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Non-singular Spherical Harmonic Expressions of Geomagnetic Vector and Gradient Tensor Fields in the Local North-oriented Reference Frame : Volume 7, Issue 6 (05/12/2014)

By Du, J.

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Book Id: WPLBN0004009795
Format Type: PDF Article :
File Size: Pages 27
Reproduction Date: 2015

Title: Non-singular Spherical Harmonic Expressions of Geomagnetic Vector and Gradient Tensor Fields in the Local North-oriented Reference Frame : Volume 7, Issue 6 (05/12/2014)  
Author: Du, J.
Volume: Vol. 7, Issue 6
Language: English
Subject: Science, Geoscientific, Model
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany


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Wang, L., Lesur, V., Chen, C., & Du, J. (2014). Non-singular Spherical Harmonic Expressions of Geomagnetic Vector and Gradient Tensor Fields in the Local North-oriented Reference Frame : Volume 7, Issue 6 (05/12/2014). Retrieved from

Description: 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 and 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 higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

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

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