Spatiospectral concentration of vector fields on a sphere

Slepian, 1961, Prolate spheroidal wave functions, Fourier analysis and uncertainty – I, Bell Syst. Tech. J., 40, 43, 10.1002/j.1538-7305.1961.tb03976.x

Landau, 1961, Prolate spheroidal wave functions, Fourier analysis and uncertainty – II, Bell Syst. Tech. J., 40, 65, 10.1002/j.1538-7305.1961.tb03977.x

Landau, 1962, Prolate spheroidal wave functions, Fourier analysis and uncertainty – III: The dimension of the space of essentially time- and band-limited signals, Bell Syst. Tech. J., 41, 1295, 10.1002/j.1538-7305.1962.tb03279.x

Slepian, 1983, Some comments on Fourier analysis, uncertainty and modeling, SIAM Rev., 25, 379, 10.1137/1025078

Thomson, 1982, Spectrum estimation and harmonic analysis, Proc. IEEE, 70, 1055, 10.1109/PROC.1982.12433

Simons, 2010, Slepian functions and their use in signal estimation and spectral analysis, 891

Simons, 2006, Spatiospectral concentration on a sphere, SIAM Rev., 48, 504, 10.1137/S0036144504445765

Simons, 2011, Spatiospectral concentration in the Cartesian plane, Internat. J. Geomath., 2, 1, 10.1007/s13137-011-0016-z

Albertella, 2001, Using Slepian functions for local geodetic computations, Boll. Geod. Sci. Affini, 60, 1

Simons, 2006, Spherical Slepian functions and the polar gap in geodesy, Geophys. J. Int., 166, 1039, 10.1111/j.1365-246X.2006.03065.x

Han, 2008, Localized analysis of satellite tracking data for studying time-variable Earthʼs gravity fields, J. Geophys. Res., 113, 10.1029/2007JB005218

Slobbe, 2012, The spherical Slepian basis as a means to obtain spectral consistency between mean sea level and the geoid, J. Geod., 86, 609, 10.1007/s00190-012-0543-x

Han, 2007, Localized spectral analysis of global satellite gravity fields for recovering time-variable mass redistributions, J. Geod., 82, 423, 10.1007/s00190-007-0194-5

Han, 2008, Implications of postseismic gravity change following the great 2004 Sumatra–Andaman earthquake from the regional harmonic analysis of GRACE inter-satellite tracking data, J. Geophys. Res., 113, 10.1029/2008JB005705

Han, 2008, Spatiospectral localization of global geopotential fields from the Gravity Recovery and Climate Experiment (GRACE) reveals the coseismic gravity change owing to the 2004 Sumatra–Andaman earthquake, J. Geophys. Res., 113, 10.1029/2007JB004927

Longuevergne, 2010, GRACE hydrological estimates for small basins: Evaluating processing approaches on the High Plains Aquifer, USA, Water Resour. Res., 46, 10.1029/2009WR008564

Harig, 2012, Mapping Greenlandʼs mass loss in space and time, Proc. Natl. Acad. Sci., 109, 19934, 10.1073/pnas.1206785109

Schott, 2011, Modelling the Earthʼs magnetic field from global to regional scales, vol. 5, 229

Simons, 2009, Efficient analysis and representation of geophysical processes using localized spherical basis functions, vol. 7446

Harig, 2010, Constraints on upper mantle viscosity inferred from the flow-induced pressure gradient across the Australian continental keel, Geochem. Geophys. Geosyst., 11, 10.1029/2010GC003038

Evans, 2010, Geophysical limitations on the erosion history within Arabia Terra, J. Geophys. Res., 115, 10.1029/2009JE003469

Goossens, 2012, Local lunar gravity field analysis over the South Pole-Aitken basin from SELENE farside tracking data, J. Geophys. Res., 117, 10.1029/2011JE003831

Han, 2009, Improved nearside gravity field of the Moon by localizing the power law constraint, Geophys. Res. Lett., 36, 10.1029/2009GL038556

