3D Frequency-domain CSEM Inversion Based On Finite Element Method With Unstructured Grid

Controlled Source Electromagnetic Method?CSEM?is an important geophysical exploration method,which has been widely used in mineral and oil and gas resources exploration,hydrology and environmental investigation,geological structure research,and disaster prediction and so on.At present,with the complexity of the electromagnetic detection environment and the increasing depth of detection,new challenges have been put forward to the theory and technology of electromagnetic exploration interpretation.This study intends to study 3D controlled source electromagnetic source forward and inversion technology based on unstructured grid finite element method to improve the interpretation accuracy of controlled source electromagnetic detection under complicated conditions such as undulating ground.By introducing unstructured tetrahedral grids to perform the geoelectric model segmentation,a precise and accurate fitting of the undulating surface is realized,and the loss of forward accuracy due to the terrain fitting error is reduced.The forward calculation depends on the Edge-Based Finite Element Method?EB-FEM?to avoid numerical errors caused by the absence of divergence conditions.The final forward equation is solved by the direct solver MUMPS,which to some extent overcomes the effect of the poor condition number caused by the unstructured tetrahedral grids.Considering the impact of all relevant units,the processing of the transmitting source adopts the strategy of piecewise integration to realize the simulation of the transmitting source with arbitrary attitude.Based on the flexibility of unstructured grids,this paper reasonably encrypts the grids near the measurement point and the emission source,while makes the grids with less influence sparse,controlling the number of forward grids,thereby ensuring the computational efficiency.In the inversion,the conventional L₂ norm is used to define the objective function to ensure the stability of the solution process.Among them,the sensitivity matrix information is calculated and stored with the forward modeling technology,which saves storage space and improves the calculation efficiency.The model roughness is calculated using the weighted square sum method.In order to suppress multiple solutions during the inversion process,logarithms with conductivity conversion method which constrains the upper and lower limits of the inversion parameters are used.Based on the GN algorithm and L-BFGS algorithm,the 3D controlled source electromagnetic inversion can be applied to different exploration environments on land and ocean.The theoretical model calculation results show that the oceanic 3D controlled source electromagnetic inversion technology in this paper can overcome the influence of undulating topography and accurately recover the position and resistivity information of the seafloor high-resistance reservoir.Furthermore,the 3D controlled source audio frequency electromagnetic inversion technology in this paper can not only invert the anomalies in the undulating terrain,but also overcome the data distortions caused by the source on near regions and the transition region,obtaining reliable inversion results.Finally,in order to further test the practicability of the three-dimensional inversion technology in this paper,3D controlled source electromagnetic inversion of the measured data in Songjianghe Town,Fusong County,Baishan City,Jilin Province was performed.The inversion results are consistent with geological expectations and the data fit well,which proves the stability and practicability of the method in this paper.