Potential-Field Estimation Using Scalar and Vector Slepian Functions at Satellite Altitude

Living reference work entry

Abstract

In the last few decades, a series of increasingly sophisticated satellite missions has brought us gravity and magnetometry data of ever improving quality. To make optimal use of this rich source of information on the structure of the Earth and other celestial bodies, our computational algorithms should be well matched to the specific properties of the data. In particular, inversion methods require specialized adaptation if the data are only locally available, if their quality varies spatially, or if we are interested in model recovery only for a specific spatial region. Here, we present two approaches to estimate potential fields on a spherical Earth, from gradient data collected at satellite altitude. Our context is that of the estimation of the gravitational or magnetic potential from vector-valued measurements. Both of our approaches utilize spherical Slepian functions to produce an approximation of local data at satellite altitude, which is subsequently transformed to the Earth’s spherical reference surface. The first approach is designed for radial-component data only and uses scalar Slepian functions. The second approach uses all three components of the gradient data and incorporates a new type of vectorial spherical Slepian functions that we introduce in this chapter.

Notes

Acknowledgements

A. P. thanks the Ulrich Schmucker Memorial Trust and the Swiss National Science Foundation, the National Science Foundation, and Princeton University for funding and the Smart family of Cape Town for their hospitality while writing this manuscript. This research was sponsored by the US National Science Foundation under grants EAR-1150145 and EAR-1245788 to F.J.S., and by the National Aeronautics & Space Administration under grant NNX14AM29G to A.P. and F.J.S.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Geosciences, Princeton UniversityPrinceton, NJUSA
  2. 2.Department of Earth and Environmental Science, California State University, FresnoFresno, CAUSA
  3. 3.Program in Applied and Computational Mathematics, Princeton UniversityPrinceton, NJUSA

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