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GOCE gravitational gradiometry

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Abstract

GOCE is the first gravitational gradiometry satellite mission. Gravitational gradiometry is the measurement of the second derivatives of the gravitational potential. The nine derivatives form a 3 × 3 matrix, which in geodesy is referred to as Marussi tensor. From the basic properties of the gravitational field, it follows that the matrix is symmetric and trace free. The latter property corresponds to Laplace equation, which gives the theoretical foundation of its representation in terms of spherical harmonic or Fourier series. At the same time, it provides the most powerful quality check of the actual measured gradients. GOCE gradiometry is based on the principle of differential accelerometry. As the satellite carries out a rotational motion in space, the accelerometer differences contain angular effects that must be removed. The GOCE gradiometer provides the components V xx , V yy , V zz and V xz with high precision, while the components V xy and V yz are of low precision, all expressed in the gradiometer reference frame. The best performance is achieved inside the measurement band from 5 × 10–3 to 0.1 Hz. At lower frequencies, the noise increases with 1/f and is superimposed by cyclic distortions, which are modulated from the orbit and attitude motion into the gradient measurements. Global maps with the individual components show typical patterns related to topographic and tectonic features. The maps are separated into those for ascending and those for descending tracks as the components are expressed in the instrument frame. All results are derived from the measurements of the period from November to December 2009. While the components V xx and V yy reach a noise level of about \({10\;\rm{\frac{mE}{\sqrt{Hz}}}}\), that of V zz and V xz is about \({20\; \rm{\frac{mE}{\sqrt{Hz}}}}\). The cause of the latter’s higher noise is not yet understood. This is also the reason why the deviation from the Laplace condition is at the \({20 \;\rm{\frac{mE}{\sqrt{Hz}}}}\) level instead of the originally planned \({11\;\rm{\frac{mE}{\sqrt{Hz}}}}\). Each additional measurement cycle will improve the accuracy and to a smaller extent also the resolution of the spherical harmonic coefficients derived from the measured gradients.

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  1. Institut für Astronomische and Physikalische Geodäsie (IAPG), Technische Universität München, Arcisstr. 21, 80290, Munich, Germany

    Reiner Rummel, Weiyong Yi & Claudia Stummer

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  1. Reiner Rummel
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  2. Weiyong Yi
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  3. Claudia Stummer
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Correspondence to Weiyong Yi.

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Rummel, R., Yi, W. & Stummer, C. GOCE gravitational gradiometry. J Geod 85, 777–790 (2011). https://doi.org/10.1007/s00190-011-0500-0

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