Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame
- 1Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics & Geomatics, China University of Geosciences, Wuhan 430074, China
- 2Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Telegrafenberg 14473, Potsdam, Germany
- 3State Key Laboratory of Geodesy and Earth's Dynamics, Chinese Academy of Sciences, Wuhan 430077, China
Abstract. 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.