Stuttgart, Univ, Studienarbeit, 2007.

Zugl.: Stuttgart, University, Diss., 2000.

Precise knowledge of the geoid contributes to the studies ofthe Earth’s interior, the long-term geophysical processesand to oceanography. An accurate regional geoid model, inparticular, enables the user in many cases to replace thetraditional height determination techniques by faster and morecost-effective GPS-levelling. In regional gravimetric geoid determination, it has becomecustomary to utilize the modified Stokes formula, whichcombines local terrestrial data with a global geopotentialmodel. The Dissertation is devoted to the determination of ahighresolution geoid model for the three Baltic countries–Estonia, Latvia and Lithuania. Six differentdeterministic and stochastic modification methods are tested.These are: Wong and Gore (1969), Vincent and Marsh (1974),Vaníèek and Kleusberg (1987) and the biased, unbiasedand optimum least squares modifications by Sjöberg (1984b,1991, 2003d). Three former methods employ originally theresidual anomaly in Stokes’integral. For the sake ofcomparison these methods are expressed such that the fullgravity anomaly is utilised in all the six methods. The contribution of different error sources for geoidmodelling is studied by means of the expected global meansquare error (MSE). The least squares methods attempt tominimise all relevant error sources in geoid modelling byspecially determined modification parameters. Part of thepresent study contributes to some important computationalaspects of the least squares parameters sn. This study employs the new geopotential model GGM01s, whichis compiled from data of the GRACE twin-satellites. Three sets(one from each country) of GPSlevelling points were used for anindependent evaluation of computed geoid models. Generally, thepost-fit residuals from the least squares modifications areslightly smaller (up to 1 cm) than the respective values ofdeterministic methods. This could indicate that the efforts putinto minimization of the global MSE have been advantageous. The geoid model computed by the unbiased LS modificationprovides the“best”post-fit statistics and it isthus preferred as the final representation of the joint Balticgeoid. The modification parameters of this model are calculatedfrom the following initial conditions: (1) upper limit of theGGM01s and the modification degree of Stokes’function areboth set to 67, (2) terrestrial anomaly error variance andcorrelation length are set to 1 mGal2 and 0.1°,respectively, (3) integration cap size is 2°. Thisapproximate geoid model is supplemented by separately computedadditive corrections (the combined topographic and atmosphericeffects and ellipsoidal correction), which completes the geoidmodelling procedures. The new geoid model for the Balticcountries is named BALTgeoid-04. The RMS of the GPS-levellingpost-fit residuals are as follows: 5.3 cm for the joint Balticgeoid model and 2.8, 5.6 and 4.2 cm for Estonia, Latvia andLithuania, respectively. This fit indicates the suitability ofthe new geoid model for many practical applications. Key words: geoid:Stokes’formula, deterministicand stochastic modifications, least squares, additivecorrections, GRACE, Baltic.

