O presente trabalho apresenta a aplicação das fórmulas de Vincenty nos cálculos das correções do terreno e do efeito indireto, que desempenham papel relevante na construção de cartas geoidais. Implementa-se um programa de processamento que realiza a integração numérica sobre o modelo digital do terreno, discretizado em células triangulares de Delaunay. O sistema foi desenvolvido com a linguagem de programação FORTRAN, para a execução de intensos algoritmos numéricos usando compiladores livres e robustos. Para o cálculo do efeito indireto, considera-se a redução gravimétrica efetuada com base no segundo método de condensação de Helmert, face ao pequeno valor de efeito indireto no cálculo do geóide, em função da mudança que este produz no potencial da gravidade devido ao deslocamento da massa topográfica. Utiliza-se, o sistema geodésico SIRGAS 2000 como sistema de referência para o cômputo das correções. Simplificando o exame dos resultados alcançados, distingue-se o processamento e desenvolvimento do trabalho em etapas como a escolha de ferramentas geodésicas para máxima precisão dos resultados, elaboração de subrotinas e comparação de resultados com cálculos anteriores. Os resultados encontrados foram de geração sadia e satisfatória e podem ser perfeitamente empregados no cálculo do geóide em qualquer área do globo. / An application of Vincentys formulas has been presented for computing terrain corrections and indirect effect, that have important hole in geoidal maps generation. A software is implemented, that performs numerical integration over a digital terrain model discretized in Delaunay triangular cells. The system had been implemented in FORTRAN Programming Language, as a natural choice for implementation of intensive numerical algorithms, using free and robust compilers. To calculate the indirect effect is used the gravimetric reductions, based on Helmert Second Condensation Method, because of small indirect effect values in calculation of the geoid, depending on the gravity potential change due to displacement of topographical masses. The Geodetic System SIRGAS 2000 is adopted as the reference system to compute the corrections. Simplifying the analysis of the obtained results, the processing and development of the study in stages like choice of geodetic tools for maximum accuracy of results, preparation of subroutines and compare results with previous calculations. The results observed were sound satisfactory and support conveniently geoid generation in any part of globe.

This study is devoted to the determination of a high resolution gravimetric geoid model for Uganda based on the optimal combination of terrestrial and satellite gravity anomalies using the method of Least Squares Modification of Stokes’ formula with additive corrections. Specifically the study investigates the current status of the existing Uganda Vertical Network relative to the requirements of a modern height datum and includes a detailed evaluation and validation of terrestrial gravity data, several digital elevation models and some recent global geopotential models. Finally a new height datum based on a gravimetric quasigeoid model and Global Navigation Satellite Systems (GNSS)/levelling is proposed. In this thesis, the Uganda Gravimetric Geoid Model 2014 (UGG2014) is computed from several datasets which, include 7839 terrestrial gravity data points from the International Gravimetric Bureau, the 3 arc second Shuttle Radar Topography Mission digital elevation model and a recent Gravity field and steady-state Ocean Circulation Explorer-only global geopotential model. To compensate for the missing gravity data in the target area, the surface gravity anomalies extracted from the World Gravity Map 2012 were used. Outliers in the terrestrial gravity data were detected using the cross-validation technique which, also estimated the accuracy of the remaining terrestrial gravity data as 9 mGal. Based on 12 GNSS/levelling data points distributed over Uganda, the root mean square fit of UGG2014 before and after the 4-parameter fit is 16 cm and 9 cm, respectively. The study has revealed that the heights of the Uganda Vertical Network are normal-orthometric heights for which the quasigeoid is the closest approximation to the zero reference surface. Consequently, the Uganda Gravimetric Quasigeoid Model 2014 (UGQ2014) was derived from the UGG2014 with the quasigeoid-geoid separation computed from the Earth Gravitational Model 2008 complete to degree/order 2160 of spherical harmonics. The root mean square fit of UGQ2014 versus GNSS/levelling is 15 cm and 8 cm before and after the 4-parameter fit, respectively, which shows that the quasigeoid model fits GNSS/levelling better than the geoid model. Thus a new height datum based on UGQ2014 and GNSS/levelling was determined as a practical solution to the determination of heights directly from GNSS. Evaluated with 4 independent GNSS/levelling points, the root mean square fit of the new height datum is 5 cm better than using the quasigeoid model alone. With an average parts-per-million of 29 in the relative test, the new height datum satisfies the precision and accuracy requirements of third order precise levelling. Overall, the results show that UGG2014 and UGQ2014 agree considerably better with GNSS/levelling than any other recent regional/global gravimetric geoid models. Therefore, both gravimetric solutions are a significant step forward in the modelling of a “1-cm geoid” over Uganda given the poor quality and quantity of the terrestrial gravity data used for computation. / <p>QC 20150831</p>

