HR: 1330h
AN: P12B-1063    [PDF]
TI: Localized Spectral Estimation on a Sphere Using Multiple Orthogonal Data Tapers: Applications for the Inversion of Admittance and Coherence Functions on the Terrestrial Planets
AU: * Wieczorek, M A
EM: wieczor@ipgp.jussieu.fr
AF: Departement de Geophysique Spatiale et Planetaire, IPGP, 4 Av. de Neptune, Saint-Maur, 94107 France
AU: Simons, F J
EM: fjsimons@alum.mit.edu
AF: Geosciences Department, Princeton, Guyot Hall 321B, Princeton, NJ 08544 United States
AB: Potential field data and topography are one of the primary sources of information on the internal and rheological structure of the terrestrial planets. As one example, the elastic properties of the lithosphere can be estimated by comparing a planet's gravity signature with its topography by analyzing the cross-spectral properties of these fields (i.e., the spectral admittance function). On the Earth, effective elastic thickness calculations are usually performed in the Fourier domain on locally flat surfaces. On the Moon, Mars and Mercury, however, the effects of curvature on both the spectral estimations and gravity calculations become too important to neglect. Moreover, without ground-truthing from land-based local surveys, spherical harmonic representations of the gravity field usually provide the primary data. The joint optimization between spectral and spatial resolution is well studied on flat surfaces and has led to a variety of methods employing multiple data tapers or wavelets. While wavelet methods have also been developed for the sphere, these methods are of limited utility in analyzing gravity-topography admittance functions as no such theoretical relationship exists in the "scale" domain. While primarily a wavelet analysis, Simons et al. (GJI, 131, 1997) developed a forward model inversion approach in which both gravity and topography data were windowed in the space domain, and the obtained windowed admittance function was compared with a similarly windowed model. The windowing function used in that paper was somewhat ad hoc (a spectrally-truncated spherical-cap was utilized), and here we refine their method in terms of finding the optimal data window (or windows) for a given spectral bandwidth. The analogous problem of finding optimally space-concentrated band-limited data windows in the spherical harmonic domain is Slepian's well-known classic Fourier concentration problem. We show how the solution of the associated eigenvalue problem leads to a class of mutually orthogonal data windows, which can be calculated semi-analytically. We study the spatial concentration properties of such tapers and discuss their spectral characteristics in function of their spherical harmonic bandwidth. In certain limiting cases, the tapers appear to be scaled versions of each other, which allows their calculation by interpolation without the repeated solution of the eigenvalue problem. In comparison with the windows employed by Simons et al., for a given spectral bandwidth, our windows are found to have a slightly greater spatial concentration (approximately 91% as opposed to 90%). However, for a bandwidth of only a few degrees greater than that used by Simons et al., our concentration factor rapidly approaches unity. The natural absence of sidelobes and the orthogonal nature of our data tapers lead to an accompanying reduction of the error bars in the spectral estimates, and further allows the analysis of spatio-spectral coherences by averaging over multiple spectral estimates. Using this method we will present localized elastic thickness estimates of the ancient martian and lunar highlands.
DE: 1214 Geopotential theory and determination
DE: 1219 Local gravity anomalies and crustal structure
DE: 1221 Lunar geodesy and gravity (6250)
DE: 1227 Planetary geodesy and gravity (5420, 5714, 6019)
DE: 5417 Gravitational fields (1227)
SC: Planetary Sciences [P]
MN: 2003 Fall Meeting