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Volumn 6701, Issue , 2007, Pages

A spatiospectral localization approach to estimating potential fields on the surface of a sphere from noisy, incomplete data taken at satellite altitudes

Author keywords

Geodesy; Inverse theory; Satellite geodesy; Spectral analysis; Spherical harmonics; Statistical methods

Indexed keywords

ASYMPTOTIC ANALYSIS; DATA ACQUISITION; GEOMETRY; GRAVITATION; MAGNETIC FIELDS;

EID: 42149084369     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.732406     Document Type: Conference Paper
Times cited : (15)

References (46)
  • 1
    • 84939751170 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty - I
    • D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty - I," Bell Syst. Tech. J. 40(1), pp. 43-63, 1960.
    • (1960) Bell Syst. Tech. J , vol.40 , Issue.1 , pp. 43-63
    • Slepian, D.1    Pollak, H.O.2
  • 2
    • 33644777655 scopus 로고    scopus 로고
    • Revised spherical cap harmonic analysis (R-SCHA): Validation and properties
    • doi:10.1029/2005JB003836
    • E. Thébault, J. J. Schott, and M. Mandea, "Revised spherical cap harmonic analysis (R-SCHA): Validation and properties," J. Geophys. Res. 111(B1), pp. B01102, doi:10.1029/2005JB003836, 2006.
    • (2006) J. Geophys. Res , vol.111 , Issue.B1
    • Thébault, E.1    Schott, J.J.2    Mandea, M.3
  • 3
    • 33646767410 scopus 로고    scopus 로고
    • Introducing localized constraints in global geomagnetic field modelling
    • V. Lesur, "Introducing localized constraints in global geomagnetic field modelling," Earth Planets Space 58(4), pp. 477-483, 2006.
    • (2006) Earth Planets Space , vol.58 , Issue.4 , pp. 477-483
    • Lesur, V.1
  • 4
    • 0033403893 scopus 로고    scopus 로고
    • Band-limited functions on a bounded spherical domain: The Slepian problem on the sphere
    • A. Albertella, F. Sansò, and N. Sneeuw, "Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere," J. Geodesy 73, pp. 436-447, 1999.
    • (1999) J. Geodesy , vol.73 , pp. 436-447
    • Albertella, A.1    Sansò, F.2    Sneeuw, N.3
  • 5
    • 33747615027 scopus 로고    scopus 로고
    • Spherical Slepian functions and the polar gap in geodesy
    • doi:10.1111/j.1365-246X.2006.03065.x
    • F. J. Simons and F. A. Dahlen, "Spherical Slepian functions and the polar gap in geodesy," Geophys. J. Int. 166, pp. 1039-1061, doi:10.1111/j.1365-246X.2006.03065.x, 2006.
    • (2006) Geophys. J. Int , vol.166 , pp. 1039-1061
    • Simons, F.J.1    Dahlen, F.A.2
  • 6
    • 0037465164 scopus 로고    scopus 로고
    • From global to regional analysis of the magnetic field on the sphere using wavelet frames
    • M. Holschneider, A. Chambodut, and M. Mandea, "From global to regional analysis of the magnetic field on the sphere using wavelet frames," Phys. Earth Planet. Inter. 135, pp. 107-124, 2003.
    • (2003) Phys. Earth Planet. Inter , vol.135 , pp. 107-124
    • Holschneider, M.1    Chambodut, A.2    Mandea, M.3
  • 7
    • 4043159197 scopus 로고    scopus 로고
    • Orthogonal zonal, tesseral and sectorial wavelets on the sphere for the analysis of satellite data
    • W. Freeden and V. Michel, "Orthogonal zonal, tesseral and sectorial wavelets on the sphere for the analysis of satellite data," Adv. Comput. Math. 21(1-2), pp. 181-217, 2004.
    • (2004) Adv. Comput. Math , vol.21 , Issue.1-2 , pp. 181-217
    • Freeden, W.1    Michel, V.2
  • 8
    • 0020786063 scopus 로고
