Research On 3D Frequency-domain Airborne Electromagnetic Forward Modeling Based On Multi-scale Finite Element Method

One of the core tasks of geophysical forward and inversion is to simulate the electromagnetic field in the quasi-static region by solving Maxwell's equations.Forward modeling is the basis of electromagnetic data inversion,is a key part of the practical application of three-dimensional electromagnetic data inversion technology.However,the structure of the underground target is complex,affected by factors such as calculation conditions,software complexity,and the difficulty of area 3D data acquisition and so on,all of which bring huge challenges to multi-dimensional numerical simulation.At this time,in order to obtain accurate simulation results,it is necessary to perform fine discretization of the underground half-space,which leads to the difficult problem of solving large linear systems.Therefore,3D inversion technology cannot be used as a conventional data processing method for actual earth exploration problems.Therefore,realizing efficient forward modeling of large-scale models is one of the most improtant development directions of electromagnetic 3D inversion in the future.Three-dimensional electromagnetic data simulation methods for complex media have been widely used.Among them,the finite element method has the advantages of high calculation accuracy,flexibility and practicability for complex underground situations,but the disadvantage is that the amount of calculation is large and timeconsuming.At present,adaptive technology and local refinement technology have also been successfully applied to the simulation of complex models,and the forward calculation of complex models can be realized with relatively few degrees of freedom,which can greatly reduce the computational cost.calculation accuracy.However,on the aone hand,when the underground conductivity structure is extremely complex,we also need to divide the computational area with fine meshes,which also result in a very large linear equation system,and secondly,fine grid cells are also required to capture complex terrain features,resulting in a large number of of filled elements and largescale linear solver systems.Here,the multi-scale finite element method is applied to Maxwell's equations.We first divide two sets of grids,coarse meshs and fine meshs,and we accurately discretize the forward modeling problem on the fine grid.Then,by solving Maxwell's equations on each coarse grid,the multi-scale basis function of each coarse grid is solved,and we traverse all coarse grids,after that,we assemble the interpolation basis functions of all coarse grids,finally,we solve the linear equation system on the coarse grid scale.and we can obtain the solution on the fine grid scale by interpolation.At the same time,since the construction of the interpolation basis functions between the coarse grids does not interfere with each other,so this step can easily be performed in parallel,thereby reducing a lot of computing cost.Another advantage of this method is that it can reduce the computational scale.It greatly saves computer memory and it is an effective numerical method for dealing with large-scale models.In order to further improve the accuracy of forward modeling,we also use the "irregular coarsening" technology.In this paper,the octree technology is used to perform fine subdivision near the source to ensure the accuracy of the result without greatly increasing the degrees of freedom.The multi-scale finite element method proposed in this paper has the ability to solve very large-scale practical problems,and its accuracy is comparable to the corresponding simulation results of the finite element method on fine grids.And the memory and computational cost are also largely reduced.This raises a new avenue for solving large-scale computational problems that are difficult to solve using direct methods.