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2010 | OriginalPaper | Buchkapitel

Spectral Approaches to Solving the Polar Gap Problem

verfasst von : Oliver Baur, Jianqing Cai, Nico Sneeuw

Erschienen in: System Earth via Geodetic-Geophysical Space Techniques

Verlag: Springer Berlin Heidelberg

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Abstract

Due to its sun-synchronous orbit, GOCE (Gravity field recovery and steady-state Ocean Circulation Explorer) observations do not cover the polar areas of the Earth. The impact of the limited spatial observation geometry on gravity field recovery is referred to as the polar gap problem. This chapter gives an overview on both spatial and spectral approaches to overcome the polar gap problem. Furthermore we confront strategies based on GOCE data only with methods augmenting additional external gravity field information. Concerning the latter, we present the combination of the GOCE normal equations system with spectral a priori information in terms of tailored regularization. With regard to a GOCE-only solution, we adopt band-limited base functions, commonly referred to as Slepian functions that are optimally concentrated within the spherical belt of GOCE data availability. In terms of regional gravity field determination this approach definitively solves the polar gap problem.

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Literatur
Zurück zum Zitat Albertella A, Sansò F, Sneeuw N (1999) Band-limited functions on a bounded spherical domain: The Slepian problem on the sphere. J. Geod. 73, 436–447.CrossRef Albertella A, Sansò F, Sneeuw N (1999) Band-limited functions on a bounded spherical domain: The Slepian problem on the sphere. J. Geod. 73, 436–447.CrossRef
Zurück zum Zitat Baur O, Sneeuw N (2007) Slepian approach revisited: New studies to overcome the polar gap. Proceedings of GOCE User Workshop, ESA SP-627. Baur O, Sneeuw N (2007) Slepian approach revisited: New studies to overcome the polar gap. Proceedings of GOCE User Workshop, ESA SP-627.
Zurück zum Zitat Baur O, Sneeuw N, Grafarend EW (2008) Methodology and use of tensor invariants for satellite gravity gradiometry. J. Geod., doi: 10.1007/s00190-007-0178-5. Baur O, Sneeuw N, Grafarend EW (2008) Methodology and use of tensor invariants for satellite gravity gradiometry. J. Geod., doi: 10.1007/s00190-007-0178-5.
Zurück zum Zitat Cai J (2004) Statistical inference of the eigenspace components of a symmetric random deformation tensor. DGK Series C 577, Munich. Cai J (2004) Statistical inference of the eigenspace components of a symmetric random deformation tensor. DGK Series C 577, Munich.
Zurück zum Zitat Ditmar P, Klees R, Kostenko F (2003) Fast and accurate computation of spherical harmonic coefficients from satellite gravity gradiometry data. J. Geod., doi: 10.1007/s00190-002-0298-x. Ditmar P, Klees R, Kostenko F (2003) Fast and accurate computation of spherical harmonic coefficients from satellite gravity gradiometry data. J. Geod., doi: 10.1007/s00190-002-0298-x.
Zurück zum Zitat ESA (1999) The four candidate Earth explorer core missions – gravity field and steady-state ocean circulation mission. ESA Report SP-1233(1), Granada. ESA (1999) The four candidate Earth explorer core missions – gravity field and steady-state ocean circulation mission. ESA Report SP-1233(1), Granada.
Zurück zum Zitat Forsberg R, Kenyon S (2004) Gravity and geoid in the arctic region – The Northern polar gap now filled. Proceedings of GOCE User Workshop, ESA-ESRIN. Forsberg R, Kenyon S (2004) Gravity and geoid in the arctic region – The Northern polar gap now filled. Proceedings of GOCE User Workshop, ESA-ESRIN.
Zurück zum Zitat van Gelderen M, Koop R (1997) The use of degree variances in satellite gradiometry. J. Geod. 71, 337–343.CrossRef van Gelderen M, Koop R (1997) The use of degree variances in satellite gradiometry. J. Geod. 71, 337–343.CrossRef
Zurück zum Zitat Grünbaum FA, Longhi L, Perlstadt M (1982) Differential operators commuting with finite convolution integral operators: some non-abelian examples. SIAM J. Appl. Math. 42, 941–955.CrossRef Grünbaum FA, Longhi L, Perlstadt M (1982) Differential operators commuting with finite convolution integral operators: some non-abelian examples. SIAM J. Appl. Math. 42, 941–955.CrossRef
Zurück zum Zitat Kusche J (2003) A Monte-Carlo technique for weight estimation in satellite geodesy. J. Geod., doi: 10.1007/s00190-002-0302-5. Kusche J (2003) A Monte-Carlo technique for weight estimation in satellite geodesy. J. Geod., doi: 10.1007/s00190-002-0302-5.
