Upward Continuation Of Magnetic Field And Magnetic Dipole Inversion Method

In modern technology,magnetic field information acquisition via magnetic imaging contributes to the research of magnetization-related problems present within samples.It is widely applicable in the domains of paleomagnetism,materials physics and biophysics.However,to understand the magnetic properties of sample,relevant parameters of the magnetic source must be obtained via magnetic field maps.Aiming at the high resolution magnetic field maps,this paper conducts related research on the upward continuation and magnetic dipole inversion.Firstly,this paper introduces the magnetic dipole inversion model.Since it’s difficult to obtain accurate magnetic field vector in magnetic imaging experiments,the inversion is performed using the single component of the magnetic field instead of the vector.In order to improve the precision and accuracy of inversion,we adopted the following scheme:(1)To address the issue of unknow background magnetic field which resulting in a decrease in inversion accuracy,the background magnetic field is set as an unknown parameter in the inversion model to obtain the accurate value.(2)To avoid errors caused by the conversion of magnetic field components in the traditional method,we set the measurement direction vector to optimize the inversion model.By modifying the measurement direction vector,the direction of the magnetic field components can be directly adjusted to avoid errors.(3)In the process of solving the model,the ADAM algorithm is used to iteratively solve the nonlinear unknown parameters.In each iteration,the linear unknown parameters can be uniquely determined.In this way,the number of unknowns to be solved iteratively are reduced and the solving process is prevented from falling into a local minimum effectively.Due to the weak dipolarity of complex magnetic field images,it is difficult to obtain results consistent with the physical law if magnetic dipole inversion is performed directly.Therefore,this paper uses the dipolarity parameter to determine the strength of the dipolarity of magnetic field map.For complex magnetic field images with weak dipolarity,upward continuation has been used to enhance the dipolarity.The later section discusses the influence of different background padding values on the accuracy of upward continuation and the inversion through simulation experiments,which emphasizes the necessity of obtaining accurate background magnetic field values.For the selection of upward continuation height,this paper proposes an optimization method.This method defines the magnetic field information loss function based on relative entropy,and obtains the optimal upward continuation height according to the change of its function value.Based on the simulated magnetic field maps,a performance comparison has been done between traditional method and the method proposed in this paper.The results show that the proposed method is more accurate and stable.Increasing the dipolarity of the magnetic field image by upward continuation also makes our method more applicable.Lastly,this method is applied to the research of the magnetic field maps of superparamagnetic beads,ferromagnetic beads,and rock samples obtained in the Chang’e-5 mission.The accurate background field and the position and moment of the equivalent magnetic dipole are obtained,which proves the effectiveness of the upward continuation of magnetic field and magnetic dipole inversion method.