A new, high-resolution geoid for Canada and part of the U.S. by the 1D-FFT method

Sideris, M. G.; She, Bin

doi:10.1007/bf00819555

Cited by 49 publications

(20 citation statements)

References 9 publications

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“…1). Notwithstanding least squares collocation (LSC), few previous studies have propagated uncertainties through Stokes's integral (e.g., Sideris and She 1995;Pavlis and Saleh 2005;Huang et al 2007). LSC was not used for the Australian gravimetric quasigeoid computations simply because of the sheer size and extent of the Australian datasets (Sect.…”

Section: Preliminariesmentioning

confidence: 99%

“…(14) and (15) assume that gravity anomaly errors in distinct grid cells are independent, since no covariance terms are considered. Sideris and She (1995) provide error propagation formulas for the 1D-FFT (Haagmans et al 1993) when using the RCR technique over a region. Huang et al (2007) provide a spectral form when using the RCR technique and a modified integration kernel over a spherical integration cap.…”

Section: Preliminariesmentioning

confidence: 99%

“…Instead, the error degree variances (diagonal of the VCV matrix) are often used to approximate σ 2 (ζ EGM ). In our error propagation, however, we use the error grids of σ 2 (ζ EGM ) and σ 2 ( g EGM ) that accompany EGM2008, and not the error degree variances of a satellite-only EGM (as used by, e.g., Sideris and She 1995;Huang et al 2007;Huang and Véron-neau 2013) and assume independence between error values at grid nodes. For a global integration with an unmodified Stokes kernel, Eq.…”

Section: Quasigeoid Error Propagationmentioning

confidence: 99%

“…2.6), but now using the squared terms. Adapted from Sideris and She (1995), in 1D-FFT form, the second and third terms in Eq. (23) are, respectively…”

Section: Quasigeoid Error Propagationmentioning

confidence: 99%

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The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates

Featherstone

McCubbine

Brown

et al. 2017

J Geod

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We describe the computation of the first Australian quasigeoid model to include error estimates as a function of location that have been propagated from uncertainties in the EGM2008 global model, land and altimeterderived gravity anomalies and terrain corrections. The model has been extended to include Australia's offshore territories and maritime boundaries using newer datasets comprising an additional ∼280,000 land gravity observations, a newer altimeter-derived marine gravity anomaly grid, and terrain corrections at 1 × 1 resolution. The error propagation uses a remove-restore approach, where the EGM2008 quasigeoid and gravity anomaly error grids are augmented by errors propagated through a modified Stokes integral from the errors in the altimeter gravity anomalies, land gravity observations and terrain corrections. The gravimetric quasigeoid errors (one sigma) are 50-60 mm across most of the Australian landmass, increasing to ∼100 mm in regions of steep horizontal gravity gradients or the mountains, and are commensurate with external estimates.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Quasigeoid Error Propagationmentioning

confidence: 99%

“…2.6), but now using the squared terms. Adapted from Sideris and She (1995), in 1D-FFT form, the second and third terms in Eq. (23) are, respectively…”

Section: Quasigeoid Error Propagationmentioning

confidence: 99%

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The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates

Featherstone

McCubbine

Brown

et al. 2017

J Geod

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“…The Helmert's second method of condensation involves generally small indirect effects, given by (SIDERIS and SHE, 1995):…”

Section: The Indirect Effect Correctionmentioning

confidence: 99%

Applications of Voronoi and Delaunay Diagrams in the solution of the geodetic boundary value problem

2012

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Voronoi and Delaunay structures are presented as discretization tools to be used in numerical surface integration aiming the computation of geodetic problems solutions, when under the integral there is a non-analytical function (e. g., gravity anomaly and height). In the Voronoi approach, the target area is partitioned into polygons which contain the observed point and no interpolation is necessary, only the original data is used. In the Delaunay approach, the observed points are vertices of triangular cells and the value for a cell is interpolated for its barycenter. If the amount and distribution of the observed points are adequate, gridding operation is not required and the numerical surface integration is carried out by point-wise. Even when the amount and distribution of the observed points are not enough, the structures of Voronoi and Delaunay can combine grid with observed points in order to preserve the integrity of the original information. Both schemes are applied to the computation of the Stokes' integral, the terrain correction, the indirect effect and the gradient of the gravity anomaly, in the State of Rio de Janeiro, Brazil area. Keywords: 2-D tessellation; Delaunay Triangulation; Voronoi Cells; Geodesy; Stokes' Integral. Quintero, C. A. B. et al. Bol. Ciênc. Geod., sec. Artigos, Curitiba, v. 18, n o 3, p.378-396, jul-set, 2012. 3 7 9 RESUMO Este trabalho apresenta as estruturas de Voronoi e Delaunay como ferramentas de discretização a serem usadas na integração numérica de superfícies com o objetivo de resolver problemas computacionais geodésicos, quando no integrando a função não é analítica. No enfoque de Voronoi, a região de trabalho é particionada em polígonos, os quais contêm um ponto por polígono o que faz desnecessária a interpolação. No enfoque de Delaunay, os pontos observados são os vértices de um triangulo, e o valor da célula é o resultado da interpolação sobre o triangulo pelo seu baricentro. Se a quantidade de pontos observados e a sua distribuição são adequadas, a interpolação em grade não é necessária, e a integração é levada a cabo ponto a ponto.Mesmo quando a quantidade e distribuição dos pontos observados não são suficientes, as estruturas de Voronoi e Delaunay podem combinar grade com pontos observados a fim de preservar a integridade da informação original. Ambos os enfoques são aplicados ao cálculo da integral de Stokes, da correção de terreno, do efeito indireto, e do gradiente da anomalia da gravidade na região do estado de Rio de Janeiro, no Brasil. Palavras-chave: Tesselação 2-D; Triangulação de Delaunay; Celulas de Voronoi; Geodésia; Integral de Stokes.

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On the Accuracy of Geoid Heights Derived from Discrete GNSS/Levelling Data Using Kriging Interpolation

Alcaras

Amoroso

Falchi

et al. 2022

International Association of Geodesy Symposia

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Local geoid models presenting higher resolution than global ones are generally derived by a combination of different datasets, integrating individual pure astrogeodetic, gravimetric and GNSS/levelling solutions. To define local geoid, different interpolators may be applied starting from dataset of geoid height values. It is well known that the accuracy of the resulting models depends not only by interpolation method, but also by points numerosity and distribution. This article aims to analyse the performance of Kriging approaches in dependence of the density of the dataset. The experiments are carried out on geoid heights extracted in random way from an already existing local geoid model: different subsets are organized containing an increasing number of points in the same area and each of them is submitted to Kriging interpolations (Universal Kriging and Ordinary Kriging). The resulting models are compared with the original one and residuals are calculated to evaluate the accuracy in dependence of point density. The results demonstrate the efficiency of the Kriging methods, highlighting the possibility to achieve higher accuracy (a few centimetres) using a point density of 1 point/100 sqkm, in absence of gravity anomalies. Ordinary Kriging provides better results than Universal Kriging but the undulations between the resulting models are minimal (a few millimetres) when a high number of points is involved. Furthermore, the results highlight the limit of the leave one out Cross validation since it supplies higher residuals than direct comparison for both Universal Kriging and Ordinary Kriging, when few points are used.

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A new, high-resolution geoid for Canada and part of the U.S. by the 1D-FFT method

Cited by 49 publications

References 9 publications

The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates

The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates

Applications of Voronoi and Delaunay Diagrams in the solution of the geodetic boundary value problem

On the Accuracy of Geoid Heights Derived from Discrete GNSS/Levelling Data Using Kriging Interpolation

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