Zurück zum Zitat Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J. Geod. 76, 359–368.CrossRef Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J. Geod. 76, 359–368.CrossRef
Zurück zum Zitat Metzler B, Pail R (2005) GOCE data processing: The spherical cap regularization approach. Stud. Geophys. Geod. 49, 441–462.CrossRef Metzler B, Pail R (2005) GOCE data processing: The spherical cap regularization approach. Stud. Geophys. Geod. 49, 441–462.CrossRef
Zurück zum Zitat Miranian L (2004) Slepian functions on the sphere, generalized Gaussian quadrature rule. Inv. Prob. 20, 877–892.CrossRef Miranian L (2004) Slepian functions on the sphere, generalized Gaussian quadrature rule. Inv. Prob. 20, 877–892.CrossRef
Zurück zum Zitat Pail R, Plank G, Schuh W-D (2001) Spatially restricted data distributions on the sphere: The method of orthonormalized functions and applications. J. Geod. 75, 44–56.CrossRef Pail R, Plank G, Schuh W-D (2001) Spatially restricted data distributions on the sphere: The method of orthonormalized functions and applications. J. Geod. 75, 44–56.CrossRef
Zurück zum Zitat Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind. J. ACM 9, 54–97.CrossRef Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind. J. ACM 9, 54–97.CrossRef
Zurück zum Zitat Rao CR, Toutenburg H (1999) Linear Models, Springer, Berlin, Heidelberg. Rao CR, Toutenburg H (1999) Linear Models, Springer, Berlin, Heidelberg.
Zurück zum Zitat Reigber C (1989) Gravity field recovery from satellite tracking data, theory of satellite geodesy and gravity field determination. In: Sansò F, Rummel R (eds.), Lecture Notes in Earth Science, Vol. 25, Springer, Berlin, Heidelberg, pp. 197–234. Reigber C (1989) Gravity field recovery from satellite tracking data, theory of satellite geodesy and gravity field determination. In: Sansò F, Rummel R (eds.), Lecture Notes in Earth Science, Vol. 25, Springer, Berlin, Heidelberg, pp. 197–234.
Zurück zum Zitat Rummel R, Sansò F, van Gelderen M, Brovelli M, Koop R, Miggliaccio F, Schrama E, Scerdote F (1993) Spherical harmonic analysis of satellite gradiometry. Netherlands Geodetic Commission, New Series 39. Rummel R, Sansò F, van Gelderen M, Brovelli M, Koop R, Miggliaccio F, Schrama E, Scerdote F (1993) Spherical harmonic analysis of satellite gradiometry. Netherlands Geodetic Commission, New Series 39.
Zurück zum Zitat Scheinert M (2005) The Antarctic geoid project: Status report and next activities. In: Jekeli C, Bastos L, Fernandes J (eds.), Gravity, Geoid and Space Missions, Vol. 129, Springer, Berlin, Heidelberg, pp. 137–142.CrossRef Scheinert M (2005) The Antarctic geoid project: Status report and next activities. In: Jekeli C, Bastos L, Fernandes J (eds.), Gravity, Geoid and Space Missions, Vol. 129, Springer, Berlin, Heidelberg, pp. 137–142.CrossRef
Zurück zum Zitat Simons FJ, Dahlen FA, Wieczorek MA (2006) Spatiospectral localization on a sphere. SIAM Rev. 48, 504–536.CrossRef Simons FJ, Dahlen FA, Wieczorek MA (2006) Spatiospectral localization on a sphere. SIAM Rev. 48, 504–536.CrossRef
Zurück zum Zitat Slepian D (1978) Prolate spheroidal wave functions, Fourier analysis and uncertainty. V. The discrete case. Bell. Syst. Tech. J. 57, 1371–1430. Slepian D (1978) Prolate spheroidal wave functions, Fourier analysis and uncertainty. V. The discrete case. Bell. Syst. Tech. J. 57, 1371–1430.
Zurück zum Zitat Sneeuw N, van Gelderen M (1997) The polar gap. In: Sansò F, Rummel R (eds.), Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture Notes in Earth Science, Vol. 65, Springer, Berlin, pp. 559–568.CrossRef Sneeuw N, van Gelderen M (1997) The polar gap. In: Sansò F, Rummel R (eds.), Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture Notes in Earth Science, Vol. 65, Springer, Berlin, pp. 559–568.CrossRef
Zurück zum Zitat Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: Mission overview and early results. Geophys. Res. Lett., doi: 10.1029/2004GL019920. Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: Mission overview and early results. Geophys. Res. Lett., doi: 10.1029/2004GL019920.
Zurück zum Zitat Tikhonov AN (1963) Regularization of incorrectly posed problems. Sov. Mat. Dokl. 4, 1035–1038. Tikhonov AN (1963) Regularization of incorrectly posed problems. Sov. Mat. Dokl. 4, 1035–1038.
Metadaten
Titel
Spectral Approaches to Solving the Polar Gap Problem
verfasst von
Oliver Baur
Jianqing Cai
Nico Sneeuw
Copyright-Jahr
2010
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-10228-8_19

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