The gradiometric-geodynamic boundary value problem

DOI: 10.1007/3-540-26932-0_61 In book: Gravity, Geoid and Space Missions, pp.352-357


The role of gravity gradients is investigated in the framework of geodetic-geodynamic boundary value problems. The time variation of the Eötvös tensor can be separated into three parts. The first part is a surface movement term, the second is the time variation of the gravity field in the original point, and the third is a coupling term. The first and third terms can be computed by a third order derivative tensor of the gravity potential. These terms can be formulated in spherical and planar approximation.
Gravity gradients have the advantage over gravity measurements that certain gravity gradient combinations are insensitive to site movements, thereby allowing the time variation of the gravity field to be determined without repeated height measurements. The solution of the corresponding gradiometric-geodynamic boundary value problem is shown with repeated gravity gradient measurements of the torsion balance.
Several test computations with a simple mass density model were performed in order to analyze the time variation of gravity gradients and give estimates of their respective magnitudes.

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  • Acta Geodaetica et Geophysica Hungarica 06/2007; 42(2). DOI:10.1556/AGeod.42.2007.2.2 · 0.35 Impact Factor
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    Journal of Geodesy 09/2012; 86(9). DOI:10.1007/s00190-012-0550-y · 2.70 Impact Factor
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    ABSTRACT: A new mathematical model for evaluation of the third-order (disturbing) gravitational tensor is formulated in this article. Firstly, we construct corresponding differential operators for the components of the third-order (disturbing) gravitational tensor in a spherical local north-oriented frame. We show that the differential operators may efficiently be decomposed into an azimuthal and an isotropic part. The differential operators are even more simplified for a certain class of isotropic kernels. Secondly, the differential operators are applied to the well-known integrals of Newton, Abel-Poisson, Pizzetti and Hotine. In this way, 40 new integral formulas are derived. The new integral formulas allow for evaluation of the components of the third-order (disturbing) gravitational tensor from density distribution, disturbing gravitational potential, gravity anomalies and gravity disturbances. Thirdly, we investigate the behaviour of the corresponding integral kernels in the spatial domain. The new mathematical formulas extend the theoretical apparatus of geodesy, i.e. the well-known Meissl scheme, and reveal important properties of the third-order gravitational tensor. They may be exploited in geophysical studies, continuation of gravitational field quantities and analysing the gradiometric-geodynamic boundary value problem.
    Journal of Geodesy 02/2015; 89(2):141-157. DOI:10.1007/s00190-014-0767-z · 2.70 Impact Factor

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