Spherical Slepian functions and the polar gap in geodesy
By Frederik J. Simons, Francis Anthony Dahlen. 2005
150 citations recorded by the source corpus.
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical.
Subfields: Applied Mathematics, Environmental Engineering, Oceanography
View Paper: https://www.semanticscholar.org/paper/1911b115fa3f50d5170282d39f2839d035605de3
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Citations in the corpus
- Gravity and Topography of the Terrestrial Planets (2015, methodology): “The case of arbitrary regions was treated by Simons et al. (2006), and the case where data are absent at the poles (the polar gap problem) was treated by Simons and Dahlen (2006).”
- Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models (2007, methodology): “Slepian problem (for a recent account cf. Simons and Dahlen 2006 and the references therein), and it leads to a series of Eigenvalue problems that are difficult to solve for non-spherical areas.”