Conhecer a altitude de um ponto é muito importante em diversas aplicações, como a implantação de uma rede de água ou para determinar se certa área está sujeita à inundação por exemplo. Esta altitude, altitude ortométrica, está referenciada ao nível médio do mar e é determinada a partir do transporte de um ponto com altitude conhecida até o ponto o qual se deseja saber a altitude. O geoide, é a superfície que representa o nível médio do mar e o seu cálculo tem sido objeto dos geodesistas há muito tempo. Devido a irregularidade da forma da Terra, utiliza-se uma figura matemática para representar a Terra, o elipsoide, onde são realizados os cálculos matemáticos. Ao elipsoide está relacionada a altitude geométrica, a qual é determinada utilizando receptores do sistema global de posicionamento por satélite. A altitude ortométrica e a altitude geométrica, relacionam-se através da ondulação geoidal, a qual é a separação geoide-elipsoide. O transporte das altitudes ortométricas exige uma densa rede com altitudes conhecidas, o que é algo difícil de ocorrer em países de dimensões continentais como o Brasil. Uma das soluções encontradas é cálculo de geoides com precisão que atenda as necessidades na determinação da altitude ortométrica. Este trabalho calculou um geoide para o município de Porto Alegre e foi avaliado a partir das alturas geoidais obtidas do posicionamento GNSS sobre referencias de nível (RRNN) as quais possuem precisão milimétrica. No cálculo do geoide utilizou-se o modelo geopotencial global EGM2008 de grau 360, para a representação dos longos comprimentos de onda; e observações gravimétricas terrestres, totalizando 277 pontos distribuídos por todo o munícipio. Para o cálculo do geoide utilizou-se da integral de Stokes, resultando em um geoide com resolução de 3” x 3” e erro médio quadrático de 7,7 centímetros. Em uma segunda fase o geoide (GEOIDEPOA2016) foi avaliado em relação ao modelo de ondulação geoidal oficial do Brasil, o MAPGEO2015 e seu antecessor, o MAPGEO2010, assim como com o modelo de alturas geoidais o qual a prefeitura municipal de Porto Alegre (NPMPA) possui. Os modelos de alturas geoidais que apresentaram melhores resultados para determinar a altitude ortométrica foram o GEOIDEPOA2016 e o NPMPA, com erro médio quadrático de 7,7 e 8,1 centímetros respectivamente. / The knowledge of an altitude point is very important in several applications, such as the implantation of a water network or to determine if a certain area is subject to flooding for example. This altitude, ortometric altitude, is referenced to the mean sea level and is determined from the transport of a point with known altitude to the point where the altitude is desired. The geoid is the surface that represents the average level of the sea and its calculation has long been object of the geodesists. Due to the irregularity of the shape of the Earth, a mathematical figure is used to represent the Earth, the ellipsoid, where the mathematical calculations are performed. The ellipsoid is related to geometric altitude, which is determined using receivers of the global satellite positioning system. The orthometric altitude and the geometric altitude are related through the geoidal undulation, which is the geoid-ellipsoid separation. The transportation of orthometric altitudes requires a dense network with known altitudes, which is difficult to achieve in countries with continental dimensions such as Brazil. One of the solutions found is accurately calculating geoids that meet the needs in determining orthometric altitude. This work calculated a geoid for the municipality of Porto Alegre and was evaluated from the geoid heights obtained from the GNSS positioning on level references (RRNN) which have millimetric precision. In the calculation of the geoid, the EGM2008 global geopotential model was used for the representation of the long wavelengths with terrestrial gravimetric observations, totaling 277 points distributed throughout the municipality. For the calculation of the geoid was used of the integral of Stokes, resulting in a geoid with resolution of 3 "x 3" and RMS 7.7 centimeters. In a second phase the geoid (GEOIDEPOA2016) was evaluated in relation to the Brazil official geoidal model, MAPGEO2015 and its predecessor, MAPGEO2010, as well as the geoid heights model, which the municipal government of Porto Alegre (NPMPA) has. The geoid heights models that presented the best results to determine the orthometric altitude were GEOIDEPOA2016 and NPMPA, with a RMS 7.7 and 8.1 cm respectively.

