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Earth, Planets and Space

, Volume 61, Issue 7, pp 835–843

First Online: 31 August 2009Received: 25 July 2008Revised: 12 March 2009Accepted: 16 March 2009


In principle, every component of a disturbing gravity gradient tensor measured in a satellite orbit can be used to obtain gravity anomalies on the Earth’s surface. Consequently, these can be used in combination with ground or marine data for further gravity field modeling or for verification of satellite data. Theoretical relations can be derived both in spectral and spatial forms. In this paper, we focus on the derivation of a spatial integral form in the geocentric spherical coordinates that seems to be the most convenient one for regional gravity field modeling. All of the second partial derivatives of the generalized Stokes’s kernel are derived, and six surface Fredholm integral equations are formulated and discretized. The inverse problems formulated for particular components clearly reveal different behaviors in terms of numerical stability of the solution. Simulated GOCE data disturbed with Gaussian noise are used to study the performance of two regularization methods: truncated singular value decomposition and ridge regression. The optimal ridge regression method shows slightly better results in terms of the root mean squared deviation of the differences from the exact solution.

Key wordsGradiometry Pizzetti integral formula inverse problem regularization  Download to read the full article text

Autor: Juraj Janák - Yoichi Fukuda - Peiliang Xu


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