Computer Science – Performance
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufmgp11a0687b&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #GP11A-0687
Computer Science
Performance
1595 Planetary Magnetism: All Frequencies And Wavelengths, 3260 Inverse Theory, 3299 General Or Miscellaneous, 5440 Magnetic Fields And Magnetism
Scientific paper
Planetary probes often have equatorial, low inclination, orbits around the planet in question, leaving polar data gaps. For example, the orbital path of the Cassini probe around Saturn is essentially limited to a narrow latitudinal band around the equator. For potential field studies this can lead to problems as such studies traditionally employ spherical harmonics, which require global support, to describe the potential field (Simons 2006, Simons 2006a, Wieczorek 2005). Here we consider the use of different basis functions that have been specifically designed to deal with such situations. In contrast to using spherical harmonics for a spectral representation of such 'equatorial' data, an approach which can be prone to errors because global support is required to achieve orthogonality over the whole sphere, Slepian functions, which are orthogonal over both the whole sphere and the region of data coverage, and which have their energy optimally concentrated in the spatial and spectral domain, should yield better results. We have set out to compare the use of these new basis functions in magnetic field analysis with the canonical spherical harmonics. Are the Slepian basis functions better for resolving the magnetic field? Such comparisons have been done in the past, (Simons 2006, Simons 2006a) but took a more theoretical stance, evaluating only a bandlimited white noise source field. We are more interested in the performance under practical circumstances. We employ a number of criteria to evaluate the performance of both basis functions such as: errors, variances, spectral leakage. We have used an Earth magnetic field model, POMME, to generate realistic magnetic field values and Cassini's trajectory scaled to Earth to generate typical equatorial coverage. Simons, F., Dahlen, F., 2006. Spherical Slepian functions and the polar gap in geodesy. Geophysical Journal International 166(3). Simons, F., Dahlen, F., Wieczorek, M. A., 2006. Spatiospectral concentration on a sphere. SIAM Review 48(3). Wieczorek, M., Simons, F., 2005. Localized spectral analysis on the sphere. Geophysical Journal International 162.
Boxham J.
Sterenborg Glenn M.
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