An ACGLSR method for multi-layer equivalent source model inversion

The equivalent source model is a stable method for processing airborne magnetic data. However, constructing a multi-layer equivalent source model is typically an ill-posed problem, and as the model complexity increases, computational efficiency decreases. Additionally, the physical property parameters are primarily concentrated in the shallow layers, leading to a pronounced “skin effect”. To address these challenges, this paper introduces a depth-weighting function during the solution process of the multi-layer equivalent source model, which optimizes the vertical distribution of equivalent source layers at different depths. The depth-weighting function compensates for the kernel matrix as well. Furthermore, an adaptive conjugate gradient least squares regularization method (ACGLSR) is employed to automatically select the regularization parameter through forward iteration, thereby simplifying the model construction process. Synthetic and field data experiments demonstrate that the proposed method effectively optimizes the depth distribution of equivalent source properties and, while maintaining solution accuracy, enhances computational efficiency. • The “skin effect” is significant in the multilayer equivalent source model, and determining the optimal regularization parameter can be time-consuming when there are too many parameters. • Adaptive conjugate gradient least squares regularization method is used to improve the efficiency in constructing the equivalent source model. • A depth-weighting function is introduced during the solution process of the multi-layer equivalent source model, which optimizes the vertical distribution of equivalent source layers, avoiding the “skin effect” and accelerating the iteration process；