<p>Precise knowledge of the geoid contributes to the studies ofthe Earth’s interior, the long-term geophysical processesand to oceanography. An accurate regional geoid model, inparticular, enables the user in many cases to replace thetraditional height determination techniques by faster and morecost-effective GPS-levelling.</p><p>In regional gravimetric geoid determination, it has becomecustomary to utilize the modified Stokes formula, whichcombines local terrestrial data with a global geopotentialmodel. The Dissertation is devoted to the determination of ahighresolution geoid model for the three Baltic countries–Estonia, Latvia and Lithuania. Six differentdeterministic and stochastic modification methods are tested.These are: Wong and Gore (1969), Vincent and Marsh (1974),Vaníèek and Kleusberg (1987) and the biased, unbiasedand optimum least squares modifications by Sjöberg (1984b,1991, 2003d). Three former methods employ originally theresidual anomaly in Stokes’integral. For the sake ofcomparison these methods are expressed such that the fullgravity anomaly is utilised in all the six methods.</p><p>The contribution of different error sources for geoidmodelling is studied by means of the expected global meansquare error (MSE). The least squares methods attempt tominimise all relevant error sources in geoid modelling byspecially determined modification parameters. Part of thepresent study contributes to some important computationalaspects of the least squares parameters sn.</p><p>This study employs the new geopotential model GGM01s, whichis compiled from data of the GRACE twin-satellites. Three sets(one from each country) of GPSlevelling points were used for anindependent evaluation of computed geoid models. Generally, thepost-fit residuals from the least squares modifications areslightly smaller (up to 1 cm) than the respective values ofdeterministic methods. This could indicate that the efforts putinto minimization of the global MSE have been advantageous.</p><p>The geoid model computed by the unbiased LS modificationprovides the“best”post-fit statistics and it isthus preferred as the final representation of the joint Balticgeoid. The modification parameters of this model are calculatedfrom the following initial conditions: (1) upper limit of theGGM01s and the modification degree of Stokes’function areboth set to 67, (2) terrestrial anomaly error variance andcorrelation length are set to 1 mGal2 and 0.1°,respectively, (3) integration cap size is 2°. Thisapproximate geoid model is supplemented by separately computedadditive corrections (the combined topographic and atmosphericeffects and ellipsoidal correction), which completes the geoidmodelling procedures. The new geoid model for the Balticcountries is named BALTgeoid-04. The RMS of the GPS-levellingpost-fit residuals are as follows: 5.3 cm for the joint Balticgeoid model and 2.8, 5.6 and 4.2 cm for Estonia, Latvia andLithuania, respectively. This fit indicates the suitability ofthe new geoid model for many practical applications.</p><p><b>Key words: geoid:</b>Stokes’formula, deterministicand stochastic modifications, least squares, additivecorrections, GRACE, Baltic.</p>

Stuttgart, Univ., Diss., 1999.

Stuttgart, Univ., Studienarb., 2004.

Esta dissertação tem como objetivo o estudo da altimetria e do modelo geoidal no Estado de São Paulo. Para isso, uma abordagem detalhada do Problema de Valor de Contorno da Geodésia foi realizada. Além disso, são apresentados conceitos relacionados ao sistema de altitudes e a determinação das ondulações geoidais. Uma investigação do movimento e deslocamento vertical da crosta terrestre por meio do processamento preciso por ponto de duas estações de monitoramento contínuo (Cananeia NEIA e Ubatuba UBAT), localizadas no litoral paulista, foi efetuada. Constatou-se uma similaridade nos resultados por meio da comparação com o processamento feito pelo IBGE. A comparação envolvendo o Nível Médio dos Mares de duas estações maregráficas com relação ao nivelamento advindo de Imbituba foi outro estudo executado, onde a diferença após algumas correções foi de 0,34 cm. Uma análise a partir de 199 estações GPS sobre nivelamento foi realizada para comparação da ondulação geoidal com as anomalias de altura. As anomalias foram calculadas a partir dos modelos do geopotencial (EIGEN-GL04, EIGEN-5C e EGM08 para diferentes valores de grau e ordem). Os modelos que apresentaram melhor consistência com as estações GPS sobre nivelamento foram o EIGEN-GL04C e EIGEN-5C grau e ordem 360 e o EGM08 grau e ordem 360 e 2160. O modelo geoidal do Estado de São Paulo foi gerado para um modelo digital de 5. Utilizou-se a integral modificada de Stokes a partir do pacote computacional canadense SHGEO para o cálculo da componente de curto comprimento de onda. Foram empregados dados gravimétricos já existentes e dados advindos dos trabalhos de campo referentes ao Projeto Temático da FAPESP. No cálculo da componente de médio e longo comprimento de onda foi utilizado o modelo do geopotencial EGM08 (grau e ordem 150). A comparação com os dados GPS sobre nivelamento apresentou média de -0,22 m e RMSD 0,21 m. A escolha do Estado de São Paulo está relacionada à grande quantidade de trabalhos geodésicos e atividades na área da engenharia e que necessitam da utilização de um sistema altimétrico. Além disso, a grande quantidade de dados gravimétricos e de estações GPS/RN é mais uma justificativa para a realização do trabalho no Estado. / The investigation of the altimetry and the geoid model in São Paulo state is the aim of this dissertation. A detailed study concerning the Geodetic Boundary Value Problem was carried out. Moreover, the concepts related to the height system are presented. The analysis of the crust vertical displacement involving two continuous monitoring GPS stations (Cananeia NEIA and Ubatuba UBAT) in the coast of the state was performed. It was detected similar results between the comparison involved IBGE processing. A comparison involving the mean sea level of two tide gauge stations with respect to levelling from Imbituba was carried out. After some corrections the difference found was 0.34 m. A comparison between height anomalies by the Global Geopotential Models (EIGEN-GL04, EIGEN-5C and EGM08 for different degree and order) and 199 GPS observations on Bench Marks of the spirit leveling network was performed. The Global Geopotential Models that presented consistency with GPS on Bench Marks were: EIGEN-GL04C and EIGEN- 5C degree and order 360 and EGM08 degree and order 2160. São Paulo state geoid model was computed in 5 digital model. The modified Stokes integral by the Canadian package SHGEO to compute the short wavelength component was used, from Helmert gravity anomalies derived. Existing gravity data and data from FAPESP Thematic Project was processed. EGM08 model was used as a reference field restricted to degree and order 150 to obtain the long and medium wavelength components. The comparison with GPS on Bench Marks presented mean -0.22 m and RMSD 0.21 m. The reason for the choice of São Paulo state is that there are a lot of geodetic activities and important engineering works that require the use of a height system. Furthermore, there are a lot of gravimetric and GPS/BM data all around the state.

