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Non-singular Spherical Harmonic Expressions of Geomagnetic Vector and Gradient Tensor Fields in the Local North-oriented Reference Frame : Volume 8, Issue 7 (07/07/2015)

By Du, J.

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Book Id: WPLBN0003974332
Format Type: PDF Article :
File Size: Pages 12
Reproduction Date: 2015

Title: Non-singular Spherical Harmonic Expressions of Geomagnetic Vector and Gradient Tensor Fields in the Local North-oriented Reference Frame : Volume 8, Issue 7 (07/07/2015)  
Author: Du, J.
Volume: Vol. 8, Issue 7
Language: English
Subject: Science, Geoscientific, Model
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Wang, L., Lesur, V., Chen, C., & Du, J. (2015). Non-singular Spherical Harmonic Expressions of Geomagnetic Vector and Gradient Tensor Fields in the Local North-oriented Reference Frame : Volume 8, Issue 7 (07/07/2015). Retrieved from

Description: Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics & Geomatics, China University of Geosciences, Wuhan 430074, China. General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16–90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

Backus, G. E., Parker, R., and Constable, C.: Foundations of Geomagnetism, Cambridge University Press, Cambridge, 1996.; Blakely, R. G.: Potential Theory in Gravity and Magnetic Applications, Cambridge University Press, New York, 1995.; Bird, P.: An updated digital model of plate boundaries, Geochem. Geophys. Geosyst., 4, 1027, doi:10.1029/2001GC000252, 2003.; Blakely, R. J. and Simpson, R. W.: Approximating edges of source bodies from magnetic or gravity anomalies, Geophysics, 51, 1494–1498, 1986.; Eshagh, M.: Non-singular expressions for the vector and gradient tensor of gravitation in a geocentric spherical frame, Comput. Geosci., 34, 1762–1768, 2008.; Eshagh, M.: Alternative expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics, Acta Geophys., 58, 215–243, 2009.; Finlay, C. C., Maus, S., Beggan, C. D., Bondar, T. N., Chambodut, A., Chernova, T. A., Chulliat, A., Golovkov, V. P., Hamilton, B., Hamoudi, M., Holme, R., Hulot, G., Kuang, W., Langlais, B., Lesur, V., Lowes, F. J., Lühr, H., Macmillan, S., Mandea, M., McLean, S., Manoj, C., Menvielle, M., Michaelis, I., Olsen, N., Rauberg, J., Rother, M., Sabaka, T. J., Tangborn, A., Tøffner-Clausen, L., Thébault, E., Thomson, A. W. P., Wardinski, I., Wei, Z., and Zvereva, T. I.: International Geomagnetic Reference Field: the eleventh generation, Geophys. J. Int., 183, 1216–1230, 2010.; Friis-Christensen, E., Lühr, H., and Hulot, G.: Swarm: A constellation to study the Earth's magnetic field, Earth Planet. Space, 58, 351–358, 2006.; Langlais, B., Lesur, V., Purucker, M. E., Connerney, J. E. P., and Mandea, M.: Crustal Magnetic Fields of Terrestrial Planets, Space Sci. Rev., 152, 223–249, 2010.; Gauss, C. F.: Allgemeine Theorie des Erdmagnetismus, in: Resultate aus den Beobachtungen des magnetischen vereins im Jahre 1838, edited by: Gauss, C. F. and Weber, W., (Leipzig, 1839), 1–57, 1838.; Golynsky, A., Bell, R., Blankenship, D., Damaske, D., Ferraccioli, F., Finn, C., Golynsky, D., Ivanov, S., Jokat, W., Masolov, V., Riedel, S., von Frese, R., Young, D., and ADMAP Working Group: Air and shipborne magnetic surveys of the Antarctic into the 21st century, Tectonophysics, 585, 3–12, 2013.; Harrison, C. and Southam, J.: Magnetic field gradients and their uses in the study of the Earth's magnetic field, J. Geomagn. Geoelectr., 43, 485–599, 1991.; Holmes, S. A. and Featherstone, W. E.: A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalized associated Legendre functions, J. Geodynam., 76, 279–299, 2002a.; Holmes, S. A. and Featherstone, W. E.: SHORT NOTES: extending simplified high-degree synthesis methods to second latitudinal derivatives of geopotential, J. Geodynam., 76, 447–450, 2002b.; Hsu, S. K., Sibuet, J. C., and Shyu, C. T.: High-resolution detection of geologic boundaries from potential-field anomalies: An enhanced analytic signal technique, Geophysics, 61, 373–386, 1996.; Ilk, K. H.: Ein eitrag zur Dynamik ausgedehnter Körper-Gravitationswechselwirkung, Deutsche Geodätische Kommission. Reihe C, Heft Nr. 288, München, 1983.; Kotsiaros, S. and Olsen, N.: The geomagnetic field gradient tensor: Properties and parametrization in terms of spherical harmonics, Int. J. Geomath., 3, 297–314, 2012.; Kotsiaros, S. and Olsen, N.: End-to-End simulation study of a full magnetic gradiometry mission, Geophys. J. Int., 196, 100–110, 2014.; Kotsiaros, S., Finlay, C. C., and Olsen, N.: Use of along-track magnetic field differences in lithospheric field modelling, Geophys. J. Int., 200, 878–887, 2015.; Langel, R. A. and Hinze, W. J.: The Magnetic Field of the Earth's Lithosphere: The Satellite Perspective, Cambridge University Press, Cambridge, United Kingdom, 1998.; Lesur, V., Rother, M., Vervelidou, F., Hamoudi, M., and Thébault, E.: Post-processing scheme for modelling the lithospheric magnetic field, Solid Earth, 4, 105–118, <


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