Fast 3D joint inversion of gravity and magnetic data based on cross gradient constraint

The gravity and magnetic data can be adopted to interpret the internal structure of the Earth. To improve the calculation efficiency during the inversion process and the accuracy and reliability of the reconstructed physical property models, the triple strategy is adopted in this paper to develop a fast cross-gradient joint inversion for gravity and magnetic data. The cross-gradient constraint contains solving the gradients of the physical property models and performing the cross-product calculation of their gradients. The sparse matrices are first obtained by calculating the gradients of the physical property models derived from the first-order finite difference. Then, the triple method is applied to optimize the storages and the calculations related to the gradients of the physical property models. Therefore, the storage compression amount of the calculations related to the gradients of the physical property models and the cross-gradient constraint are reduced to one-fold of the number of grid cells at least, and the compression ratio increases with the increase of the number of grid cells. The test results from the synthetic data and field data prove that the structural coupling is achieved by using the fast cross-gradient joint inversion method to effectively reduce the multiplicity of solutions and improve the computing efficiency.