The geomagnetic field gradient tensor: Properties and parametrization in terms of spherical harmonics

GEM - International Journal on Geomathematics

Volumn 3, Issue 2, 2012, Pages 297-314

  Kotsiaros, Stavros ^a   Olsen, Nils ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Geomagnetic field; Gradient tensor; Space magnetic gradiometry

Indexed keywords

EARTH (PLANET); GEOMAGNETISM; HARMONIC ANALYSIS; SPHERES;

EARTH'S MAGNETIC FIELD; GEOMAGNETIC FIELD VECTORS; GEOMAGNETIC FIELDS; GRADIENT TENSORS; MAGNETIC GRADIENT TENSOR; SMALL-SCALE STRUCTURES; SPACE MAGNETIC GRADIOMETRY; SPHERICAL COORDINATES;

TENSORS;

GEOMAGNETIC FIELD; LITHOSPHERIC STRUCTURE; PARAMETERIZATION; POTENTIAL FIELD; SPHERICAL HARMONICS;

EID: 84867446535     PISSN: 18692672     EISSN: 18692680     Source Type: Journal    
DOI: 10.1007/s13137-012-0041-6     Document Type: Article

References (23)

1. Arfken G. B., Weber H. J.: Mathematical Methods for Physicists, 6th edn. Elsevier Academic Press, Amsterdam (2005).
2. Backus G.: Poloidal and toroidal fields in geomagnetic field modeling. Rev. Geophys. 24, 75-109 (1986).
3. Backus G., Parker R., Constable C.: Foundations of Geomagnetism. Cambridge University Press, Cambridge (1996).
4. Cain, J. C.: POGO (OGO-2, -4 and -6 spacecraft). In: Gubbins, D., Herrero-Bervera, E. (eds.) Encyclopedia of Geomagnetism and Paleomagnetism, pp. 828-829, Springer, Heidelberg (2007).
5. Christensen A., Rajagopalan S.: The magnetic vector and gradient tensor in mineral and oil exploration. Preview 84, 77 (2000).
6. Freeden W., Nutz H.: Satellite gravity gradiometry as tensorial inverse problem. GEM Int. J. Geomath. 2, 177-218 (2011).
7. Harrison C., Southam J.: Magnetic field gradients and their uses in the study of the Earth's magnetic field. J. Geomagn. Geoelectr. 43, 585-599 (1991).
8. Langel, R. A.: The main field. In: Jacobs, J. A. (ed) Geomagnetism, vol. 1, pp. 249-512. Academic Press, London (1987).
9. Lowes F. J.: Mean-square values on sphere of spherical harmonic vector fields. J. Geophys. Res. 71, 2179 (1966).
10. Mie G.: Considerations on the optic of turbid media, especially colloidal metal sols. Ann. Phys. 25, 377-442 (1908).
11. Olsen N.: Ionospheric F region currents at middle and low latitudes estimated from Magsat data. J. Geophys. Res. 102(A3), 4563-4576 (1997).
12. Olsen, N., Kotsiaros, S.: Magnetic satellite missions and data. In: Mandea, M., Korte, M. (eds.) Geomagnetic Observations and Models, IAGA Special Sopron Book Series, Chap. 2, vol. 5, pp. 27-44. Springer, Heidelberg. doi: 10. 1007/978-90-481-9858-0_2 (2011).
13. Olsen, N., Friis-Christensen, E., Hulot, G., Korte, M., Kuvshinov, A. V., Lesur, V., Lühr, H., Macmillan, S., Mandea, M., Maus, S., Purucker, M., Reigber, C., Ritter, P., Rother, M., Sabaka, T., Tarits, P., Thomson, A.: Swarm: End-to-End Mission Performance Simulator Study, ESA Contract No 17263/03/NL/CB. DSRI Report 1/2004, Danish Space Research Institute, Copenhagen (2004).
14. Olsen N., Hulot G., Sabaka T. J.: Measuring the Earth's magnetic field from space: concepts of past, present and future missions. Space Sci. Rev. 155, 65-93 (2010). doi: 10. 1007/s11214-010-9676-5.
15. Pedersen L. B., Rasmussen T. M.: The gradient tensor of potential field anomalies: Some implications on data collection and data processing of maps. Geophysics 55(12), 1558-1566 (1990).
16. Purucker M., Sabaka T., Le G., Slavin J. A., Strangeway R. J., Busby C.: Magnetic field gradients from the st-5 constellation: improving magnetic and thermal models of the lithosphere. Geophys. Res. Lett. 34(24), L24, 306 (2007).
17. Reed, G. B.: Application of kinematical geodesy for determining the short wave length components of the gravity field by satellite gradiometry. Reports of the Department of Geodetic Science (Report No. 201) (1973).
18. Rummel R., Colombo O.: Gravity field determination from satellite gradiometry. J. Geodesy 59, 233-246 (1985).
19. Rummel, R., van Gelderen, M., Koop, R., Schrama, E., Sanso, F., Brovelli, M., Miggliaccio, F., Sacerdote, F.: Spherical harmonic analysis of satellite gradiometry. Technical Report (1993).
20. Sabaka, T. J., Hulot, G., Olsen, N.: Mathematical properties relevant to geomagnetic field modelling. In: Freeden, W., Nashed, Z., Sonar, T. (eds.) Handbook of Geomathematics. Springer, Heidelberg (2010).
21. Schmidt P., Clark D.: Advantages of measuring the magnetic gradient tensor. Preview 85, 26-30 (2000).
22. Schmidt P., Clark D.: The magnetic gradient tensor: its properties and uses in source characterization. Lead. Edge 25(1), 75-78 (2006).
23. Talpaert Y.: Tensor analysis and continuum mechanics. Kluwer Academic Publishers, Dordrecht (2002).