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

2014 ◽  
Vol 7 (6) ◽  
pp. 8477-8503
Author(s):  
J. Du ◽  
C. Chen ◽  
V. Lesur ◽  
L. Wang
Keyword(s):  
Magnetic Field ◽  
Reference Frame ◽  
Field Model ◽  
Main Magnetic Field ◽  
Tensor Fields ◽  
Gradient Tensor ◽  
Potential Vector ◽  
Magnetic Field Model ◽  
Lithospheric Magnetic Field ◽  
Derivatives Of

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 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.

scholarly journals A high resolution lithospheric magnetic field model over southern Africa based on a joint inversion of CHAMP, Swarm, WDMAM and ground magnetic field data

2018 ◽  
Author(s):  
Foteini Vervelidou ◽  
Erwan Thébault ◽  
Monika Korte
Keyword(s):  
Magnetic Field ◽  
Southern Africa ◽  
Field Model ◽  
Joint Inversion ◽  
Field Measurements ◽  
Magnetic Field Data ◽  
Magnetic Field Model ◽  
Lithospheric Magnetic Field ◽  
The Mean ◽  
Ground Magnetic

Abstract. We derive a lithospheric magnetic field model up to equivalent Spherical Harmonic degree 1000 over southern Africa. We rely on a joint inversion of satellite, near-surface and ground magnetic field data. The input data set consists of magnetic field vector measurements from the CHAMP satellite, across-track magnetic field differences from the Swarm mission, the World Digital Magnetic Anomaly Map and magnetic field measurements from repeat stations and three local INTERMAGNET observatories. For the inversion scheme, we use the Revised-Spherical Cap Harmonic Analysis (R-SCHA), a regional analysis technique able to deal with magnetic field measurements obtained at different altitudes. The model is carefully assessed and displayed at different altitudes and its spectral content is compared to high resolution global lithospheric field models. By comparing the shape of its spectrum to a statistical power spectrum of Earth's lithospheric magnetic field, we infer the mean magnetic thickness and the mean magnetization over southern Africa.

scholarly journals Fifth-generation lithospheric magnetic field model from CHAMP satellite measurements

2007 ◽  
Vol 8 (5) ◽  
pp. n/a-n/a ◽  
Author(s):  
Stefan Maus ◽  
Hermann Lühr ◽  
Martin Rother ◽  
Kumar Hemant ◽  
George Balasis ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Model ◽  
Satellite Measurements ◽  
Champ Satellite ◽  
Fifth Generation ◽  
Magnetic Field Model ◽  
Lithospheric Magnetic Field

A high resolution lithospheric magnetic field model over China

2013 ◽  
Vol 56 (10) ◽  
pp. 1759-1768 ◽  
Author(s):  
JiaMing Ou ◽  
AiMin Du ◽  
E. Thébault ◽  
WenYao Xu ◽  
XiaoBo Tian ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Field Model ◽  
Magnetic Field Model ◽  
Lithospheric Magnetic Field

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

2015 ◽  
Vol 8 (7) ◽  
pp. 1979-1990 ◽  
Author(s):  
J. Du ◽  
C. Chen ◽  
V. Lesur ◽  
L. Wang
Keyword(s):  
Reference Frame ◽  
Potential Field ◽  
Spherical Harmonic ◽  
Magnetic Potential ◽  
Tensor Fields ◽  
Third Order ◽  
Gradient Tensor ◽  
Partial Derivatives ◽  
The Third ◽  
Derivatives Of

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.

scholarly journals A Swarm lithospheric magnetic field model to SH degree 80

2016 ◽  
Vol 68 (1) ◽  
Author(s):  
Erwan Thébault ◽  
Pierre Vigneron ◽  
Benoit Langlais ◽  
Gauthier Hulot
Keyword(s):  
Magnetic Field ◽  
Field Model ◽  
Magnetic Field Model ◽  
Lithospheric Magnetic Field

scholarly journals A high-resolution lithospheric magnetic field model over southern Africa based on a joint inversion of CHAMP, Swarm, WDMAM, and ground magnetic field data

Solid Earth ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 897-910 ◽  
Author(s):  
Foteini Vervelidou ◽  
Erwan Thébault ◽  
Monika Korte
Keyword(s):  
Magnetic Field ◽  
Southern Africa ◽  
Field Model ◽  
Joint Inversion ◽  
Field Measurements ◽  
Magnetic Field Data ◽  
Magnetic Field Model ◽  
Lithospheric Magnetic Field ◽  
The Mean ◽  
Ground Magnetic

Abstract. We derive a lithospheric magnetic field model up to equivalent spherical harmonic degree 1000 over southern Africa. We rely on a joint inversion of satellite, near-surface, and ground magnetic field data. The input data set consists of magnetic field vector measurements from the CHAMP satellite, across-track magnetic field differences from the Swarm mission, the World Digital Magnetic Anomaly Map, and magnetic field measurements from repeat stations and three local INTERMAGNET observatories. For the inversion scheme, we use the revised spherical cap harmonic analysis (R-SCHA), a regional analysis technique able to deal with magnetic field measurements obtained at different altitudes. The model is carefully assessed and displayed at different altitudes and its spectral content is compared to high-resolution global lithospheric field models. By comparing the shape of its spectrum to a statistical power spectrum of Earth's lithospheric magnetic field, we infer the mean magnetic thickness and the mean magnetization over southern Africa.

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