On calculation of the vertical deflection and the geoid undulation from gravity anomalies

Boyarsky, E. A.; Afanasyeva, L. V.; Koneshov, V. N.; Rozhkov, Yu. E.

doi:10.1134/s106935131006008x

Cited by 7 publications

(2 citation statements)

References 1 publication

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“…With the obtained measurements available, only changes in gravity are assessed [2]; however, variations in gravity direction and the deformations of the equipotential surfaces of the gravity field are not considered. The increasing accuracy of measurements [3,4,5] requires changes of all gravity field elements to be taken into account and thus a more precise assessment of their impact is required. The above mentioned issues are also significant when carrying out geodynamic and geophysical studies or precise navigation [6].…”

Section: Introductionmentioning

confidence: 99%

The Effect of the Disturbing Potential for the Gravity Field

Petroškevičius

Birvydienė

Popovas

2015

SSP

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The Earth’s gravity field tends to change due to various reasons. These are diverse processes occurring inside the Earth or changes initiated by human activity. The increasing accuracy of measurements has enabled to take into consideration fluctuations in the gravity field. The article presents research study on the effect of gravity potential describing variations in the gravity field affecting gravity field elements related to the performed measurements. Due to the effect of the disturbing potential, a change in gravity and the deviation of vertical and equipotential surface deformation have been determined. The paper has analyzed the disturbing effect of the material point or homogeneous sphere and has specified the possibilities of assessing the disturbing effect of any form of the homogeneous body. Based on the tidal potential induced by the celestial body, the disturbing effect of the Moon and Sun onto the Earth’s gravity field has been assessed. The carried out research indicates that the range of deformation changes in the equipotential surface of the Earth’s gravity field induced by the effect of the Moon is equal to 0.4824 m, whereas that of the Sun makes 0.1861 m. The conducted studies prove that, due to the effect of the Moon, the direction of the vertical, in terms of the Earth’s surface, tends to change up to 0.0541", and as a result of the Sun’s effect it could reach 0.0204". Having assessed the Lunisolar effect in the first order vertical network measurements in Lithuania, in a polygon with the perimeter of 451 km, it has been determined that the closing error of normal height difference has decreased by the factor of 1.3.

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Section: Introductionmentioning

confidence: 99%

The Effect of the Disturbing Potential for the Gravity Field

Petroškevičius

Birvydienė

Popovas

2015

SSP

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“…Significant periodical changes of vertical or deflections of vertical are caused by attraction of closer located and heavy weighted celestial bodies. Mainly it's the Moon and the Sun pull [3]. Increasing accuracy of the geodetic and astronomical measurements [4,5,6,7] requires a deeper analysis of the celestial bodies effects on the vertical deviation and more precise assessment of these effects.…”

Section: Introductionmentioning

confidence: 99%

Analysis of vertical deflection periodic variations

Obuchovski

Petroškevičius

Popovas

2014

The 9th International Conference "Environmental Engineering 2014"

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Most of the geodetic measurements are related with the direction of gravity or vertical. Angular, height difference measurements are performed in horizontal coordinate system. Geodetic measurement data are reduced to a uniform coordinate system prior to processing, taking into account gravity field nonhomogenity. However, increasing accuracy of geodetic measurements requires to assess deviations of the vertical caused by the celestial body effect. The aim of this study is to analyze periodic changes to the direction of the vertical, due to effect of the celestial body, and to assess the impact of the closest celestial bodies which have greater impact. Celestial body effect in the vertical deflection components in meridian and prime vertical was examined. Zonal and nonzonal wave's effect and their amplitude was investigated and evaluated. Results of this work can be used in precise angular measurements and height difference determination, and in the determination of the deflection of the vertical using geodetic astronomy techniques to clarify the shape of the geoid. Results also can be used to assess effect of zonal waves of deflection of the vertical.

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On the accurate numerical evaluation of geodetic convolution integrals

Hirt

Featherstone

Claessens

2011

J Geod

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In the numerical evaluation of geodetic convolution integrals, whether by quadrature or discrete/fast Fourier transform (D/FFT) techniques, the integration kernel is sometimes computed at the centre of the discretised grid cells. For singular kernels -a common case in physical geodesy -this approximation produces significant errors near the computation point, where the kernel changes rapidly across the cell. Rigorously, mean kernels across each whole cell are required. We present one numerical and one analytical method capable of providing estimates of mean kernels for convolution integrals. The numerical method is based on Gauss-Legendre quadrature (GLQ) as efficient integration technique. The analytical approach is based on kernel weighting factors, computed in planar approximation close to the computation point, and used to convert non-planar kernels from point to mean representation. A numerical study exemplifies the benefits of using mean kernels in Stokes's integral. The method is validated using closed-loop tests based on the EGM2008 global gravity model, revealing that using mean kernels instead of point kernels reduces numerical integration errors by a factor of ~5 (at a grid-resolution of 10 arc minutes). Analytical mean kernel solutions are then derived for 14 other commonly used geodetic convolution integrals: Hotine, Eötvös, Green-Molodensky, tidal displacement, ocean tide loading, deflection-geoid, Vening-Meinesz, inverse Vening-Meinesz, inverse Stokes, inverse Hotine, terrain correction, primary indirect effect, Molodensky's G1 term and the Poisson integral. We recommend that mean kernels be used to accurately evaluate geodetic convolution integrals, and the two methods presented here are effective and easy to implement.

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On calculation of the vertical deflection and the geoid undulation from gravity anomalies

Cited by 7 publications

References 1 publication

The Effect of the Disturbing Potential for the Gravity Field

The Effect of the Disturbing Potential for the Gravity Field

Analysis of vertical deflection periodic variations

On the accurate numerical evaluation of geodetic convolution integrals

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