Esta dissertação tem como objetivo o estudo da altimetria e do modelo geoidal no Estado de São Paulo. Para isso, uma abordagem detalhada do Problema de Valor de Contorno da Geodésia foi realizada. Além disso, são apresentados conceitos relacionados ao sistema de altitudes e a determinação das ondulações geoidais. Uma investigação do movimento e deslocamento vertical da crosta terrestre por meio do processamento preciso por ponto de duas estações de monitoramento contínuo (Cananeia NEIA e Ubatuba UBAT), localizadas no litoral paulista, foi efetuada. Constatou-se uma similaridade nos resultados por meio da comparação com o processamento feito pelo IBGE. A comparação envolvendo o Nível Médio dos Mares de duas estações maregráficas com relação ao nivelamento advindo de Imbituba foi outro estudo executado, onde a diferença após algumas correções foi de 0,34 cm. Uma análise a partir de 199 estações GPS sobre nivelamento foi realizada para comparação da ondulação geoidal com as anomalias de altura. As anomalias foram calculadas a partir dos modelos do geopotencial (EIGEN-GL04, EIGEN-5C e EGM08 para diferentes valores de grau e ordem). Os modelos que apresentaram melhor consistência com as estações GPS sobre nivelamento foram o EIGEN-GL04C e EIGEN-5C grau e ordem 360 e o EGM08 grau e ordem 360 e 2160. O modelo geoidal do Estado de São Paulo foi gerado para um modelo digital de 5. Utilizou-se a integral modificada de Stokes a partir do pacote computacional canadense SHGEO para o cálculo da componente de curto comprimento de onda. Foram empregados dados gravimétricos já existentes e dados advindos dos trabalhos de campo referentes ao Projeto Temático da FAPESP. No cálculo da componente de médio e longo comprimento de onda foi utilizado o modelo do geopotencial EGM08 (grau e ordem 150). A comparação com os dados GPS sobre nivelamento apresentou média de -0,22 m e RMSD 0,21 m. A escolha do Estado de São Paulo está relacionada à grande quantidade de trabalhos geodésicos e atividades na área da engenharia e que necessitam da utilização de um sistema altimétrico. Além disso, a grande quantidade de dados gravimétricos e de estações GPS/RN é mais uma justificativa para a realização do trabalho no Estado. / The investigation of the altimetry and the geoid model in São Paulo state is the aim of this dissertation. A detailed study concerning the Geodetic Boundary Value Problem was carried out. Moreover, the concepts related to the height system are presented. The analysis of the crust vertical displacement involving two continuous monitoring GPS stations (Cananeia NEIA and Ubatuba UBAT) in the coast of the state was performed. It was detected similar results between the comparison involved IBGE processing. A comparison involving the mean sea level of two tide gauge stations with respect to levelling from Imbituba was carried out. After some corrections the difference found was 0.34 m. A comparison between height anomalies by the Global Geopotential Models (EIGEN-GL04, EIGEN-5C and EGM08 for different degree and order) and 199 GPS observations on Bench Marks of the spirit leveling network was performed. The Global Geopotential Models that presented consistency with GPS on Bench Marks were: EIGEN-GL04C and EIGEN- 5C degree and order 360 and EGM08 degree and order 2160. São Paulo state geoid model was computed in 5 digital model. The modified Stokes integral by the Canadian package SHGEO to compute the short wavelength component was used, from Helmert gravity anomalies derived. Existing gravity data and data from FAPESP Thematic Project was processed. EGM08 model was used as a reference field restricted to degree and order 150 to obtain the long and medium wavelength components. The comparison with GPS on Bench Marks presented mean -0.22 m and RMSD 0.21 m. The reason for the choice of São Paulo state is that there are a lot of geodetic activities and important engineering works that require the use of a height system. Furthermore, there are a lot of gravimetric and GPS/BM data all around the state.

