Revised spherical cap harmonic analysis (R-SCHA): Validation and properties

Journal of Geophysical Research: Solid Earth

Volumn 111, Issue 1, 2006, Pages

  Thébault, Erwan ^a   Schott, Jean Jacques ^b   Mandea, Mioara ^a  

^a GFZ GERMAN RESEARCH CENTRE FOR GEOSCIENCES   (Germany)

^b UNIVERSITÉ DE STRASBOURG EOST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

SPHERICAL HARMONICS;

EID: 33644777655     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/2005JB003836     Document Type: Article

References (45)

1. Abramowitz, M., and A. Stegun (1965), Handbook of Mathematical Functions, Dover, Mineola, N. Y.
2. Achache, J., Y. Cohen, and G. Unal (1991), The French program of circumterrestrial magnetic surveys using stratospheric balloons, Eos Trans. AGU, 72, 97, 100-101.
3. Alldredge, L. R. (1981), Rectangular harmonic analysis applied to the geomagnetic field, J. Geophys. Res., 86(B4), 3021-3026.
4. Arkani-Hamed, J., and W. J. Hinze (1990), Limitations of the long-wave-length components of the North American magnetic anomaly map, Geophysics, 55(12), 1577-1588.
5. Backus, G., R. Parker, and C. Constable (1996), Foundations of Geomagnetism, Cambridge Univ. Press, New York.
6. Baranov, W. (1975), Potential Fields and Their Transformations in Applied Geophysics 1, vol. 6, Gebrüder Borntraeger, Stuttgart, Germany.
7. Blakely, R. J. (1995), Potential Theory in Gravity and Magnetic Applications, Cambridge Univ. Press, New York.
8. Bosch, W. (2000), On the computation of derivatives of Legendre functions, Phys. Chem. Earth, 25(9-11), 655-659.
9. Bullard, E. C. (1967), The removal of trend from magnetic surveys, Earth Planet. Sci Lett., 2, 293-300.
10. Chambodut, A. (2004), Le Champ Magnétique Terrestre: Structures Spatiales et Variations Temporelles Vues Par Les Ondelettes, Ph.D. thesis, Inst. de Phys. du Globe de Paris, Paris.
11. Chiappini, M., R. R. B. Von Frese, and J. Feris (1998), Effort to develop magnetic anomaly database aids Antarctic research, Eos Trans. AGU, 79, 290.
12. De Santis, A., and C. Falcone (1995), Spherical cap models of Laplacian potentials and general fields, in Geodetic Theory Today, pp. 141-150, Springer, New York.
13. De Santis, A., J. M. Torta, and C. Falcone (1996), A simple approach to the transformation of spherical harmonic models under coordinate system rotation, Geophys. J. Int., 126, 263-270.
14. De Santis, A., J. M. Torta, and F. J. Lowes (1999), Spherical cap harmonics revisited and their relationship to ordinary spherical harmonics, Phys. Chem. Earth, 24(11-12), 935-941.
15. European Space Agency (ESA) (2004), Swarm - The Earth's magnetic field and environment explorers, Tech. Rep. SP-1279(6). (Available at http:// www.esa.int/esaLP/LPswarm.html)
16. Gaya-Pique, L. R. (2004), Analysis of the geomagnetic field in Antarctica from near-surface and satellite data, Ph.D. thesis, Univ. Ramon Llull, Barcelona, Spain.
17. Grauch, V. J. S. (1993), Limitations on digital filtering of the DNAG magnetic data set for the conterminous U.S., Geophysics, 58(9), 1281-1296.
18. Haines, G. V. (1985a), Spherical cap harmonic analysis, J Geophys. Res., 90, 2583-2591.
19. Haines, G. V. (1985b), Magsat vertical field anomalies above 40°N from spherical cap harmonic analysis, J, Geophys. Res., 90, 2593-2598.
20. Haines, G. V. (1990a), Modelling by series expansions: A discussion, J. Geomagn. Geoelectr., 42, 1037-1049.