    • Some comments on Fourier analysis, uncertainty and modeling
    • D. Slepian, "Some comments on Fourier analysis, uncertainty and modeling," SIAM Rev. 25(3), pp. 379-393, 1983.
    • (1983) SIAM Rev , vol.25 , Issue.3 , pp. 379-393
    • Slepian, D.1
  • 9
    • 30144440852 scopus 로고    scopus 로고
    • Localized spectral analysis on the sphere
    • doi:10.1111/j.1365-246X.2005.02687.x
    • M. A. Wieczorek and F. J. Simons, "Localized spectral analysis on the sphere," Geophys. J. Int. 162(3), pp. 655-675, doi:10.1111/j.1365-246X.2005.02687.x, 2005.
    • (2005) Geophys. J. Int , vol.162 , Issue.3 , pp. 655-675
    • Wieczorek, M.A.1    Simons, F.J.2
  • 10
    • 33746171197 scopus 로고    scopus 로고
    • Spatiospectral concentration on a sphere
    • doi:10.1137/S0036144504445765
    • F. J. Simons, F. A. Dahlen, and M. A. Wieczorek, "Spatiospectral concentration on a sphere," SIAM Rev. 48(3), pp. 504-536, doi:10.1137/S0036144504445765, 2006.
    • (2006) SIAM Rev , vol.48 , Issue.3 , pp. 504-536
    • Simons, F.J.1    Dahlen, F.A.2    Wieczorek, M.A.3
  • 11
    • 0035017520 scopus 로고    scopus 로고
    • Spatially restricted data distributions on the sphere: The method of orthonormalized functions and applications
    • R. Pail, G. Plank, and W.-D. Schuh, "Spatially restricted data distributions on the sphere: the method of orthonormalized functions and applications," J. Geodesy 75, pp. 44-56, 2001.
    • (2001) J. Geodesy , vol.75 , pp. 44-56
    • Pail, R.1    Plank, G.2    Schuh, W.-D.3
  • 12
    • 33747601494 scopus 로고
    • Doubly orthogonal concentrated polynomials
    • E. N. Gilbert and D. Slepian, "Doubly orthogonal concentrated polynomials," SIAM J. Math. Anal. 8(2), pp. 290-319, 1977.
    • (1977) SIAM J. Math. Anal , vol.8 , Issue.2 , pp. 290-319
    • Gilbert, E.N.1    Slepian, D.2
  • 13
    • 0020191169 scopus 로고
    • Differential operators commuting with finite convolution integral operators: Some non-Abelian examples
    • F. A. Grünbaum, L. Longhi, and M. Perlstadt, "Differential operators commuting with finite convolution integral operators: some non-Abelian examples," SIAM J. Appl. Math. 42(5), pp. 941-955, 1982.
    • (1982) SIAM J. Appl. Math , vol.42 , Issue.5 , pp. 941-955
    • Grünbaum, F.A.1    Longhi, L.2    Perlstadt, M.3
  • 15
    • 0027035652 scopus 로고
    • The value of minimum norm estimation of geopotential fields
    • P. Xu, "The value of minimum norm estimation of geopotential fields," Geophys. J. Int. 111, pp. 170-178, 1992.
    • (1992) Geophys. J. Int , vol.111 , pp. 170-178
    • Xu, P.1
  • 16
    • 0029503470 scopus 로고
    • Alleviation of the Backus effect in geomagnetic field modelling
    • R. Holme and J. Bloxham, "Alleviation of the Backus effect in geomagnetic field modelling," Geophys. Res. Lett. 22(13), pp. 1641-1644, 1995.
    • (1995) Geophys. Res. Lett , vol.22 , Issue.13 , pp. 1641-1644
    • Holme, R.1    Bloxham, J.2
  • 18
    • 84984522369 scopus 로고
    • Spatial power spectrum of the main geomagnetic field and extrapolation to core
    • F. J. Lowes, "Spatial power spectrum of the main geomagnetic field and extrapolation to core," Geophys. J. R. Astron. Soc. 36(3), pp. 717-730, 1974.
    • (1974) Geophys. J. R. Astron. Soc , vol.36 , Issue.3 , pp. 717-730
    • Lowes, F.J.1
  • 19
    • 0021086287 scopus 로고
    • Geomagnetic field analysis - I. Stochastic inversion
