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

摘要

General expressions of magnetic vector (MV) and magnetic gradient tensor(MGT) in terms of the first- and second-order derivatives of sphericalharmonics at different degrees/orders are relatively complicated andsingular at the poles. In this paper, we derived alternative non-singularexpressions for the MV, the MGT and also the third-order partial derivativesof the magnetic potential field in the local north-oriented reference frame.Using our newly derived formulae, the magnetic potential, vector andgradient tensor fields and also the third-order partial derivatives of themagnetic potential field at an altitude of 300 km are calculated based on aglobal lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version0.0) with spherical harmonic degrees 16–90. The correspondingresults at the poles are discussed and the validity of the derived formulasis verified using the Laplace equation of the magnetic potential field.