Análise do termo de primeira ordem das séries de Molodenskii para o problema de valor de contorno da geodésia

Ferreira, Vagner G.; Freitas, Sílvio Rogério Correia de

doi:10.1590/s1982-21702010000400005

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…In the quasigeoid computation, based on the Molodensky formulation (Molodensky, Yeremeyev, and Yurkina 1962) for a solution of an oblique problem, the height anomaly ()  at a point P is (Forsberg 1984), the 1 g term becomes insignificant. On the other hand, in the theory view for an accurate geoid, it is necessary a rigorous formulation because the terrain corrections are closer to the zeroth-order approximation (Ferreira and De Freitas 2010). In the BVRF 2018 context and for a 5' geoid resolution, it was considered acceptable.…”

Section: Boletim Dementioning

confidence: 99%

The Geoid and Quasigeoid of São Paulo State Using the Updated Gravimetric Data and the 2018 BVRF

et al. 2021

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The combination of physical and geometric heights, required for geodetic purposes, uses Global Geopotential Models (GGMs), local geoid, or quasigeoid models. The geoid height and the height anomaly, provided by GGMs, are not accurate enough for most engineering applications. Considering the normal height system of Brazil and the physical concepts of the involved reference surfaces, a quasigeoid model is more appropriate than the current Brazilian geoid model MAPGEO2015. This paper shows the determination of the geoid and the quasigeoid models for São Paulo state using the updated gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). The computation of the quasigeoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e GGM truncated at degree and order 250 and 720. The geoid model was derived from the Bouguer gravity anomalies. The quasigeoid model validation has shown a Root Mean Square (RMS) difference of 18 cm compared with the Global Positioning System (GPS) measurements in the levelling network.

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Section: Boletim Dementioning

confidence: 99%

The Geoid and Quasigeoid of São Paulo State Using the Updated Gravimetric Data and the 2018 BVRF

et al. 2021

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The Spatial Age and the New Paradigms in Geodesy: Implications for Surveying and Mapping in Brazil

Freitas

Dalazoana

Ferreira

2012

Rev. Bras. Cartogr.

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The satellite platforms allowed a very quick transition from local or regional Geodetic Reference Systems (GRSs) to the global ones. The evolution of methods also brought changes in the standards of precision and accuracy. Networks based on local Datums which had relative precision in the order of 1:100,000 to 1:150,000, like the classical networks in the Brazilian Geodetic System (BGS), could be easily replaced by networks constrained in geocentric Datums which reach relative precision of 1:10,000,000 or better and placed inside a concept of a Global Hierarchy. Besides the facilities for positioning, the modern satellite platforms of remote sensors are also applied for satellite altimetry, multi spectral imagery and on-board satellite gravimetry. This allows relevant geodetic information linked directly in global geocentric GRSs. Then, the modern orbital platforms changed completely the ability to capture, model and manage spatial data with strong implications in Geodesy and Cartography. The associated new data bases for Cartography have several new implications coming from the applied surveying methods and present paradigms of precision. Most of the implications come from the need of relating geometric and physical aspects. This happen due the necessary association of local measurements affected by the local gravity field to global oriented geocentric GRS. The modern Global Geopotential Models (GGMs) have a strong expectation for uses in the referred integration. In this paper are discussed the impacts of "spatial age" on the geodetic methods for surveying and mapping. The possible applications of GGMs for realizing fundamental geodetic networks, surveying and mapping are also discussed.

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Problema de valor de contorno da Geodésia: uma abordagem conceitual

Guimarães

Blitzkow

2011

Bol. Ciênc. Geod.

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RESUMOUm dos problemas da Geodésia é determinar o campo de gravidade externo às 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 Molodensky em 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 da Geodésia (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 dos anos algumas alternativas foram elaboradas (super determinado, misto, solução de Brovar). Este trabalho tem como objetivo retratar as formulações de Stokes e Molodensky, bem como as principais alternativas do PVCG. Palavras-chave: Geodésia; Problema de Valor de Contorno; Superfície limitante. ABSTRACTOne of the Geodesy's problems is to determine the masses external gravity field, beyond the boundary surface, as well as the temporal variation. Stokes proposed a formulation in the 18 th century to solve this problem, however some problems were implied. The formulation proposed by Molodensky in the middle of the -20 th century opened a new perspective to solve this problem. Throughout the years, in Geodesy, the relevance of the Boundary Value Problem of Geodesy (BVPG) has been recognized as a theoretical basis for that discipline. In addition, the BVPG gained new impulse with the spatial era and in the maentime, many alternatives

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Análise do termo de primeira ordem das séries de Molodenskii para o problema de valor de contorno da geodésia

Cited by 3 publications

References 9 publications

The Geoid and Quasigeoid of São Paulo State Using the Updated Gravimetric Data and the 2018 BVRF

The Geoid and Quasigeoid of São Paulo State Using the Updated Gravimetric Data and the 2018 BVRF

The Spatial Age and the New Paradigms in Geodesy: Implications for Surveying and Mapping in Brazil

Problema de valor de contorno da Geodésia: uma abordagem conceitual

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