image: The dipole is located at point with the axial orientation along , which is determined by its polar angle and azimuthal angle in the planetocentric coordinate. In the frame of , we can set up a dipole coordinate (see the details in the text). Note that the origin of the dipole coordinate is at point O (center of the planet). The magenta line labels the trajectory of the spacecraft. At the moment of ti, the spacecraft makes a magnetic field measurement at location , whose relative position vector to the dipole center is .
Credit: Beijing Zhongke Journal Publising Co. Ltd.
This study is led by Dr. Zhaojin Rong (Institute of Geology and Geophysics, the Chinese Academy of Sciences). The magnetic field is the fundamental field in the universe. Any magnetic source can be roughly seen as a magnetic dipole from the first-order approximation. Accurately characterising the magnetic dipole (including its position, orientation, magnetic moment, etc.) is of great significance to understand the magnetic source structure and to localise the magnetic source. The traditional spherical harmonic analysis (SHA) method is usually used to construct the distribution of the magnetic field as a series of associated Legendre functions, and the first three terms describe the central dipole component (located at the origin point of a given coordinate). Nonetheless, SHA is unable to derive the true parameters of a given dipole directly; for example, a real eccentric dipole could be expanded by SHA as the superposition of a central dipole and a series of components of higher multipole. In earlier stages of geomagnetism study, many researchers have attempted to fit the in situ measurements of the magnetic field directly, based on models of one or multiple magnetic dipoles or current loops. However, the classic fitting methods require simultaneous fitting of all model parameters, and it is difficult to guarantee that the derived optimized solution is the global optimal solution in the parameter space. “The inversion of magnetic field is nonunique; the model fitting can mitigate this issue. However, the challenge of fitting is how to avoid the dilemma of simultaneous fitting of multiple parameters to find the best solution”, Rong says.
Regarding this fitting issue, Rong was motivated to develop a novel technique to invert the multiple parameters of a single dipole/ current loop model. This technique can successively separate and exactly invert the model parameters according to the geometric properties of the dipolar field. The algorithm test and model tests demonstrate the robustness and validity of this technique.
The application of this technique to the geomagnetic field model yields a set of parameters for an eccentric dipole, which is consistent with parameters derived from other methods previously. In particular, this technique can also be applied to diagnose the local magnetic anomaly. The application of the Martian remanent field model demonstrates that some local magnetic anomalies can be well represented as a dipole field, with the dipole source depth ranging from 90 to 100 km.
This method is expected to be widely applied in various fields related to the inversion of dipolar fields, including magnetic prospecting, medical magnetism, palaeomagnetism, geomagnetism, and planetary magnetism etc.
See the article:
The fitting of a dipolar magnetic field by a dipole model
http://www.eppcgs.org/article/doi/10.26464/epp2025078
Journal
Earth and Planetary Physics
Article Title
The fitting of a dipolar magnetic field by a dipole model
Article Publication Date
25-Jul-2025