PROBLEMA DE VALOR DE CONTORNO DA GEODÉSIA: UMA ABORDAGEM CONCEITUAL

massas, além da superfície limitante, bem como a variação temporal do mesmo.Stokes propôs no século XVIII uma formulação para a solução desse problema,porém implicava em algumas dificuldades. A formulação proposta por Molodenskyem meados do século XX abriu uma nova perspectiva para a solução do problema.Ao longo dos anos, na Geodésia, a relevância do Problema de Valor de Contorno daGeodésia (PVCG) tem sido reconhecida como base teórica para essa disciplina.Além disso, o PVCG ganhou novo impulso com a era espacial e com o passar dosanos algumas alternativas foram elaboradas (super determinado, misto, solução deBrovar). Este trabalho tem como objetivo retratar as formulações de Stokes eMolodensky, bem como as principais alternativas do PVCG

A NEW PERSPECTIVE FOR PHYSICAL HEIGHTS IN BRAZIL

The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights.The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights

Strategy for Connecting to the IHRF: Case Study for the Tide Gauge of Cananeia-SP

In July 2018, IBGE launched the new heights of the Brazilian Geodetic System (BGS), the normal height, which has associated gravity. These new heights are replacing the old normal-orthometric ones, in which there was only the non-parallelism correction. The IBGE informs that the values farther from the origin, have less accuracy. This lower accuracy may interfere in the future, the connection of the local tide gauges to IHRF (International Reference Frame Height). Thus, this paper proposes the integration of the local tide gauge of Cananeia-SP to the IHRF. In order to validate the methodology, the normal, Helmert, and rigorous orthometric heights using two distinct references: the Imbituba-SC tide gauge, as the origin of the BGS and the Cananeia-SP tide gauge, as a local tide gauge to be integrated into the IHRF. Calculating the three heights through these two origins, we analyzed the discrepancies in comparison to the heights calculated by IBGE. Numerical tests indicate that there was an improvement in terms of a mean and standard deviation when using the Cananeia gauge as origin in the calculation of normal, Helmert, and rigorous heights. In the congruence analysis, the calculations indicate that the highest standard deviation is presented when using IBGE normal heights. Thus, we have a new origin that is reliable and functional, can be integrated with the IHRF, where the Helmert and rigorous orthometric heights have the best statistical results

The computation of the geoid model in the state of São Paulo using two methodologies and GOCE models

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes' integral through the Fast Fourier Transform - FFT and Least Squares Collocation - LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes' integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT

ANÁLISE DE DADOS DE GRAVIMETRIA MARINHA: ESTUDO DAS ESTAÇÕES GEODÉSICAS PRÓXIMAS AO LITORAL BRASILEIRO NO CONTEXTO DA INFRAESTRUTURA INTERNACIONAL DE REFERÊNCIA ALTIMÉTRICA: Analysis of marine gravity data: study to the Brazilian near coast geodetic stations in the context of the international height reference frame

The need for an integrated geodetic framework has brought together many researchers in geodesy in order to provide a consistent realization that includes temporal variations of the Earth and, for this purpose, it is necessary to use quantities measured on the earth's surface. The acceleration of gravity is one of those quantities, but its measurement is often hampered by natural conditions, such as in oceanic areas where measurement is of lesser quality than on the Earth's surface, requiring greater attention in the data treatment before use. Despite this, marine gravity data can provide greater detail to coastal areas that are not provided by satellite data. Therefore, in this research, the analysis of marine gravity data was developed around two geodetic stations, CEFT e IMBT, that will be part of the International Height Reference Frame (IHRF). For this, different methodologies of adjustment and/or comparison were used, in which marine gravity data from different surveys were compared with two global gravity models resulting from satellite altimetry. After analysis, the area adjustment method showed more consistent results.A busca por um referencial geodésico integrado tem movimentado grande parte da comunidade geodésica afim de proporcionar uma realização consistente e que acompanhe as variações sofridas pela Terra. Para atingir tal objetivo é necessário aplicar grandezas medidas sobre a superfície terrestre. A aceleração de gravidade é uma destas grandezas, porém sua mensuração muitas das vezes é dificultada pelas condições naturais, como por exemplo, em áreas oceânicas, onde a mensuração é mais onerosa e de menor qualidade que na superfície terrestre, provocando assim, a necessidade de tratamento dos dados antes de seu uso. Apesar desse fator, dados gravimétricos marinhos podem fornecer maior riqueza de detalhes, não proporcionados por dados satelitais, às áreas costeiras. Assim, este trabalho buscou desenvolver metodologias de análise de dados gravimétricos marinhos dispostos ao redor das estações CEFT e IMBT, que farão parte do International Heigh Reference Frame (IHRF). Foram analisados dados fornecidos pelo BGI, ANP e Marinha do Brasil, juntamente com dois modelos gravimétricos globais marinhos o DTU17 e GRAV31.1. Foram desenvolvidas sete metodologias de análise, destas, seis apresentaram resultados satisfatórios, o método de ajuste em área apresentou resultados mais consistentes. Verificou-se que os dados da Marinha do Brasil não são adequados para a área de estudo

EVOLUÇÃO DA INFRAESTRUTURA GRAVIMÉTRICA NO BRASIL

Com o avanço das técnicas de medição da aceleração de gravidade, houve considerável aumento das aplicações gravimétricas em diversos segmentos de atividades mundo afora. Por conseguinte, uma profusão de dados gravimétricos espaciais, aéreos, marinhos e terrestres tem sido adquirida, sobretudo desde meados do século passado. Ao desafio de aprimorar as aplicações, soma-se o interesse da comunidade científica em estabelecer padrões acerca da aquisição e manutenção do acervo auferido, visando dar maior homogeneidade às informações obtidas e disponibilizadas ao usuário. No quadro brasileiro, a falta de uma política gravimétrica nacional tem acarretado iniciativas difusas, fazendo com que cada instituição preencha suas necessidades de forma independente e sem a devida padronização. O presente artigo visa a trazer à tona informações que possibilitem um melhor conhecimento das atividades gravimétricas até então empreendidas em território brasileiro, retratando as principais técnicas e instrumentos utilizados. Adicionalmente, retrata-se brevemente a trajetória das principais instituições que atuam no campo da gravimetria, no intuito de conhecer o passado, compreender o presente e antever futuras ações devidamente concatenadas

THE COMPUTATION OF THE GEOID MODEL IN THE STATE OF SÃO PAULO USING TWO METHODOLOGIES AND GOCE MODELS

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes’ integral through the Fast Fourier Transform - FFT and Least Squares Collocation – LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes’ integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT