Spatially Restricted Integrals in Gradiometric Boundary Value Problems

Albertella A., Sansò F. and Sneeuw N. (1999) Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere. Journal of Geodesy, Vol. 73, 436-447.10.1007/PL00003999Search in Google Scholar

Albertella A., Migliaccio F. and Sansò F. (2002) GOCE: The Earth Field by Space Gradiometry. Celestial Mechanics and Dynamical Astronomy, Vol. 83, 1-15.10.1023/A:1020104624752Search in Google Scholar

Balmino G., Perosanz F., Rummel R., Sneeuw N., Sünkel H. and Woodworth P. (1998) European Views on Dedicated Gravity Field Missions: GRACE and GOCE. An Earth Sciences Division Consultation Document, ESA, ESD-MAG-REP-CON-001.Search in Google Scholar

Balmino G., Perosanz F., Rummel R., Sneeuw N. and Sünkel H. (2001) CHAMP, GRACE and GOCE: Mission Concepts and Simulations. Bollettino di Geofisica Teoricae Applicata, Vol. 40, 3-4, 309-320.Search in Google Scholar

Eshagh M. (2008) Non-singular expressions for the vector and the gradient tensor of gravitation in a geocentric spherical frame, Computers & Geosciences, Vol. 34, 1762-1768.Search in Google Scholar

Eshagh M. (2009a) On satellite gravity gradiometry, Doctoral dissertation in Geodesy, TRITA-TEC-PHD-09004, ISSN 1653-4468Royal Institute of Technology (KTH), Stockholm, Sweden.Search in Google Scholar

Eshagh M. (2009b) Complementary studies in satellite gravity gradiometry, Postdoctoral report in Geodesy, TRITA-TEC-RR 09-006, ISSN 1653-4484, ISBN 13:978-91-85539-47-5, Royal Institute of Technology (KTH), Stockholm, Sweden.Search in Google Scholar

Eshagh M. (2009c) The effect of polar gaps on the solutions of gradiometric boundary value problems, Artificial Satellites, Vol. 43, No. 3, 97-108.10.2478/v10018-009-0011-xSearch in Google Scholar

Eshagh M. (2010) Alternative expression for gravity gradients in local north-oriented frame and tensor spherical harmonics, Acta Geophysica, Vol. 58, 215-243.Search in Google Scholar

Grünbaum F.A., Longhi L. and Perlstadt M. (1982) Differential operators commuting with finite convolution integral operators: some non-abelian examples. SIAM Journal of Applied Mathematics, Vol. 42, 941-955.10.1137/0142067Search in Google Scholar

Heiskanen W. and Moritz H. (1967) Physical Geodesy, W. H. Freeman and company, San Francisco and London.10.1007/BF02525647Search in Google Scholar

Hwang C. (1991) Orthogonal Functions Over the Oceans and Applications to the Determination of Orbit Error, Geoid and Sea Surface Topography from Satellite Altimetry, PhD dissertation, JPL 958121, OSURF 720426, 229 pp, Dec, 1991.Search in Google Scholar

Ilk K.H. (1983) Ein Beitrag zur Dynamik ausgedehnter Körper-Gravitationswechselwirkung. Deutsche Geodätische Kommission, Reihe C, Heft Nr. 288, München.Search in Google Scholar

Kim M.C. and Tapley B. (2000) Formation of surface spherical harmonic normal matrices and application to high-degree geopotential modeling, Journal of Geodesy, Vol. 74, 359-375.Search in Google Scholar

Koop R. (1993) Global gravity field modeling using satellite gravity gradiometry. Publ Geodesy, New series, No. 38. Netherland Geodetic Commission, Delft.Search in Google Scholar

Mainville A. (1986) The altimetry-gravimetry problem using orthonormal base functions, Report No. 373, Dept. of Geod Sci, The Ohio state University, Columbus, Ohio.Search in Google Scholar

Martinec Z. (2003) Green's function solution to spherical gradiometric boundaryvalue problems, Journal of Geodesy, Vol. 77, 41-49.Search in Google Scholar

Miranian L. (2004) Slepian functions on the sphere, generalized Gaussian quadrature rule. Inverse Problems, Vol. 20, 877-892.10.1088/0266-5611/20/3/014Search in Google Scholar

Pail R., Plank G. and Schuh W. D. (2001) Spatially restricted data distribution on the sphere: the method of orthonormalized functions and applications, Journal of Geodesy, Vol. 75, 44-56.Search in Google Scholar

Paul M.K. (1978) Recurrence relations for integrals of associated Legendre functions, Bulletin Geod esique, Vol. 52, 177-190.Search in Google Scholar

Rummel R. (1997) Spherical spectral properties of the Earth gravitational potential and its first and second derivatives, Geodetic boundary value problems in view of the one centimeter geoid, Lecture notes in Earth sciences Edited by Sanso F. and Rummel R., p.359-401.Search in Google Scholar

Rummel R., Sanso F., Gelderen M., Koop R., Schrama E., Brovelli M., Migiliaccio F. and Sacerdote F. (1993) Spherical harmonic analysis of satellite gradiometry. Publ Geodesy, New Series, No. 39 Netherlands Geodetic Commission, Delft.Search in Google Scholar

Sebilleau D. (1998) On the computation of the integrated products of three spherical harmonics, Journal of Physics A: Mathematical and General, Vol. 31, 7157-7168.Search in Google Scholar

Slepian D. (1983) Some comments on Fourier-analysis, uncertainty and modeling, SIAM, Vol. 25, 379-393.Search in Google Scholar

Simons M., Solomon S.C. and Hager B. H. (1997) Localization of gravity and topography: constraints on the tectonic and mantle dynamics of Venus, Geophysical Journal International, Vol. 131, 24-44.Search in Google Scholar

Simons F.J. Dahlen F.A. and Wieczorek M.A. (2006) Spatiospectral concentration on a sphere, SIAM Review, Vol. 48, 3, 504-536.Search in Google Scholar

van Gelderen M. and Rummel R. (2001) The solution of the general boundary value problem by least-squares, Journal of Geodesy, Vol. 75, 1-11.Search in Google Scholar

van Gelderen M. and Rummel R. (2002) Corrections to "The solution of the general geodetic boundary value problem by least squares". Journal of Geodesy, Vol. 76, 121-122.10.1007/s00190-001-0229-2Search in Google Scholar

Varshalovich D.A., Moskalev A.N. and Khersonskii V.K. (1989) Quantum theory of angular momentum. World Scientific Publ, Singapore.10.1142/0270Search in Google Scholar

Wieczorek M.A. and Simons F.J. (2005) Localized spectral analysis on the sphere, Geophysical Journal International, Vol. 162, 655-675.Search in Google Scholar

Xu Y.L. (1996) Fast evaluation of the Gaunt coefficients, Mathematical Computations, Vol. 65, 1601-1612.Search in Google Scholar

Zerilli F.J. (1970) Tensor harmonics in canonical form for gravitational radiation and other application. Journal of mathematical Physics, Vol. 11, 2203-2208.10.1063/1.1665380Search in Google Scholar