Auteur ; Sten Claessens, Auteur ; Reiner Rummel, Auteur Année de publication : 2017 Article en page(s) : pp 1179 – 1205 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] corrélation [Termes IGN] Earth Gravity Model 2008 [Termes IGN] erreur systématique [Termes IGN] modèle de géopotentiel [Termes IGN] potentiel de pesanteur terrestre Résumé : (Auteur) Comparisons between high-degree models of the Earth’s topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (quantifying the amount of topographic signal contained in the gravitational potential) are indicators used in a number of contemporary studies. However, depending on the modelling techniques and underlying levels of approximation, the correlation at high degrees may vary significantly, as do the conclusions drawn. The present paper addresses this problem by attempting to provide a guide on global correlation measures with particular emphasis on approximation effects and variants of topographic potential modelling. We investigate and discuss the impact of different effects (e.g., truncation of series expansions of the topographic potential, mass compression, ellipsoidal versus spherical approximation, ellipsoidal harmonic coefficient versus spherical harmonic coefficient (SHC) representation) on correlation measures. Our study demonstrates that the correlation coefficients are realistic only when the model’s harmonic coefficients of a given degree are largely independent of the coefficients of other degrees, permitting degree-wise evaluations. This is the case, e.g., when both models are represented in terms of SHCs and spherical approximation (i.e. spherical arrangement of field-generating masses). Alternatively, a representation in ellipsoidal harmonics can be combined with ellipsoidal approximation. The usual ellipsoidal approximation level (i.e. ellipsoidal mass arrangement) is shown to bias correlation coefficients when SHCs are used. Importantly, gravity models from the International Centre for Global Earth Models (ICGEM) are inherently based on this approximation level. A transformation is presented that enables a transformation of ICGEM geopotential models from ellipsoidal to spherical approximation. The transformation is applied to generate a spherical transform of EGM2008 (sphEGM2008) that can meaningfully be correlated degree-wise with the topographic potential. We exploit this new technique and compare a number of models of topographic potential constituents (e.g., potential implied by land topography, ocean water masses) based on the Earth2014 global relief model and a mass-layer forward modelling technique with sphEGM2008. Different to previous findings, our results show very significant short-scale correlation between Earth’s gravitational potential and the potential generated by Earth’s land topography (correlation +0.92, and 60% of EGM2008 signals are delivered through the forward modelling). Our tests reveal that the potential generated by Earth’s oceans water masses is largely unrelated to the geopotential at short scales, suggesting that altimetry-derived gravity and/or bathymetric data sets are significantly underpowered at 5 arc-min scales. We further decompose the topographic potential into the Bouguer shell and terrain correction and show that they are responsible for about 20 and 25% of EGM2008 short-scale signals, respectively. As a general conclusion, the paper shows the importance of using compatible models in topographic/gravitational potential comparisons and recommends the use of SHCs together with spherical approximation or EHCs with ellipsoidal approximation in order to avoid biases in the correlation measures. Numéro de notice : A2017-541 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1016-z En ligne : https://doi.org/10.1007/s00190-017-1016-z Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=86596 [article]

Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by rock-equivalent topography (RET) / Michael Kuhns in Journal of geodesy, vol 90 n° 9 (September 2016)  

Public [article]  inJournal of geodesy > vol 90 n° 9 (September 2016) . - pp 883 – 902 Titre : Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by rock-equivalent topography (RET) Type de document : Article/Communication Auteurs : Michael Kuhns, Auteur ; Christian Hirt, Auteur Année de publication : 2016 Article en page(s) : pp 883 – 902 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] erreur d'approximation [Termes IGN] glace [Termes IGN] masse d'eau [Termes IGN] masse de la Terre [Termes IGN] modèle de densité [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] roche Résumé : (auteur) In gravity forward modelling, the concept of Rock-Equivalent Topography (RET) is often used to simplify the computation of gravity implied by rock, water, ice and other topographic masses. In the RET concept, topographic masses are compressed (approximated) into equivalent rock, allowing the use of a single constant mass–density value. Many studies acknowledge the approximate character of the RET, but few have attempted yet to quantify and analyse the approximation errors in detail for various gravity field functionals and heights of computation points. Here, we provide an in-depth examination of approximation errors associated with the RET compression for the topographic gravitational potential and its first- and second-order derivatives. Using the Earth2014 layered topography suite we apply Newtonian integration in the spatial domain in the variants (a) rigorous forward modelling of all mass bodies, (b) approximative modelling using RET. The differences among both variants, which reflect the RET approximation error, are formed and studied for an ensemble of 10 different gravity field functionals at three levels of altitude (on and 3 km above the Earth’s surface and at 250 km satellite height). The approximation errors are found to be largest at the Earth’s surface over RET compression areas (oceans, ice shields) and to increase for the first- and second-order derivatives. Relative errors, computed here as ratio between the range of differences between both variants relative to the range in signal, are at the level of 0.06–0.08 % for the potential, ∼3–7 % for the first-order derivatives at the Earth’s surface (∼0.1 % at satellite altitude). For the second-order derivatives, relative errors are below 1 % at satellite altitude, at the 10–20 % level at 3 km and reach maximum values as large as ∼20 to 110 % near the surface. As such, the RET approximation errors may be acceptable for functionals computed far away from the Earth’s surface or studies focussing on the topographic potential only. However, for derivatives of the functionals computed near the Earth’s surface, the use of RET introduces very spurious errors, in some cases as large as the signal, rendering it useless for smoothing or reducing of field observation, thus rigorous mass modelling should be used for both spatial and spectral domain methods. Numéro de notice : A2016-657 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0917-6 En ligne : http://dx.doi.org/10.1007/s00190-016-0917-6 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81859 [article]

Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation / Robert Tenzer in Journal of geodesy, vol 90 n° 1 (January 2016)  

Public [article]  inJournal of geodesy > vol 90 n° 1 (January 2016) . - pp 65-80 Titre : Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation Type de document : Article/Communication Auteurs : Robert Tenzer, Auteur ; Christian Hirt, Auteur ; Pavel Novák, Auteur ; et al., Auteur Année de publication : 2016 Article en page(s) : pp 65-80 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] anomalie de pesanteur [Termes IGN] champ de pesanteur terrestre [Termes IGN] harmonique sphérique [Termes IGN] masse de la Terre [Termes IGN] modèle de densité [Termes IGN] quasi-géoïde [Termes IGN] topographie Résumé : (auteur) The geoid-to-quasigeoid separation is often computed only approximately as a function of the simple planar Bouguer gravity anomaly and the height of the computation point while disregarding the contributions of terrain geometry and anomalous topographic density as well as the sub-geoid masses. In this study we demonstrate that these contributions are significant and, therefore, should be taken into consideration when investigating the relation between the normal and orthometric heights particularly in the mountainous, polar and geologically complex regions. These contributions are evaluated by applying the spectral expressions for gravimetric forward modelling and using the EIGEN-6C4 gravity model, the Earth2014 datasets of terrain, ice thickness and inland bathymetry and the CRUST1.0 sediment and (consolidated) crustal density data. Since the global crustal density models currently available (e.g. CRUST1.0) have a limited accuracy and resolution, the comparison of individual density contributions is—for consistency—realized with a limited spectral resolution up to a spherical harmonic degree 360 (or 180). The results reveal that the topographic contribution globally varies between −0.33 and 0.57 m, with maxima in Himalaya and Tibet. The contribution of ice considerably modifies the geoid-to-quasigeoid separation over large parts of Antarctica and Greenland, where it reaches ∼0.2 m. The contributions of sediments and bedrock are less pronounced, with the values typically varying only within a few centimetres. These results, however, have still possibly large uncertainties due to the lack of information on the actual sediment and bedrock density. The contribution of lakes is mostly negligible; its maxima over the Laurentian Great Lakes and the Baikal Lake reach only several millimetres. The contribution of the sub-geoid masses is significant. It is everywhere negative and reaches extreme values of −4.43 m. According to our estimates, the geoid-to-quasigeoid separation globally varies within −4.19 and 0.26 m while the corresponding values computed according to a classical definition are only negative and reach extreme values of −3.5 m. A comparison of these results reveals that inaccuracies caused by disregarding the terrain geometry and mass density heterogeneities distributed within the topography and below the geoid surface can reach ±2 m or more in the mountainous regions. Numéro de notice : A2016-019 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-015-0858-5 Date de publication en ligne : 01/10/2015 En ligne : https://doi.org/10.1007/s00190-015-0858-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=79466 [article]

Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics / Moritz Rexer in Journal of geodesy, vol 88 n° 4 (April 2014)  

Public [article]  inJournal of geodesy > vol 88 n° 4 (April 2014) . - pp 319 - 333 Titre : Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics Type de document : Article/Communication Auteurs : Moritz Rexer, Auteur ; Christian Hirt, Auteur ; Roland Pail, Auteur ; Sten Claessens, Auteur Année de publication : 2014 Article en page(s) : pp 319 - 333 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] Australie [Termes IGN] données géophysiques [Termes IGN] données GOCE [Termes IGN] évaluation des données [Termes IGN] harmonique sphérique [Termes IGN] levé gravimétrique Résumé : (Auteur) In March 2013, the fourth generation of European Space Agency’s (ESA) global gravity field models, DIR4 (Bruinsma et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010b) and TIM4 (Migliaccio et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010), generated from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity observation satellite was released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with Gravity Recovery and Climate Experiment (GRACE) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude ( h=250 km) show both fourth generation models to improve significantly w.r.t. their predecessors. Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors, TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manusrcipta Geodaetica 20:379–385, 1995). Numéro de notice : A2014-158 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0680-x Date de publication en ligne : 14/12/2013 En ligne : https://doi.org/10.1007/s00190-013-0680-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=33063 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-2014041	SL	Revue	Centre de documentation	Revues en salle	Disponible