Adaptive Finite Element Simulation And Inversion For Two-dimensional Passive Source Airborne Electromagnetic

The passive source airborne electromagnetic method regards the natural electromagnetic field as the signal source for detecting the target of the underground electrical anomaly.The airborne and ground electromagnetic sensors are used to measure the vertical magnetic field component and the horizontal magnetic field component respectively to obtain the complex relationship(tipper)between the two.The spatial distribution characteristics and physical properties of the electrical anomaly are obtained by inverting the tipper data.The method is flexible,maneuverable and low-cost,which can be used to map large-scale structures in complex working environments and collect large amount of data containing much information rapidly.As a result,the method has been widely used in mineral resources exploration,oil and gas exploration,basic geological surveys and so on in abroad,while the domestic research is rare.In view of this situation,this paper systematically studies the numerical simulation and inversion of the passive source airborne electromagnetic method funded by National Key R&D Program of China.And the joint inversion of tipper and impedance(the apparent resistivity)is realized furtherly.In the forward modeling study,the governing equation of passive source airborne electromagnetic method is derived from Maxwell's equations,and then the one-dimensional analytical solution of the background model is calculated as the boundary condition to construct the boundary value problem.In order to relieve the contradiction between calculation accuracy and computational requirements of finite element method,the adaptive finite element method for passive source airborne electromagnetic is realized,which guides the grid to local refinement by estimating the posterior error of each unit.The quadrilateral grid is used in the refinement process and the biquadratic interpolation function is constructed on each unit.The linear equations are solved directly.The numerical simulation results show that the algorithm can obtain high-precision numerical solutions with less computational complexity.Finally,the response characteristics of the tipper are analyzed and summarized based on the algorithm.In the inversion,the objective function with the constraint of the smoothest model is constructed and minimized by the nonlinear conjugate gradient method.In the process,the product of the matrix and the vector is solved to avoid the calculation and storage of the elements of the Jacobian matrix.The inversion of the two-dimensional passive source airborne electromagnetic tipper is realized finally.And the inversion results performed by using the synthetic data show that the tipper has a high lateral resolution for the good conductor in the ground,which can rightly show the lateral boundary of the anomalous body.However,the inversion result of the tipper data is more susceptible to the initial model than the apparent resistivity.For this problem,this paper proposes a joint inversion objective function with the apparent resistivity data constraint.And a weighted factor is introduced to weight apparent resistivity data constraint.Then the joint inversion algorithm of the air tipper data and the ground apparent resistivity data is derived.The inversion results show that the dependence of the inversion result of tipper on the initial model can be effectively reduced by adding a small amount of ground apparent resistivity data and the robustness of inversion is improved.