21. Haines, G. V. (1990b), Regional magnetic field modelling: A review, J. Geomagn. Geoelectr., 42, 1001-1018.
22. Haines, G. V., and L. R. Newitt (1986), The Canadian geomagnetic reference field 1985, J. Geomagn. Geoelectr., 38, 895-921.
23. Hemant, K. (2003), Modelling and interpretation of global lithospheric magnetic anomalies, Ph.D. thesis, Freie Univ., Berlin.
24. Hobson, E. W. (1965), The Theory of Spherical and Ellipsoidal Harmonics, 2nd reprint ed., Chelsea, New York.
25. Hwang, C., and S. K. Chen (1997), Fully normalized spherical cap harmonics: application to the analysis of sea-level data from TOPEX/ POSEIDON and ERS-1, Geophys. J. Int., 129, 450-460.
26. Korte, M., and R. Holme (2002), Regularisation of spherical cap harmonics, Geophys. J. Int., 153(1), 253-262.
27. Langel, R. A., and R. H. Estes (1982), A geomagnetic field spectrum, Geophys. Res. Lett., 9, 250-253.
28. Langel, R. A., and W. J. Hinze (1998), The Magnetic Field of the Earth's Lithosphere, Cambridge Univ. Press, New York.
29. Le Mouël, J. L. (1969), Sur la distribution des éléments magnétiques en France, Ph.D. thesis, Univ. de Paris, Paris.
30. Lowes, F. J. (1974), Spatial power spectrum of the main geomagnetic field and extrapolation to the core, Geophys. J. R. Astron. Soc., 36, 717-730.
31. Lowes, F. J. (1999), Orthogonality and mean squares of vector fields given by spherical harmonic potentials, Geophys. J. Int., 136, 781-783.
32. Maus, S., M. Rother, R. Holme, H. Lühr, N. Olsen, and V. Haak (2002), First scalar magnetic anomaly map from CHAMP satellite data indicates weak lithospheric field, Geophys. Res. Lett., 29(14), 1702, doi:10.1029/2001GL013685.
33. Maus, S., M. Rother, K. Hemant, C. Stolle, H. Lühr, A. Kuvshinov, and N. Olsen (2005), Earth's crustal magnetic field determined to spherical harmonic degree 90 from CHAMP satellite measurements, Geophys. J. Int., in press.
34. Mehler, E. G. (1868), Über die verteilung der statischen electrizität in einem von zwei kugelkalotten begrenzten körper, J. Reine Angew. Math, 68, 134-150.
35. Powers, D. L. (1999), Boundary Value Problems, 4th ed., Elsevier, New York.
36. Ravat, D., K. A. Whaler, M. Pilkington, T. Sabaka, and M. Purucker (2002), Compatibility of high-altitude and satellite-altitude magnetic anomalies over Canada, Geophysics, 67, 546-554.
37. Reddy, J. N. (1993), Introduction to the Finite Element Method, McGraw-Hill, New York.
38. Robin, L. (1959), Fonctions Sphériques de Legendre et Fonctions Sphéroidales, vols. I-III, Gauthier-Villars, Paris.
39. Sabaka, T., N. Olsen, and M. Purucker (2004), Extending comprehensive models of the Earth's magnetic field with Ørsted and CHAMP data, Geophys. J. Int., 159, 521-547.
40. Schwartz, L. (1965), Mthodes Mathématiques pour les Sciences Physiques, Hermann, Paris.
41. Thébault, E. (2003), Modélisation régionale do champ magnétique terrestre, Ph.D. thesis, Univ. Louis Pasteur, Strasbourg, France.
42. Thébault, E., J. J. Schott, M. Mandea, and J. P. Hoffbeck (2004), A new proposal for spherical cap harmonic modelling, Geophys. J. Int., 159, 83-103.
43. Torta, J. M., A. Garica, J. J. Curto, and A. De Santis (1992), New representation of geomagnetic secular variation over restricted regions by means of Spherical Cap Harmonic Analysis: Application to the case of Spain, Phys. Earth Planet. Inter., 74, 209-217.
44. Walker, J. S. (1998), Fourier Analysis, Oxford Univ. Press, New York.
45. m(z), Elsevier, New York.