    • D. Gubbins, "Geomagnetic field analysis - I. Stochastic inversion," Geophys. J. R. Astron. Soc. 73(3), pp. 641-652, 1983.
    • (1983) Geophys. J. R. Astron. Soc , vol.73 , Issue.3 , pp. 641-652
    • Gubbins, D.1
  • 20
    • 0000083018 scopus 로고    scopus 로고
    • A method for extracting maximum resolution power spectra from microwave sky maps
    • M. Tegmark, "A method for extracting maximum resolution power spectra from microwave sky maps," Mon. Not. R. Astron. Soc 280, pp. 299-308, 1996.
    • (1996) Mon. Not. R. Astron. Soc , vol.280 , pp. 299-308
    • Tegmark, M.1
  • 21
    • 0001345917 scopus 로고
    • Statistical analysis of catalogs of extragalactic objects. I. Theory
    • P. J. E. Peebles, "Statistical analysis of catalogs of extragalactic objects. I. Theory," Astroph. J. 185, pp. 413-440, 1973.
    • (1973) Astroph. J , vol.185 , pp. 413-440
    • Peebles, P.J.E.1
  • 22
    • 11944250836 scopus 로고
    • A method for extracting maximum resolution power spectra from galaxy surveys
    • M. Tegmark, "A method for extracting maximum resolution power spectra from galaxy surveys," Astroph. J. 455, pp. 429-438, 1995.
    • (1995) Astroph. J , vol.455 , pp. 429-438
    • Tegmark, M.1
  • 28
    • 84968465441 scopus 로고
    • On the eigenvalue behavior of certain convolution equations
    • H. J. Landau, "On the eigenvalue behavior of certain convolution equations," Trans. Am. Math. Soc. 115, pp. 242-256, 1965.
    • (1965) Trans. Am. Math. Soc , vol.115 , pp. 242-256
    • Landau, H.J.1
  • 29
    • 84944817831 scopus 로고
    • Eigenvalues associated with prolate spheroidal wave functions of zero order
    • D. Slepian and E. Sonnenblick, "Eigenvalues associated with prolate spheroidal wave functions of zero order," Bell Syst. Tech. J. 44(8), pp. 1745-1759, 1965.
    • (1965) Bell Syst. Tech. J , vol.44 , Issue.8 , pp. 1745-1759
    • Slepian, D.1    Sonnenblick, E.2
  • 30
    • 84916160159 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty - IV: Extensions to many dimensions; generalized prolate spheroidal functions
    • D. Slepian, "Prolate spheroidal wave functions, Fourier analysis and uncertainty - IV: Extensions to many dimensions; generalized prolate spheroidal functions," Bell Syst. Tech. J. 43(6), pp. 3009-3057, 1964.
    • (1964) Bell Syst. Tech. J , vol.43 , Issue.6 , pp. 3009-3057
    • Slepian, D.1
  • 31
    • 33748362797 scopus 로고
    • Semiclassical methods and the summation of the scattering partial wave series
    • R. D. Amado, K. Stricker-Bauer, and D. A. Sparrow, "Semiclassical methods and the summation of the scattering partial wave series," Phys. Rev. C 32(1), pp. 329-332, 1985.
    • (1985) Phys. Rev. C , vol.32 , Issue.1 , pp. 329-332
    • Amado, R.D.1    Stricker-Bauer, K.2    Sparrow, D.A.3
  • 32
    • 0018917921 scopus 로고
    • A uniformly valid asymptotic representation of normal mode multiplet spectra on a laterally heterogeneous Earth
    • F. A. Dahlen, "A uniformly valid asymptotic representation of normal mode multiplet spectra on a laterally heterogeneous Earth," Geophys. J. R. Astron. Soc. 62(2), pp. 225-247, 1980.
    • (1980) Geophys. J. R. Astron. Soc , vol.62 , Issue.2 , pp. 225-247
    • Dahlen, F.A.1
  • 33
    • 0942297581 scopus 로고
    • Über die Laplacesche Reihe
    • E. Hilb, "Über die Laplacesche Reihe," Math. Z. 5, p. 17, 1919.
    • (1919) Math. Z , vol.5 , pp. 17
    • Hilb, E.1
  • 34
    • 0004073954 scopus 로고