O presente trabalho apresenta a aplicação das fórmulas de Vincenty nos cálculos das correções do terreno e do efeito indireto, que desempenham papel relevante na construção de cartas geoidais. Implementa-se um programa de processamento que realiza a integração numérica sobre o modelo digital do terreno, discretizado em células triangulares de Delaunay. O sistema foi desenvolvido com a linguagem de programação FORTRAN, para a execução de intensos algoritmos numéricos usando compiladores livres e robustos. Para o cálculo do efeito indireto, considera-se a redução gravimétrica efetuada com base no segundo método de condensação de Helmert, face ao pequeno valor de efeito indireto no cálculo do geóide, em função da mudança que este produz no potencial da gravidade devido ao deslocamento da massa topográfica. Utiliza-se, o sistema geodésico SIRGAS 2000 como sistema de referência para o cômputo das correções. Simplificando o exame dos resultados alcançados, distingue-se o processamento e desenvolvimento do trabalho em etapas como a escolha de ferramentas geodésicas para máxima precisão dos resultados, elaboração de subrotinas e comparação de resultados com cálculos anteriores. Os resultados encontrados foram de geração sadia e satisfatória e podem ser perfeitamente empregados no cálculo do geóide em qualquer área do globo. / An application of Vincentys formulas has been presented for computing terrain corrections and indirect effect, that have important hole in geoidal maps generation. A software is implemented, that performs numerical integration over a digital terrain model discretized in Delaunay triangular cells. The system had been implemented in FORTRAN Programming Language, as a natural choice for implementation of intensive numerical algorithms, using free and robust compilers. To calculate the indirect effect is used the gravimetric reductions, based on Helmert Second Condensation Method, because of small indirect effect values in calculation of the geoid, depending on the gravity potential change due to displacement of topographical masses. The Geodetic System SIRGAS 2000 is adopted as the reference system to compute the corrections. Simplifying the analysis of the obtained results, the processing and development of the study in stages like choice of geodetic tools for maximum accuracy of results, preparation of subroutines and compare results with previous calculations. The results observed were sound satisfactory and support conveniently geoid generation in any part of globe.

