Determination of the boundary values for the Stokes-Helmert problem

Vaníček, Petr; Huang, Jianliang; Novák, Pavel; Pagiatakis, Spiros; Véronneau, M.; Martinec, Z.; Featherstone, Will

doi:10.1007/s001900050235

Cited by 63 publications

(58 citation statements)

References 5 publications

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“…Several methods are used in practice, among others, methods based on the Stokes integral or Stokes-type integrals (e.g., Jekeli, 1981;Vaníček et al, 1999;Novák et al, 2001;Sjöberg, 2003), least-squares collocation (Moritz, 1978;Tscherning, 1978Tscherning, , 1985, and least-squares techniques (e.g., Eicker, 2008;Klees et al, 2007Klees et al, , 2008Schmidt et al, 2007;Wittwer, 2009). Each method deals with the data noise in a different way, hence, they may lead to different estimations of the commission error.…”

Section: 1 M E T H O D O L O G Ymentioning

confidence: 99%

Data requirements for a 5-mm quasi-geoid in the Netherlands

2017

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Section: 1 M E T H O D O L O G Ymentioning

confidence: 99%

Data requirements for a 5-mm quasi-geoid in the Netherlands

2017

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“…A simplified Poincaré-Prey relationship for mean gravity can be given as (Heiskanen and Moritz 1967, Equations 4 to 25;Torge 1991) …”

Section: Description Of Orthometric Height Systemsmentioning

confidence: 99%

Comparison of Helmert and rigorous orthometric heights over Japan

Odera

2015

Earth, Planets and Space

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The local vertical datum in Japan is based on the Helmert's approximation of mean gravity along the plumbline. However, determination of a rigorous orthometric height requires that the integral-mean value of gravity along the plumbline between the geoid and the Earth surface has to be known precisely. An attempt has been made to obtain rigorous orthometric heights at 816 GPS/levelling points distributed over four main islands of Japan (Hokkaido, Honshu, Shikoku and Kyushu) by applying corrections to the Helmert orthometric heights. The corrections to Helmert orthometric heights are evaluated from the differences between the integral-mean gravity and the approximate mean gravity along the plumbline. The corrections to Helmert orthometric heights vary from −30.9 cm to 0.0 cm with a mean value of −0.4 cm and standard deviation of ±1.7 cm. An improved high-resolution gravimetric geoid model covering four main islands of Japan from our previous study is used to compare the consistency of the two height systems to a regionally defined gravimetric geoid model. The standard deviation of the differences between gravimetric and GPS/levelling geoid undulations is ±7.5 cm, when Helmert orthometric heights are used. The standard deviation of the differences between gravimetric and GPS/levelling geoid undulations reduces to ±7.3 cm, when rigorous orthometric heights are used. This indicates that rigorous orthometric heights are more consistent with the gravimetric geoid model than Helmert orthometric heights.

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“…The other applied reductions include a secondary indirect topographical effect (Vaníček et al 1999), a second-order free-air reduction (Heiskanen and Moritz 1967), and an atmospheric correction (Wichiencharoen 1982a). The residual gravity anomalies are obtained from the reduced gravity anomalies on the geoid and gravity anomalies obtained from EGM2008 (degree 2,190 and order 2,159) in the three islands (Hokkaido, Honshu, and Kyushu), and GOCO02S/EGM2008 (degree 2,190 and order 2,159) in Shikoku.…”

Section: Gravity Data Reductions and Griddingmentioning

confidence: 99%

Improvement of the geoid model over Japan using integral formulae and combination of GGMs

Odera

2014

Earth Planet Sp

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An improved high-resolution gravimetric geoid model covering the four main islands of Japan (Hokkaido, Honshu, Shikoku, and Kyushu) was developed on a 1 × 1.5 arc-minute grid from EGM2008, GOCO02S/EGM2008, and terrestrial gravity data. A modified form of the Stokes-Helmert scheme was applied for the determination of the geoid using an empirically determined optimal spherical cap size. Handling of the topographical effects on gravity was accomplished using the integral formulae of Martinec and Vaníček, which were found to be more suitable for geoid modeling over Japan than the classical formulae. EGM2008 was used in Hokkaido, Honshu, and Kyushu Islands, whereas a combination of GOCO02S and EGM2008 was used in Shikoku Island and its immediate surroundings. The global geopotential models (GGMs) used in this study were chosen based on our earlier evaluation of the performance of EGM2008-and GOCE-related GGMs in Japan. In comparison with the previous geoid model for Japan, our new model shows an improvement in the standard deviation from ±8.3 to ±7.5 cm.

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Determination of the boundary values for the Stokes-Helmert problem

Cited by 63 publications

References 5 publications

Data requirements for a 5-mm quasi-geoid in the Netherlands

Data requirements for a 5-mm quasi-geoid in the Netherlands

Comparison of Helmert and rigorous orthometric heights over Japan

Improvement of the geoid model over Japan using integral formulae and combination of GGMs

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