A Sparse Bayesian Learning Method for Efficient Magnetization Vector Inversion

Abstract

Magnetization vector inversion (MVI) is a key method for recovering the magnetization characteristics of subsurface targets. It plays an important role in the processing and interpretation of magnetic measurement data. Based on the measured total magnetic field data, MVI can recover the physical properties such as spatial locations and magnetization parameters of subsurface targets. However, under fine-grid discretization conditions, the iterative solution of magnetic inversion usually involves large-scale matrix operations, which significantly increase the computational cost. To address these issues, this article proposes a sparse Bayesian learning (SBL) framework for MVI. Construct an observation model under the Gaussian noise assumption and introduce the Gaussian prior for the magnetization vector controlled by prior variance hyperparameters. By maximizing the likelihood function, key hyperparameters such as prior variance and noise variance are adaptively updated. This allows the sparsity degree and noise level to be adjusted automatically without manual parameter tuning, realizing an adaptive solution of the inversion process. The simulation and field-data results demonstrate that the proposed method improves computational efficiency while maintaining inversion accuracy, and can provide effective technical support for the quantitative interpretation of magnetic field measurement data. In the simulation, the correlation coefficient of the proposed method is 0.87, the magnetization declination and inclination errors are 8.5° and 9.1°, respectively, and the computation time is only 40.3 s. In the field experiment, the center offset error and misidentification rate are 0.36 m and 3.4 %, respectively, with a computation time of 45.7 s. The results show that the proposed method significantly improves computational efficiency while maintaining high inversion accuracy and localization reliability.