Conhecer a altitude de um ponto é muito importante em diversas aplicações, como a implantação de uma rede de água ou para determinar se certa área está sujeita à inundação por exemplo. Esta altitude, altitude ortométrica, está referenciada ao nível médio do mar e é determinada a partir do transporte de um ponto com altitude conhecida até o ponto o qual se deseja saber a altitude. O geoide, é a superfície que representa o nível médio do mar e o seu cálculo tem sido objeto dos geodesistas há muito tempo. Devido a irregularidade da forma da Terra, utiliza-se uma figura matemática para representar a Terra, o elipsoide, onde são realizados os cálculos matemáticos. Ao elipsoide está relacionada a altitude geométrica, a qual é determinada utilizando receptores do sistema global de posicionamento por satélite. A altitude ortométrica e a altitude geométrica, relacionam-se através da ondulação geoidal, a qual é a separação geoide-elipsoide. O transporte das altitudes ortométricas exige uma densa rede com altitudes conhecidas, o que é algo difícil de ocorrer em países de dimensões continentais como o Brasil. Uma das soluções encontradas é cálculo de geoides com precisão que atenda as necessidades na determinação da altitude ortométrica. Este trabalho calculou um geoide para o município de Porto Alegre e foi avaliado a partir das alturas geoidais obtidas do posicionamento GNSS sobre referencias de nível (RRNN) as quais possuem precisão milimétrica. No cálculo do geoide utilizou-se o modelo geopotencial global EGM2008 de grau 360, para a representação dos longos comprimentos de onda; e observações gravimétricas terrestres, totalizando 277 pontos distribuídos por todo o munícipio. Para o cálculo do geoide utilizou-se da integral de Stokes, resultando em um geoide com resolução de 3” x 3” e erro médio quadrático de 7,7 centímetros. Em uma segunda fase o geoide (GEOIDEPOA2016) foi avaliado em relação ao modelo de ondulação geoidal oficial do Brasil, o MAPGEO2015 e seu antecessor, o MAPGEO2010, assim como com o modelo de alturas geoidais o qual a prefeitura municipal de Porto Alegre (NPMPA) possui. Os modelos de alturas geoidais que apresentaram melhores resultados para determinar a altitude ortométrica foram o GEOIDEPOA2016 e o NPMPA, com erro médio quadrático de 7,7 e 8,1 centímetros respectivamente. / The knowledge of an altitude point is very important in several applications, such as the implantation of a water network or to determine if a certain area is subject to flooding for example. This altitude, ortometric altitude, is referenced to the mean sea level and is determined from the transport of a point with known altitude to the point where the altitude is desired. The geoid is the surface that represents the average level of the sea and its calculation has long been object of the geodesists. Due to the irregularity of the shape of the Earth, a mathematical figure is used to represent the Earth, the ellipsoid, where the mathematical calculations are performed. The ellipsoid is related to geometric altitude, which is determined using receivers of the global satellite positioning system. The orthometric altitude and the geometric altitude are related through the geoidal undulation, which is the geoid-ellipsoid separation. The transportation of orthometric altitudes requires a dense network with known altitudes, which is difficult to achieve in countries with continental dimensions such as Brazil. One of the solutions found is accurately calculating geoids that meet the needs in determining orthometric altitude. This work calculated a geoid for the municipality of Porto Alegre and was evaluated from the geoid heights obtained from the GNSS positioning on level references (RRNN) which have millimetric precision. In the calculation of the geoid, the EGM2008 global geopotential model was used for the representation of the long wavelengths with terrestrial gravimetric observations, totaling 277 points distributed throughout the municipality. For the calculation of the geoid was used of the integral of Stokes, resulting in a geoid with resolution of 3 "x 3" and RMS 7.7 centimeters. In a second phase the geoid (GEOIDEPOA2016) was evaluated in relation to the Brazil official geoidal model, MAPGEO2015 and its predecessor, MAPGEO2010, as well as the geoid heights model, which the municipal government of Porto Alegre (NPMPA) has. The geoid heights models that presented the best results to determine the orthometric altitude were GEOIDEPOA2016 and NPMPA, with a RMS 7.7 and 8.1 cm respectively.