Wieczorek, 2008, Constraints on the composition of the Martian south polar cap from gravity and topography, Icarus, 196, 506, 10.1016/j.icarus.2007.10.026

Maniar, 2005, The concentration problem for vector fields, Int. J. Bioelectromagn., 7, 142

Mitra, 2006, Concentration maximization and local basis expansions (LBEX) for linear inverse problems, IEEE Trans. Biomed. Eng., 53, 1775, 10.1109/TBME.2006.876629

Dahlen, 2008, Spectral estimation on a sphere in geophysics and cosmology, Geophys. J. Int., 174, 774, 10.1111/j.1365-246X.2008.03854.x

Das, 2009, Efficient power spectrum estimation for high resolution CMB maps, Phys. Rev. D, 79, 083008, 10.1103/PhysRevD.79.083008

Lessig, 2010, On the effective dimension of light transport, 1399

Yeo, 2008, On the construction of invertible filter banks on the 2-sphere, IEEE Trans. Image Process., 17, 283, 10.1109/TIP.2007.915550

SenGupta, 2012, Concentration problems for bandpass filters in communication theory over disjoint frequency intervals and numerical solutions, J. Fourier Anal. Appl., 18, 182, 10.1007/s00041-011-9197-y

Khalid, 2012, Spatio-spectral analysis on the sphere using spatially localized spherical harmonics transform, IEEE Trans. Signal Process., 60, 1487, 10.1109/TSP.2011.2177265

Wei, 2011, Quadratic variational framework for signal design on the 2-sphere, IEEE Trans. Signal Process., 59, 5243, 10.1109/TSP.2011.2162506

Marinucci, 2010, Representations of SO(3) and angular polyspectra, J. Multivariate Anal., 191, 77, 10.1016/j.jmva.2009.04.017

Michel, 2011, Optimally localized approximate identities on the 2-sphere, Numer. Funct. Anal. Optim., 32, 877, 10.1080/01630563.2011.587073

Mitra, 2005, Local basis expansions for MEG source localization, Int. J. Bioelectromagn., 7, 30

Eshagh, 2009, Spatially restricted integrals in gradiometric boundary value problems, Artif. Satell., 44, 131, 10.2478/v10018-009-0025-4

Stockmann, 2009, Imaging Earthʼs crustal magnetic field with satellite data: A regularized spherical triangle tessellation approach, Geophys. J. Int., 179, 929, 10.1111/j.1365-246X.2009.04345.x

Gubbins, 2011, Analysis of lithospheric magnetization in vector spherical harmonics, Geophys. J. Int., 187, 99, 10.1111/j.1365-246X.2011.05153.x

Friis-Christensen, 2006, Swarm: A constellation to study the Earthʼs magnetic field, Earth Planets Space, 58, 351, 10.1186/BF03351933

Shure, 1982, Harmonic splines for geomagnetic modeling, Phys. Earth Planet. Inter., 28, 215, 10.1016/0031-9201(82)90003-6

Parker, 1982, Efficient modeling of the Earthʼs magnetic field with harmonic splines, Geophys. Res. Lett., 9, 812, 10.1029/GL009i008p00812

Langel, 1987, The main field, 249

Haines, 1985, Spherical cap harmonic analysis, J. Geophys. Res., 90, 2583, 10.1029/JB090iB03p02583

De Santis, 1991, Translated origin spherical cap harmonic analysis, Geophys. J. Int., 106, 253, 10.1111/j.1365-246X.1991.tb04615.x

Korte, 2003, Regularization of spherical cap harmonics, Geophys. J. Int., 153, 253, 10.1046/j.1365-246X.2003.01898.x

Thébault, 2006, Global lithospheric magnetic field modelling by successive regional analysis, Earth Planets Space, 58, 485, 10.1186/BF03351944

Thébault, 2006, Revised spherical cap harmonic analysis (R-SCHA): Validation and properties, J. Geophys. Res., 111, 10.1029/2005JB003836

Holschneider, 2003, From global to regional analysis of the magnetic field on the sphere using wavelet frames, Phys. Earth Planet. Inter., 135, 107, 10.1016/S0031-9201(02)00210-8

