Browsing by Author "Vaníček, Petr"

Now showing 1 - 3 of 3
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    A calculation of the correction to Helmert orthometric heights for the spherical terrain effect
    (University of New Brunswick, 2005) Kingdon, Robert; Vaníček, Petr
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    Accuracy of the classical height system
    (University of New Brunswick, 2018) Foroughi, Ismael; Santos, Marcelo; Vaníček, Petr
    Measuring the quality of the classical height system through its self-consistency (congruency) is investigated in this dissertation. Measuring the congruency is done by comparing the geoidal heights determined from a gravimetric geoid model with test geoidal heights derived at GNSS/Leveling points. The components of this measurement are computed as accurately as possible, e.g., the Stokes-Helmert approach is used to determine the geoid model, gravimetric and topographic corrections are applied to the spirit leveling observations to derive rigorous orthometric heights at test points, and finally, the geodetic heights are taken from GNSS observations. Four articles are included in this dissertation, one is discussing a modification to the Stokes-Helmert approach for using the optimal contribution of the Earth gravitational models and the local data. The second paper applies the methodology presented in the first paper and presents the detail results for a test area. The third paper is a discussion on the accuracy of the classical height system against Molodensky’s system and presents a numerical study to show that the classical system can be computed as accurately as Molodensky’s. The last paper presents a methodology to find the most probable solution of the downward continuation of surface gravity to the geoid level using the least-squares technique. The uncertainties of the geoidal heights are estimated using least-square downward continuation and a priori variance matrix of the input gravity data. The total estimation of the uncertainties of the geoidal heights confirms that geoid can be determined with sub-centimetre accuracy in the flat areas when, mainly, the effect of topographic mass density is taken into account properly, the most probable solution of downward continuation is used, and the improved satellite-only global gravitational models are merged with local data optimally.
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    Improvements to satellite global gravity field modelling
    (University of New Brunswick, 2019) Sheng, Michael Baier; Santos, Marcelo; Vaníček, Petr
    Modelling the gravity field of the Earth is important for many scientific disciplines. Global gravity models allow for the investigation of long-wavelength properties of the gravity field. Global models derived from satellite observations provide an additional benefit: they are uncorrelated with any error contaminating regional terrestrial gravity information; this makes them ideal for combination with terrestrial gravity data in order to formulate high-precision regional geoid models. This dissertation investigates several possible areas of improvement to both the formulation and evaluation of satellite-only global gravity models. The first major barrier is due to what is known to the geodetic community as the “polar-gap problem”: the lack of data collected by the satellites over the poles due to the inclination angle of their orbit. The second is the rigorous application of these models inside of the topographical masses (and most pertinent, on the surface of the geoid). These problems are addressed in three articles. The first presents a mathematical tool that can be used in order to address the polar-gap problem by performing the global integration making use of the additivity property of Riemann integrals. The second article presents a computational scheme that allows for the evaluation of various quantities derived from global gravity models inside the topographical masses. Finally, the third article describes the production and validation of a 2D global topographical density model that is required for the rigorous evaluation of the gravity field as prescribed in the second article.