O sistema GPS tem sido largamente usado para posicionamento. Vislumbra-se o potencial uso deste sistema para determinação de altitudes ortométricas, substituindo o oneroso e demorado processo de nivelamento geométrico. Para isso, um modelo geoidal com precisão absoluta submétrica e precisão relativa da ordem de 2 ppm é necessário. Este modelo pode ser dividido em duas componentes: longo e curto comprimento de onda. O modelo do geopotencial fornece a componente de longo comprimento de onda da altura geoidal, enquanto que a gravimetria associada a um modelo digital do terreno permite calcular a componente de curto comprimento de onda através da integral modificada de Stokes. Algumas das modificações da função de Stokes são comparadas. Dois métodos de avaliação desta integral, integração direta e FFT são mostrados no trabalho. Como resultado dessas comparações, obtém-se um modelo geoidal para o Estado de São Paulo / The GPS system has been used broadly for positioning. It is glimpsed the potential use of this system for the determination of orthometric height, substituting the expensive and slow process of geometric leveling. For this propose, it is necessary a geoid model with submetric absolute accuracy and relative accuracy on the order of 2 ppm. This model can be divided in two components: long and short wavelengths. The model of the geopotential supplies the long wavelength component of the geoid height, while gravimetry associated with a digital terrain model, allows the estimation of the short wavelength component, through the modified Stokes´s integral. Comparisons of some of these modifications of the Stokes´s function are carried out. Two methods of evaluation of the integral, numerical integration and FFT are shown in the work. As a result of those comparisons, it is obtained a geoid model for the State of São Paulo

In order to be able to use the operational Moldavian GNSS Positioning System MOLDPOS efficiently for the determination of normal heights in surveying engineering, e.g. during the construction of a road, an accurate quasigeoid model is needed. The main goal of this thesis is to present a new gravimetric quasigeoid model for Moldova (Mold2012), which has been determined by applying the Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA), also called the KTH method. Due to limited coverage of gravity data, the integration area is often limited to a small spherical cap around the computation point, which leads to a truncation error for geoid height. Molodensky et al. (1962) showed that the truncation error can be reduced by the modification of Stokes’ formula, where the measured gravity data are combined with the low-frequency component of the geoid from a Global Gravitational Model (GGM). The LSMSA technique combines the GGM and the terrestrial data in an optimum way. In order to find the most suitable modification approach or cap size it is necessary to compare the gravimetric height anomalies with the GPS/levelling derived height anomalies, and for this purpose we use a GPS/levelling dataset that consists of 1042 points with geodetic coordinates in the MOLDREF99 reference system and normal heights at the same points given in the height system Baltic 77. The magnitude of the additive corrections varies within an interval from -0.6 cm to -4.3 cm over the area of Moldova. The quasigeoid model which results from combining the ITG-Grace02s solution (with n = M = 170, ψ0 = 3° and σΔg = 10 mGal) and the solution obtained from the modified Stokes’ formula together with the additive correction gives the best fit for the GPS/levelling data with a standard deviation (STD) of ±7.8 cm. The evaluation of the computed gravimetric quasigeoid is performed by comparing the gravimetric height anomalies with the GPS/levelling derived height anomalies for 1042 points. However, the above heterogeneous data include outliers, and in order to find and eliminate these, a corrector surface model is used. This surface provides a connection to the local vertical when the GNSS technique is used. After the elimination of the suspicious outliers (170 points) according to a 2-RMS test, a new corrective surface was computed based on the remaining 872 GPS/levelling points, and the STD of residuals became ±4.9 cm. The STD value for the residuals according to the order of the levelling network for the Mold2012 fitted to the local vertical datum is 3.8 cm for the I-order, 4.3 cm for the II-order, 4.5 cm for the III-order and 5.0 cm for the IV-order levelling network. But the STD of the residuals for the 18 control points indicates a better result where the STD is 3.6 cm and RMS is 3.9 cm and the min and max value of residuals is -5.3 cm and 9.0 cm, respectively. As the STD of the differences in height anomaly are not just the standard error of the height anomalies (quasigeoid model), but it contains also the standard errors of GPS heights and of normal heights. Assuming that the latter STDs are 3 cm and 3.5 cm, respectively, the STD of Mold2012 is estimated to 1.7 cm. / <p>QC 20121127</p>

No description available.

