Wavelet mie representations for solenoidal vector fields with applications to ionospheric geomagnetic data

SIAM Journal on Applied Mathematics

Volumn 65, Issue 6, 2005, Pages 1888-1912

  Maier, Thorsten ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Geomagnetic field modeling; Helmholtz decomposition; Mie representation; Vectorial wavelets

Indexed keywords

EARTH (PLANET); GEOMAGNETISM; IONOSPHERIC MEASUREMENT; MAGNETIC FIELDS; SOLENOIDS; VECTORS;

CHAMP SATELLITE MISSION; MIE REPRESENTATION; SOLENOIDAL VECTOR FIELDS; SPHERICAL VECTOR FIELDS;

WAVELET TRANSFORMS;

EID: 29144519429     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040603796     Document Type: Article

References (35)

1. G. E. BACKUS, Poloidal and toroidal fields in geomagnetic field modeling, Rev. Geophys., 24 (1986), pp. 75-109.
2. G. E. BACKUS, R. PARKER, AND C. CONSTABLE, Foundations of Geomagnetism, Cambridge University Press, Cambridge, UK, 1996.
3. M. BAYER, S. BETH, AND W. FREEDEN, Geophysical field modeling by multiresolution analysis, Acta Geod. Geophys. Hung., 33 (1998), pp. 289-319.
4. M. BAYER, W. FREEDEN, AND T. MAIER, A vector wavelet approach to iono- And magnetospheric geomagnetic satellite data, J. Atmospher. Solar-Terrestrial Phys., 63 (2001), pp. 581-597.
5. S. BETH, Multiscale Approximation by Vector Radial Basis Functions on the Sphere, Shaker Verlag, Aachen, Germany, 2000.
6. C. K. CHUI, An Introduction to Wavelets, Academic Press, New York, 1992.
7. I. DAUBECHIES, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, 36 (1990), pp. 961-1005.
8. P. DEUFLHARD, On algorithms for the summation of certain special functions, Computing, 17 (1976), pp. 37-48.
9. E. F. DONOVAN, Modeling the magnetic effects of field-aligned currents, J. Geophys. Res., 98 (1993), pp. 529-543.
10. J. R. DRISCOLL AND D. M. HEALY, Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math., 15 (1994), pp. 202-250.
11. U. ENGELS AND N. OLSEN, Computation of magnetic fields within source regions of ionospheric and magneto spheric currents, J. Atmospher. Solar-Terresterial Phys., 60 (1998), pp. 1585-1592.
12. W. FREEDEN, On Approximation by Harmonic Splines, Manuscr. Geod., 6 (1981), pp. 193-244.
13. W. FREEDEN, Multiscale Modeling of Spaceborne Geodata, B. G. Teubner, Stuttgart, Leipzig, 1999.
14. W. FREEDEN AND T. GERVENS, Vector spherical spline interpolation - Basic theory and computational aspects, Math. Methods Appl. Sci., 16 (1993), pp. 151-183.
15. W. FREEDEN, T. GERVENS, AND M. SCHREINER, Constructive Approximation on the Sphere (With Applications to Geomathematics), Oxford Science Publications, Clarendon, Oxford, UK, 1998.
16. W. FREEDEN AND U. WINDHEUSER, Spherical wavelet transform and its discretization, Adv. Comput. Math., 5 (1996), pp. 51-94.
17. W. FREEDEN AND U. WINDHEUSER, Combined spherical harmonic and wavelet expansion-a future concept in earth's gravitational potential determination, Appl. Comput. Harm. Anal., 4 (1997), pp. 1-37.
18. G. GERLICH, Magnetfeldbeschreibung mit verallgemeinerten poloidalen und toroidalen Skalaren, Z. Naturforsch., 8 (1972), pp. 1167-1172.
19. R. V. HOGG, An introduction to robust estimation, in Robustness in Statistics, G. N. Launer and R. L. Wilkinson, eds., Academic, San Diego, CA, 1979, pp. 1-17.
20. T. IIJIMA AND A. POTEMRA, Large-scale characteristics of field-aligned currents associated with substorms, J. Geophys. Res., 90 (1978), pp. 2593-2598.
21. R. A. LANGEL AND R. H. ESTES, The near-Earth magnetic field at 1980 determined from MAGSAT data, J. Geophys. Res., 90 (1985), pp. 2495-2510.
22. R. A. LANGEL, N. OLSEN, AND T. J. SABAKA, A Comprehensive Model of the Near-Earth Magnetic Field: Phase 3, Technical Report TM-2000-209894, NASA, Washington, DC, 2000.
23. R. A. LANGEL, T. J. SABAKA, R. T. BALDWIN, AND J. A. CONRAD, The near-earth magnetic field from magnetospheric and quiet-day ionospheric sources and how it is modeled, Phys. Earth Planet. Interiors, 98 (1996), pp. 235-267.
24. T. MAIER, Multiscale Geomagnetic Field Modeling from Satellite Data-Theoretical Aspects and Numerical Applications, Ph.D. thesis, Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany, 2003; available online from http://kluedo.ub.uni-kl.de/volltexte/2003/1553/.
25. S. MAUS, New Statistical Methods in Gravity and Magnetics, Habilitation, Gemeinsame Naturwissenschaftliche Fakultät der Technischen Universität Carolo-Wilhelmina zu Braunschweig, Braunschweig, Germany, 2001.
26. C. MAYER, Wavelet Modelling of Ionospheric Currents and Induced Magnetic Fields From Satellite Data, Ph.D. thesis, Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany, 2003; available online from http://kluedo.ub.uni-kl.de/volltexte/2003/1623/.
27. C. MAYER AND T. MAIER, Multiscale determination of radial current distribution from CHAMP FGM-data, in First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, C. Reigber, H. Luehr, and P. Schwintzer, eds., Springer, New York, 2003, pp. 339-345.
28. N. OLSEN, A new tool for determining ionospheric currents from magnetic satellite data, Geophys. Res. Lett., 24 (1996), pp. 3635-3638.
29. N. OLSEN, Ionospheric F region currents at middle and low latitudes estimated from MAGSAT data, J. Geophys. Res. A, 3 (1997), pp. 4563-4576.
30. A. D. RICHMOND, The computation of magnetic effects of field-aligned magnetospheric currents, J. Atmospher. Terrest. Phys., 36 (1974), pp. 245-252.
31. P. RITTER, A. VILJANEN, H. LUEHR, O. AMM, AND N. OLSEN, Ionospheric currents from CHAMP magnetic field data - Comparison with ground based measurements, in First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, C. Reigber, H. Luehr, and P. Schwintzer, eds., Springer, New York, 2003, pp. 346-352.
32. B.J. SCHMITT, The poloidal-toroidal representation of solenoidal fields in spherical domains, Analysis, 15 (1995), pp. 257-277.
33. L. SHURE, R. L. PARKER, AND G. E. BACKUS, Harmonic splines for geomagnetic modeling, Phys. Earth Planet. Interiors, 28 (1982), pp. 215-229.
34. D. P. STERN, Representation of magnetic fields in space, Rev. Geophys., 14 (1976), pp. 199-214.
35. J. WATERMAN, F. CHRISTIANSEN, V. POPOV, P. STAUNING, AND O. RASMUSSEN, Field-aligned currents inferred from low-altitude earth-orbiting satellites and ionospheric currents inferred from ground-based magnetometers - Do they render consistent results?, in First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, C. Reigber, H. Luehr, and P. Schwintzer, eds., Springer, New York, 2003, pp. 361-368.