Abstract
Satellite gravity gradiometry (SGG) is an ultra-sensitive 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 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.
Keywords
- Spherical Harmonic
- Gravitational Potential
- Pseudodifferential Operator
- European Space Agency
- Tensor Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Freeden, W., Schreiner, M. (2010). Satellite Gravity Gradiometry (SGG): From Scalar to Tensorial Solution. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01546-5_9
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