L'objectif principal de cette thèse est d'acquérir de nouvelles connaissances sur la structure tectonique et la lithosphérique de la région des Carpates et du bassin pannonien. Nous avons appliqué trois méthodes différentes: modélisation 1D,modélisation 2D géophysique intégrée et inversion 3D pour atteindre cet objectif. Ces méthodes sont similaires concernant les bases de données utilisées, mais diffèrent par le traitement et l'interprétation de données. Au début, nous avons appliqué la modélisation automatique 1D pour obtenir un premier aperçu de la région étudiée. Deuxièmement, nous avons appliqué la modélisation 2D intégré de la lithosphère qui combine l'interprétation du flux de chaleur,du géoïde, de la gravité et des données topographiques de la région des Carpates et du bassin pannonien et des régions avoisinantes. Cette approche est capable de contraindre des structures lithosphériques compliquées de la région étudiée mieux que l'interprétation de chaque donnée indépendamment. Nous présentons quatre modèles intégrés 2Dde la lithosphère dans la région des Carpates et du bassin pannonien et des régions avoisinantes. Enfin, sur la base de l'algorithme d'inversion 3D, nous présentons les modèles géophysiques de la lithosphère dans la région des Carpates et du bassin pannonien. L'algorithme calcule la structure de la densité lithosphèrique par l'inversion conjointe de la gravité, géoïde et données topographiques basé sur une approche bayésienne. Les modèles sont basés sur différents ensembles de données d'entrée et ils sont contraints par différentes données a priori. Sur la base de notre modélisation, nous ne pouvons pas confirmer l'amincissement extrême (moins de 70 km)de la lithosphère du bassin pannonien proposé par d'autres auteurs. D'autre part, les résultats montrent la tendance à l'augmentation de l'épaisseur lithosphérique de Carpates d'occidentales vers de Carpates de l'est ce que confirme les théories antérieures sur la propagation du processus de subduction. Nous avons obtenu des résultats controversés dans la région des Carpates du sud.Les résultats basés sur l'inversion 3D montrent une lithosphère extrêmement mince dans ce domaine mais les résultats basés sur la modélisation 2D intégrée ne supportent pas cet amincissement. Cependant, les deux méthodes indiquent qu'il est plausible que la plateforme Moésienne soit courbée et chevauchée sous les Carpates du sud. Dans le modèle 3D, le bord sud-est du bassin Pannonien montre une lithosphère inattendue et étonnamment mince. Puisque la zone est assez grande, nous pouvons exclure un effet de flexion, par conséquent, cette région pourrait être potentiellement intéressante pour une recherche plus approfondie. / The main aim of this thesis is to gain new knowledge about the lithospherical structure and tectonics of the Carpathian–Pannonian Basin region. We applied three different methods: 1Dautomatic modelling, 2D integrated geophysical modelling and 3D inversion to achieve this goal.These methods are similar concerning the used databases but differ by used processing andinterpretation. At first we apply 1D automatic modelling to get a very first overview of thestudied region. Secondly, we apply 2D integrated modelling of the lithosphere which combines the interpretation of surface heat flow, geoid, gravity, and topography data in the Carpathian–Pannonian Basin region and surrounding areas. This approach is able to constrain the complicated lithospheric structures of the studied region better than interpreting each data set onits own. We present four 2D integrated models of the lithosphere in the Carpathian–PannonianBasin region and surrounding areas. Finally, based on the 3D Inversion algorithm, we present the geophysical models of the lithosphere in the Carpathian–Pannonian region. The algorithm returns the density structure of the lithosphere from joint inversion of free air gravity, geoid andtopography data based on a Bayesian approach. The models are based on different input data sets and constrained by different a priori data. Based on our modelling we cannot confirm theextreme thinning (less than 70 km) of the Pannonian Basin lithosphere proposed by other authors.On the other hand, the results show the increasing trend of the lithospherical thickness of theCarpathian Arc from the Western Carpathians toward the Eastern Carpathians which confirms theprevious theories about the propagation of subduction process. We got some controversial resultsin the area of the Southern Carpathians. The results based on 3D inversion show extremely thinlithosphere in the area; on the other hand, the results based on 2D integrated modelling do notsupport such thinning. However both methods indicate that it is probable that the MoesianPlatform is bend and underthrusted underneath the