Three-dimensional CSEM Forward Modeling By Finite Element Method Based On Joint Application Of Electric Field And Coupled Potential Formulations

Three-dimensional controlled-source electromagnetic forward modeling is the basis of sensitivity analysis and three-dimensional inversion.The fast and high-precision forward modeling algorithm is of great significance for the practical application of three-dimensional electromagnetic inversion and interpretation.I study the CSEM forward modeling problem by the finite element method and mainly focus on the fast iterative solution of the forward linear equations.Firstly,the forward problem is established based on the secondary electric field and the iterative solution process is accelerated with the divergence correction technique.Then,the forward equation based on the secondary coupling potential is established,and the preconditioning matrix used for the iterative solution based on the secondary electric field is constructed from approximating the stiffness matrix from the coupled potential formulation,thus construct the three-dimensional joint forward algorithm.The accuracy and efficiency of the joint forward algorithm are verified by several theoretical model examples.Compared with the previous acceleration technology based on divergence correction,the convergence speed of the joint forward algorithm is significantly faster and the forward efficiency is higher.In order to further explore the reasons affecting the iterative convergence speed,two sets of grids were designed to calculate a large number of models.The results show that the speed of the iterative solution is closely related to the skin depth.The iteration speed will become faster with the skin depth smaller.In addition,in terms of divergence correction technology,a preconditioning matrix based on incomplete Cholesky decomposition of the block diagonal matrix is constructed.Theoretical examples show that the combination of the preconditioner and divergence correction is further accelerated compared with conventional divergence correction technology.The forward algorithm is used to calculate and analyze the electromagnetic responses of typical geoelectric models,which further verifies the simulation ability of the forward algorithm to 3D complex models,and lays a foundation for sensitivity analysis detection and 3D electromagnetic inversion.