    • American Mathematical Society, Providence, R.I, 4 ed
    • G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, R.I., 4 ed., 1975.
    • (1975) Orthogonal Polynomials
    • Szegö, G.1
  • 38
    • 0005958029 scopus 로고
    • Practical considerations for the generation of large-order spherical harmonics
    • K. G. Libbrecht, "Practical considerations for the generation of large-order spherical harmonics," Solar Physics 99(1-2), pp. 371-373, 1985.
    • (1985) Solar Physics , vol.99 , Issue.1-2 , pp. 371-373
    • Libbrecht, K.G.1
  • 39
    • 0343469259 scopus 로고    scopus 로고
    • On the efficient calculation of ordinary and generalized spherical harmonics
    • G. Masters and K. Richards-Dinger, "On the efficient calculation of ordinary and generalized spherical harmonics," Geophys. J. Int. 135(1), pp. 307-309, 1998.
    • (1998) Geophys. J. Int , vol.135 , Issue.1 , pp. 307-309
    • Masters, G.1    Richards-Dinger, K.2
  • 40
    • 0028576062 scopus 로고
    • Global spherical harmonic-analysis by least-squares and numerical quadrature methods in historical perspective
    • N. Sneeuw, "Global spherical harmonic-analysis by least-squares and numerical quadrature methods in historical perspective," Geophys. J. Int. 118(3), pp. 707-716, 1994.
    • (1994) Geophys. J. Int , vol.118 , Issue.3 , pp. 707-716
    • Sneeuw, N.1
  • 41
    • 3042577550 scopus 로고    scopus 로고
    • Slepian functions on the sphere, generalized Gaussian quadrature rule
    • L. Miranian, "Slepian functions on the sphere, generalized Gaussian quadrature rule," Inv. Prob. 20, pp. 877-892, 2004.
    • (2004) Inv. Prob , vol.20 , pp. 877-892
    • Miranian, L.1
  • 42
    • 0037440439 scopus 로고    scopus 로고
    • Continuous wavelet-like filter for a spherical surface and its application to localized admittance function on Mars
    • M. Kido, D. A. Yuen, and A. P. Vincent, "Continuous wavelet-like filter for a spherical surface and its application to localized admittance function on Mars," Phys. Earth Planet. Inter. 135, pp. 1-14, 2003.
    • (2003) Phys. Earth Planet. Inter , vol.135 , pp. 1-14
    • Kido, M.1    Yuen, D.A.2    Vincent, A.P.3
  • 44
    • 0031438340 scopus 로고    scopus 로고
    • Localization of the gravity field and the signature of glacial rebound
    • December
    • M. Simons and B. H. Hager, "Localization of the gravity field and the signature of glacial rebound," Nature 390, pp. 500-504, December 1997.
    • (1997) Nature , vol.390 , pp. 500-504
    • Simons, M.1    Hager, B.H.2
  • 45
    • 0031473691 scopus 로고    scopus 로고
    • Localization of gravity and topography: Constraints on the tectonics and mantle dynamics of Venus
    • October
    • M. Simons, S. C. Solomon, and B. H. Hager, "Localization of gravity and topography: Constraints on the tectonics and mantle dynamics of Venus," Geophys. J. Int. 131, pp. 24-44, October 1997.
    • (1997) Geophys. J. Int , vol.131 , pp. 24-44
    • Simons, M.1    Solomon, S.C.2    Hager, B.H.3
  • 46
    • 0347874846 scopus 로고    scopus 로고
    • Evaluation of the rotation matrices in the basis of real spherical harmonics
    • M. A. Blanco, M. Flórez, and M. Bermejo, "Evaluation of the rotation matrices in the basis of real spherical harmonics," J. Mol. Struct. (Theochem) 419, pp. 19-27, 1997.
    • (1997) J. Mol. Struct. (Theochem) , vol.419 , pp. 19-27
    • Blanco, M.A.1    Flórez, M.2    Bermejo, M.3


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