No description available.

Este estudo apresenta o teste da eficiência do Earth Global Model 2008 (EGM2008) na geração de um modelo geoidal local, através da compatiblização com a ondulação obtida por posicionamento GPS (Global Positioning System) em 63 Referências de Nível (RN’s) localizadas no município de Porto Alegre, Rio Grande do Sul. O objetivo geral da dissertação foi analisar a exatidão do modelo geoidal gerado a partir dos coeficientes do modelo geopotencial EGM2008 para nivelamento por GPS no município de Porto Alegre e os objetivos específicos foram: a avaliação do modelo na região de Porto Alegre, a comparação das ondulações geoidais do EGM2008 (NEGM2008) com as ondulações geoidais em 63 RN’s (NGPS), o ajustamento da componente sistemática do geoide que é a diferença entre NEGM2008 e NGPS e a geração do modelo geoidal local compatibilizado para Porto Alegre. O método adotado apresenta as seguintes etapas: cálculo das ondulações geoidais nas RN’s; eliminação de erros grosseiros; geração do modelo geoidal através dos dados do EGM2008 com resolução de 7” de arco; cálculo da componente sistemática do geoide; ajustamento da componente sistemática através de transformação por polinômio de 2° grau com seis parâmetros pelo Método dos Mínimos Quadrados (MMQ). Os resultados obtidos foram: os parâmetros que compatibilizam o modelo geoidal global com o local e modelo geoidal local compatibilizado no formato raster, contendo as ondulações geoidais para todo o município. O novo modelo apresentou erro médio de 1,9 cm e desvio padrão de 7,2 cm. Os resultados da dissertação confirmam que é possível reduzir o erro associado ao modelo global através dos procedimentos adotados. Dessa maneira, conclui que o método utilizado reduziu o valor médio da componente sistemática de 15,4 cm para 1,9 cm após o ajustamento. / This study presents the Earth Global Model 2008’s (EGM2008) efficiency test on the conception of a local geoid model. The results were acquired through the undulation compatibility obtained by GPS (Global Positioning System) in 63 Bench Mark (BM) located in Porto Alegre, Rio Grande do Sul state, Brazil. The aim of this research was to analyze the accuracy of the geoid model generated from the geopotential model EGM2008’s coefficients to GPS leveling in Porto Alegre. The specific goals were the evaluation of the model in Porto Alegre region’s, the comparison between the EGM2008 (NEGM2008) geoid undulations and the geoid undulations in 63 BM (NGPS), and the adjustment of geoid’s systematic component, that is the difference between NEGM2008 and NGPS and the local geoid model’s conception to Porto Alegre. The method used presents the following steps: geoid undulation on RN’s’s computation; elimination of gross errors; geoid model’s conception through EGM2008’s data with resolution of 7” of arch; geoid’s systematic component computation; adjustment of the systematic component through transformation of 2nd degree polynomial with six parameters by the method of Least Squares. The results were: the parameters that make the models global and local compatible, and local geoid model compatible in raster format, containing the geoid undulations for the entire municipality. The new model showed 1.9 of mean error and 7.2 cm of standard deviation. Through the procedures adopted, the dissertation results’ confirm that it is possible to reduce the error associated of the the global model. Therefore, the conclusion is that the method used reduced the mean error of the systematic component from 15,4 cm to 1.9 cm, after the adjustment.