A simple approach to the transformation of spherical harmonic models under coordinate system rotation

Geophysical Journal International

Volumn 126, Issue 1, 1996, Pages 263-270

  De Santis, A ^a   Torta, J M ^b   Falcone, C ^a  

^a ISTITUTO NAZIONALE DI GEOFISICA E VULCANOLOGIA   (Italy)

^b CSIC URL Observatorio de Fisica Cosmica del Ebro OE   (Spain)

Author keywords

Geomagnetic field; Numerical techniques; Spherical harmonics

Indexed keywords

COORDINATE SYSTEM ROTATION; GEOMAGNETIC FIELD; SPHERICAL HARMONICS;

EID: 0030455080     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1365-246X.1996.tb05284.x     Document Type: Article

References (30)

1. Abramowitz, N. & Stegun, I.A., 1972. Handbook of Mathematical Functions, Dover Publ. Inc., New York, NY.
2. Backus, G.E., 1964. Geographical interpretation of measurements of average phase velocities of surface waves over great circular and great semicircular paths, Bull. seism. Soc. Am., 54, 571-610.
3. Banks, R.J., 1972. The overall conductivity distribution of the Earth, J. Geomag. Geoelectr., 24, 337-351.
4. Barraclough, D.R., 1978. Spherical harmonic models of the geomagnetic field, Geomag. Bull. Inst. Geol. Sci., 8, 1-66.
5. Bernard, J., Kosik, J.-C., Laval, G., Pellat, R. & Philippon, J.-P., 1969. Représentation optimale du potentiel géomagnétique dans le repère d'un dipole décentré, incliné, Ann. Géophys., 25, 659-665.
6. Brink, D.M. & Satchler, G.R., 1962. Angular Momentum, Clarendon Press, Oxford.
7. Campbell, W.H., 1989. The regular geomagnetic-field variations during quiet solar conditions, in Geomagnetism, vol. 3, pp. 385-460, ed. Jacobs, J.A., Academic Press, London.
8. Chapman, S. & Bartels, J., 1940. Geomagnetism, Clarendon Press, Oxford.
9. Courant, R. & Hilbert, D, 1953. Methods of Mathematical Physics, vol. I, J. Wiley & S., New York, NY.
10. De Franceschi, G., Bianchi, C., Gregori, G.P. & Zolesi, B., 1992. The planetary pattern of the ionosphere: 15 coefficients to synthesize the bottom of the F-layer, Ann. Geophys., 10, 407-415.
11. De Santis, A., De Franceschi, G. & Kerridge, D.J., 1994. Regional spherical modelling of 2-d functions: the case of the critical frequency of the F2 ionospheric layer, Comput. & Geosci. 20, 849-871.
12. Doornbos, D.J., 1988. Asphericity and ellipticity corrections, in Seismological Algorithms, pp. 47-85, Academic Press, London.
13. Edmonds, A.R., 1957. Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, NJ.
14. Gubbins, D. & Zhang, K., 1993. Symmetry properties of the dynamo equations for paleomagnetism and geomagnetism, Phys. Earth planet. Inter., 75, 225-241.
15. Haines, G.V. & Torta, J.M., 1994. Determination of equivalent current sources from spherical cap harmonic models of geomagnetic field variations, Geophys. J. Int., 118, 499-514.
16. Hobbs, B.A. & Dawes, G.J.K., 1980. The effect of a simple model of the Pacific ocean on Sq variations, J. Geomag. Geoelectr., 32, Suppl. I, SI 59-SI 66.
17. James, R.W., 1970. A Taylor series approach to the rotation and evaluation of spherical harmonics, Geophys. J. R. astr. Soc., 19, 203-205.
18. Langel, R.A. & Estes, R.H., 1982. A geomagnetic field spectrum, Geophys. Res. Lett., 9, 250-253.
19. Lowes, F.J., 1966. Mean-square values on sphere of spherical harmonic vector fields, J. geophys. Res., 71, 2179.
20. Maeda, H., 1953. On the residual part of the geomagnetic Sq-field in the middle and lower latitudes during the International Polar Year, 1932-1933, J. Geomag. Geoelectr., 5, 39-51.
21. Malin, S.R.C. & Gupta, J.C., 1977. The Sq current system during the International Geophysical Year, Geophys. J. R. astr. Soc., 49, 515-529.
22. Malin, S.R.C. & Barraclough, D.R. & Hodder, B.M., 1982. A Compact algorithm for the formation and solution of normal equations, Comput. & Geosci., 8, No. 3-4, 355-358.
23. Matsushita, S. & Maeda, H., 1965. On the geomagnetic solar quiet daily variation field during I.G.Y., J. geophys. Res., 70, 2535-2558.
24. Mead, G.D., 1970. International Geomagnetic Reference Field 1965 in Dipole coordinates, J. geophys. Res., 75, 4372-4374.
25. Minster, J.B., 1976. Transformation of multipolar sources fields under a change of reference frame, Geophys. J. R. astr. Soc., 47, 397-409.
26. Mochizuki, E., 1993. Spherical harmonic analysis in terms of line integral, Phys. Earth planet. Int., 76, 97-101.
27. Phinney, R.A. & Burridge, R., 1973. Representation of the elastic-gravitational excitation of spherical earth model by generalized spherical harmonics, Geophys. J. R. astr. Soc., 34, 451-487.
28. Risbo, T., 1996. Fourier transform summation of Legendre series and D-functions, J. Geodes. 70, 383-396.
29. Schmidt, A., 1935. Tafeln der normierten Kugelfunktionen und ihrer Ableitungen Nebst den Logarithmen dieser Zahlen sowie Formeln zur Entwicklung nach Kugelfunktionen, Engelhard-Reyher Verlag, Gotha.
30. Smith, M.L., 1974. The scalar equations of infinitesimal elastic-gravitational motion for a rotating, slightly elliptical earth, Geophys. J. R. astr. Soc., 37, 491-526.