Chambodut, 2005, Wavelet frames: An alternative to spherical harmonic representation of potential fields, Geophys. J. Int., 163, 875, 10.1111/j.1365-246X.2005.02754.x

Mayer, 2006, Separating inner and outer Earthʼs magnetic field from CHAMP satellite measurements by means of vector scaling functions and wavelets, Geophys. J. Int., 167, 1188, 10.1111/j.1365-246X.2006.03199.x

Dahlen, 1998

Jeans, 1923, The propagation of earthquake waves, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 102, 554, 10.1098/rspa.1923.0015

Edmonds, 1996

Messiah, 2000

Ilk, 1983, Ein Beitrag zur Dynamik ausgedehnter Körper: Gravitationswechselwirkung, Dtsch. Geod. Komm. C, 288

Paul, 1978, Recurrence relations for integrals of associated Legendre functions, Bull. Geod., 52, 177, 10.1007/BF02521771

Freeden, 2009

Slepian, 1964, Prolate spheroidal wave functions, Fourier analysis and uncertainty – IV: Extensions to many dimensions; generalized prolate spheroidal functions, Bell Syst. Tech. J., 43, 3009, 10.1002/j.1538-7305.1964.tb01037.x

Horn, 1990

Tricomi, 1970

Landau, 1965, On the eigenvalue behavior of certain convolution equations, Trans. Amer. Math. Soc., 115, 242, 10.1090/S0002-9947-1965-0199745-4

Landau, 1967, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math., 117, 37, 10.1007/BF02395039

Flandrin, 1999

Kanwal, 1971

Blanco, 1997, Evaluation of the rotation matrices in the basis of real spherical harmonics, J. Mol. Struct., Theochem, 419, 19, 10.1016/S0166-1280(97)00185-1

Wieczorek, 2005, Localized spectral analysis on the sphere, Geophys. J. Int., 162, 655, 10.1111/j.1365-246X.2005.02687.x

Percival, 1993

Slepian, 1965, Eigenvalues associated with prolate spheroidal wave functions of zero order, Bell Syst. Tech. J., 44, 1745, 10.1002/j.1538-7305.1965.tb04200.x

Maus, 2006, Simulation of the high-degree lithospheric field recovery for the Swarm constellation of satellites, Earth Planets Space, 58, 397, 10.1186/BF03351936

C.D. Beggan, J. Saarimäki, K.A. Whaler, F.J. Simons, Spectral and spatial decomposition of lithospheric magnetic field models using spherical Slepian functions, Geophys. J. Int. (2013), http://dx.doi.org/10.1093/gji/ggs122, in press.

Sabaka, 2006, Enhancing comprehensive inversions using the Swarm constellation, Earth Planets Space, 58, 371, 10.1186/BF03351935

Langlais, 2010, Crustal magnetic fields of terrestrial planets, Space Sci. Rev., 152, 223, 10.1007/s11214-009-9557-y

Lewis, 2012, Local spectral variability and the origin of the Martian crustal magnetic field, Geophys. Res. Lett., 39, 10.1029/2012GL052708

M.G. Sterenborg, J. Bloxham, Application of Slepian basis functions to magnetic field analysis of Saturn, in: Eos Trans. AGU, Fall Meet. Suppl., Abstract GOP33A-0928, 2007.

Maus, 2010, An ellipsoidal harmonic representation of Earthʼs lithospheric magnetic field to degree and order 720, Geochem. Geophys. Geosyst., 11, 06015, 10.1029/2010GC003026

Schachtschneider, 2010, Error distribution in regional inversion of potential field data, Geophys. J. Int., 181, 1428

Schachtschneider, 2012, Error distribution in regional modelling of the geomagnetic field, Geophys. J. Int., 191, 1015

Jahn, 2012, Vector Slepian basis functions with optimal energy concentration in high numerical aperture focusing, Opt. Commun., 285, 2028, 10.1016/j.optcom.2011.11.107