3D inversion of magnetic gradient data based on equivalent source weighting method

3D magnetic inversion is an important method for detecting underwater or underground magnetic objects, which can obtain the physical parameters and geometric features of the target. In order to solve the problem of smooth inversion results of L2 norm regularization, this paper proposes a three-dimensional inversion method of magnetic gradient data based on equivalent source weighting. First, the center position of the magnetic object is estimated using the correlation imaging method, and then the equivalent source weighting function is constructed based on the acquired center position. The weights are calculated according to the distance from the grid to the center of the magnetic object. The further away the grid is, the higher weight will be given. The Euclidean distance and Chebyshev distance are used for calculating the weights of grids. Finally, the equivalent source weighting function is added to the total objective function and solved by conjugate gradient method. Simulation experiments show that the equivalent source weighting function can reduce the root-mean-square error of the inversion results and improve the structural similarity. Compared with the Euclidean distance, the inversion result of the edges and corners of cubic magnetic body model is better when weighted with the Chebyshev distance. The proposed method does not require iterative solving and can avoid generating too smooth results, which improves the inversion accuracy.