Minimum-variance multitaper spectral estimation on the sphere

Journal of Fourier Analysis and Applications

Volumn 13, Issue 6, 2007, Pages 665-692

  Wieczorek, Mark A ^a   Simons, Frederik J ^b,c  

^a INSTITUT DE PHYSIQUE DU GLOBE DE PARIS   (France)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

Multitaper spectral analysis; Spherical harmonics

Indexed keywords

EID: 35548934617     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-006-6904-1     Document Type: Article

References (31)

1. Belleguic, V., Lognonné, P., and Wieczorek, M. A. (2005). Constraints on the Martian lithosphere from gravity and topography data, J. Geophys. Res. 110.
2. Blakely, R. J. (1995). Potential Theory in Gravity and Magnetic Applications, Cambridge University Press, New York.
3. Dahlen, F. A. and Tromp, J. (1998). Theoretical Global Seismology, Princeton University Press, Princeton, NJ.
4. Dahlen, F. A. and Simons, F. J. (2007). Spectral estimation on a sphere in geophysics and cosmology, Geophys. J. Int., submitted manuscript.
5. Driscoll, J. R. and Healy, D. M. (1994). Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math. 15, 202-250.
6. Grünbaum, F. A., Longhi, L., and Perlstadt, M. (1982). Differential operators commuting with finite convolution integral operators: Some non-abelian examples, SIAM, J. Appl. Math. 42, 941-955.
7. Han, S.-C. and Simons, F. J. (2007). Spatiospectral localization of global geopotential fields from GRACE reveals the coseismic gravity change due to the 2004 Sumatra-Andaman earthquake, J. Geophys. Res., in press.
8. Hansen, F. K., Górski, K. M., and Hivon, E. (2002). Gabor transforms on the sphere with applications to CMB power spectrum estimation, Mon. Not. R. Astron. Soc. 336, 1304-1328.
9. Hinshaw, G., Nolta, M.R., Bennett, C.L., Bean, R., Doré, O., Greason, M.R., Halpern, M., Hill, R.S., Jarosik, N., Kogut, A., Komatsu, E., Limon, M., Odegard, N., Meyer, S. S., Page, L., Peiris, H. V., Spergel, D. N., Tucker, G. S., Verde, L., Weiland, J. L., Wollack, E., and Wright, E. L. (2006). Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Temperature analysis, arXiv, astro-ph/0603451.
10. Hivon, E., Górski, K. M., Netterfield, C. B., Crill, B. P., Prunet, S., and Hansen, F. (2002). MASTER of the Cosmic Microwave Background anisotropy power spectrum: A fast method for statistical analysis of large and complex Cosmic Microwave Background data sets, Astroph. J. 567, 2-17.
11. Holmes, S.A. and Featherstone, W.E. (2002). A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions, J. Geod. 76, 279-299.
12. Kaula, W. M. (1967). Theory of statistical analysis of data distributed over a sphere, Rev. Geophys. 5, 83-107.
13. Lawson, C. L. and Hanson, R. J. (1995). Solving least squares problems, Classics Appl. Math. SIAM 15.
14. Luscombe, J. J. and Luban, M. (1998). Simplified recursive algorithm for Wigner 3j and 6j symbols, Phys. Rev. E 57, 7274-7277.
15. McCoy, E. J., Walden, A. T., and Percival, D. B. (1998). Multitaper spectral estimation of power law processes, IEEE Tians. Signal Proc. 46, 655-688.
16. McGovern, P. J., Solomon, S. C., Smith, D. E., Zuber, M. T., Simons, M., Wieczorek, M. A., Phillips, R. J., Neumann, G. A., Aharonson, O., and Head, J. W. (2002). Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution, J. Geophys. Res. 107, 5136.
17. Peebles, P. J. E. (1973). Statistical analysis of catalogs of extragalactic objects, I. Theory, Astroph. J. 185, 413-440.
18. Percival, D.B. and Walden, A.T. (1993). Spectral Analysis for Physical Applications, Multitaper and Conventional Univariate Techniques, Cambridge University Press.
19. Schulten, K. and Gordon, R. G. (1975). Exact recursive evaluation of 3j-coefficients and 6j-coefficients for quantum-mechanical coupling of angular momenta, J. Math. Phys. 16, 1961-1970.
20. Simons, F. J. and Dahlen, F. A. (2006). Spherical Slepian functions and the polar gap in geodesy, Geophys. J. Int. 166, 1039-1061.
21. Simons, F. J., Dahlen, F. A., and Wieczorek, M. A. (2006). Spatiospectral localization on the sphere, SIAM Rev. 48, 504-536.
22. Simons, M., Solomon, S. C., and Hager, B. H. (1997). Localization of gravity and topography: Constraints on the tectonics and mantle dynamics of Venus, Geophys. J. Int. 131, 24-44.
23. Slepian, D. and Pollak, H. O. (1960). Prolate spheroidal wave functions, Fourier analysis and uncertainty - I, Bell Syst. Tech. J. 40, 43-63.
24. Slepian, D. (1983). Some comments on Fourier-analysis, uncertainty andmodeling, SIAMRev. 25, 379-393.
25. Spergel, D.N., Bean, R., Doré, O., Nolta, M.R., Bennett, C.L., Hinshaw, G., Jarosik, N., Komatsu, E., Page, L., Peiris, H. V., Verde, L., Barnes, C., Halpern, M., Hill, R. S., Kogut, A., Limon, M., Meyer, S. S., Odegard, N., Tucker, G. S., Weiland, J. L., Wollack, E., and Wright, E. L. (2006). Wilkinson Microwave Anisotropy Probe (WMAP) three year results: Implications for cosmology, arXiv, astro-ph/0603449.
26. Thomson, D. J. (1982). Spectrum estimation and harmonic analysis, Proc. IEEE 70, 1055-1096.
27. Varshalovich, D. A., Moskalev, A. N., and Khersonskii, V. K. (1988). Quantum, theory of angular momentum, World Scientific, Singapore.
28. Walden, A. T., McCoy, E. J., and Percival, D. B. (1994). The variance of multitaper spectrum estimates for real Gaussian processes, IEEE Trans. Signal Process. 2, 479-482.
29. Wieczorek, M. A. (2007). Gravity and topography of the terrestrial planets, in Treatise on Geophyics, 10, Eds. Spohn, T. and Schubert, T., Elsevier-Pergamon, Oxford, in press.
30. Wieczorek, M. A. (2007). Constraints on the composition of the Martian south polar cap from gravity and topography, Icarus, in press.
31. Wieczorek, M. A. and Simons, F. J. (2005). Localized spectral analysis on the sphere, Geophys. J. Int. 162, 655-675.