Satellite Gravity Gradiometry (SGG): From Scalar to Tensorial Solution

Willi Freeden () and Michael Schreiner ()
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Willi Freeden: University of Kaiserslautern, Geomathematics Group
Michael Schreiner: University of Buchs, Institute for Computational Engineering

A chapter in Handbook of Geomathematics, 2015, pp 339-379 from Springer

Abstract: Abstract Satellite gravity gradiometry (SGG) is an ultrasensitive detection technique of the space gravitational gradient (i.e., the Hesse tensor of the Earth’s gravitational potential). In this note, SGG – understood as a spacewise inverse problem of satellite technology – is discussed under three mathematical aspects: First, SGG is considered from potential theoretic point of view as a continuous problem of “harmonic downward continuation.” The space-borne gravity gradients are assumed to be known continuously over the “satellite (orbit) surface”; the purpose is to specify sufficient conditions under which uniqueness and existence can be guaranteed. In a spherical context, mathematical results are outlined by the decomposition of the Hesse matrix in terms of tensor spherical harmonics. Second, the potential theoretic information leads us to a reformulation of the SGG-problem as an ill-posed pseudodifferential equation. Its solution is dealt within classical regularization methods, based on filtering techniques. Third, a very promising method is worked out for developing an immediate interrelation between the Earth’s gravitational potential at the Earth’s surface and the known gravitational tensor.

Date: 2015
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DOI: 10.1007/978-3-642-54551-1_9

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