Southern Carpathians. The south-eastern edge of the Pannonian Basin based on 3D inversion shows unexpected and surprisingly thinlithosphere. Since the area is quite large, we could exclude an effect of flexure, therefore this area might be potentially interesting for further investigation. / Hlavnou myšlienkou tejto práce bolo rozšírenie poznatkov o štruktúre a tektonike karpatsko–panónskej oblasti. Na výskum študovanej oblasti sme použili tri rôzne metódy, 1D automatickémodelovanie, 2D integrované geofyzikálne modelovanie a 3D inverziu. Tieto metódy sú podobnév zmysle použitých vstupných databáz, ale líšia sa spôsobom spracovania a interpretácie. Akoprvé sme aplikovali 1D automatické modelovanie, ktoré slúžilo ako prvý náhľad na študovanéúzemie. Ako druhé sme použili 2D integrované geofyzikálne modelovanie litosféry, ktorékombinuje interpretáciu povrchového toku, geoidu, tiažových anomálií a topografie v karpatsko–panónskej oblasti a okolitých tektonických jednotkách. Tento prístup k interpretácii je schopnývymedziť komplikované štrúktúry v litosfére lepšie, ako interpretácia každého jednéhogeofyzikálneho poľa samostatne. V tejto práci predstavíme štyri 2D integrované modely litosféryv karpatsko–panónskej oblasti a okolitých jednotiek. Ako posledné, predstavíme geofyzikálnemodely litosféry študovanej oblasti na základe modelovania použitím 3D inverzie. Algoritmus jeschopný vypočítať hustotnú distribúciu v litosfére na základe Bayesianského prístupu zospoločnej inverzie tiažovej anomálie na voľný vzduch, geoidu a topografie. Tieto modely súvypočítavané na základe rôznych vstupných datových setov a a priori informácií. Na základenášho modelovania nemôžeme potvrdiť extrémne stenčenie (menej ako 70 km) litosférypanónskej panvy. Na druhej strane naše výsledky poukazujú na narastajúci trend litosférickéhohrubnutia Karpatského oblúka od Západných Karpát smerom do Východných, čo potvrdzujepredchádzajúce teórie o postupnom procese subdukcie. V oblasti Južných Karpát sme dosiahliprotichodné výsledky. Výsledky získané na základe 3D inverzie poukazujú na extrémne stenčenúlitosféru na druhej strane 2D integrované modelovania takéto extrémne stenčenie v danej oblastinepodporuje. Napriek tomu je pravdepodobnejšie, že moezíjska platforma je ohnutá a podsunutápod Južné Karpaty. Ďalšia zaujímavá vec sa ukazuje v juhovýchodnej oblasti panónskej panvy,kde výsledky 3D inverzie odhaľujú taktiež výrazné stenčenie litosféry. Táto oblasť môže byťpotenciálne zaujímavá a bolo by vhodné ďalej pokračovať vo výskume danej oblasti.

It is the purpose of this thesis to investigate different regional geoid determination methods with respect to their feasibility for use with a future GOCE satellite-only Earth Gravity Model (EGM). This includes investigations of various techniques, which involve different approximations, as well as the expected accuracy. Many, but not all, of these tasks are tested by means of Synthetic Earth Gravity Models (SEGMs). The study is limited to remove-compute-restore methods using Helmert condensation and to Sjöberg's combined approach (method with additive corrections). First, a number of modifications of Stokes' formula are tested with respect to their compatibility with a GOCE EGM having negligible commission error. It is concluded that the least squares modification method should be preferred. Next, two new point-mass SEGMs are constructed in such a way that the resulting models have degree variances representative for the full and topographically reduced gravity fields, respectively. These SEGMs are then used to test different methods for modified Stokes' integration and downward continuation. It is concluded that the combined method requires dense observations, obtained from the given surface anomalies by interpolation using a reduction for all known density anomalies, most notably the topography. Examples of other conclusions are that the downward continuation method of Sjöberg (2003a) performs well numerically. To be able to test topographic corrections, another SEGM is constructed starting from the reduced point-mass model, to which the topography, bathymetry and isostatic compensation are added. This model, which is called the Nordic SEGM, is then applied to test one strict and one more approximate approach to Helmert's condensation. One conclusion here is that Helmert's 1st method with the condensation layer 21 km below sea level should be preferred to Helmert's 2nd condensation strategy. The thesis ends with a number of investigations of Sjöberg's combined approach to geoid determination, which include tests using the Nordic SEGM. It is concluded that the method works well in practice for a region like Scandinavia. It is finally shown how the combined strategy may preferably be used to estimate height anomalies directly.