Summary
Satellite gravity gradiometry is a recent method for a detailed determination of the gravitational potential of the earth. The measurements provided by a gradiometer are – for a so-called full gradiometer – all second-order derivatives of the potential, that is, the Hessian tensor. This leads to a nonstandard problem in potential theory.
After a short description of satellite gradiometry, we focus on uniqueness and existence problems. For this, a certain decomposition of the Hessian tensor is of importance. The decomposition allows in addition to transfer modern solution methods for scalar functions on the sphere to the tensorial case, by generalizing zonal functions to zonal tensor kernels.
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Schreiner, M. (2009). The Role of Tensor Fields for Satellite Gravity Gradiometry. In: Laidlaw, D., Weickert, J. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88378-4_10
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DOI: https://doi.org/10.1007/978-3-540-88378-4_10
Publisher Name: Springer, Berlin, Heidelberg
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