Three-dimensional Forward Modeling And Inversion Of Frequency-domain Airborne Electromagnetic Data

The frequency-domain airborne electromagnetic(FAEM) method has been proved an effective method in geophysics exploration in the past decades, which widely used in mineral exploration, geological mapping, groundwater investigation and environmental monitoring. At present, the data interpretation of this method are almost based on one-dimensional inversion method with the conductivity is isotropic and neglecting the effect of permeability. However, the underground medium is usually a complex three-dimensional structure and the conductivity is anisotropic in some cases. As show in many studies, the permeability of some earth materials is much greater than that of free space, ignoring it may not only cause the interpretation to be erroneous, but may also result in the loss of potentially useful information about the earth. It has been demonstrated that one-dimensional inversion method often fail to recover simple 3D targets, particularly in those cases where 2D or 3D geological complexity is present. Furthermore, this method is usually carried out in mountain area, the topography effect is also a problem that can not be ignored. This article developed a 3D FAEM forward modelling based on edge finite element with topography, which can also be used for permeability and arbitrary anisotropic conductivity simulation. Then, based on the forward modelling, we developed a 2D inversion with topography based on Gauss-Newton method and 3D inversion based on nonlinear conjugate gradient(NLCG) method.We developed a 3D FAEM simulation based on edge finite element with topography, and the electric field are spilt into primary(background) field and secondary(scattering) field to eliminate source singularities. The primary field are calculated in uniform whole space using analytical method and the secondary field are solved by using the edge finite element. The linear system equation are solved by using large-scale sparse matrix shared memory parallel direct solver, which solve the multi-source problem very efficiently, and we compare the performance between iterative solver and directive solver. Compare with 1D analytical and 3D finite difference method solution's results which demonstrate our proposed approach is robust and accuracy. Then we carried out the simulation for typical terrain model and analysis the topography effect for electric and magnetic field.We developed a 3D FAEM simulation for arbitrary anisotropic conductivity with Euler rotation. We compare it with 1D analytical solution's results which demonstrated its accuracy. Then we carried out the 3D simulation for arbitrary anisotropic conductivity and analysis anisotropy effect for the magnetic fields.We developed the 3D FAEM simulation for permeability and compare it with analytical solution to demonstrate its accuracy. We simulated the different device type, different frequency, and different flight altitude for permeability. We give the constructive suggestions for realistic production and data interpretation based on summing up the permeability influence law for electric and magnetic field data.We developed the 2D FAEM inversion solution based on Gauss-Newton method with topography, the Jacobian matrix are calculated by using adjoint equation. We tested it on synthetic data, the results indicate that the horizontal coplanar(HCP) coil system has higher lateral resolution while the vertical coaxial(VCX) systems has higher vertical resolution. Ignoring the topography effect can lead to incorrect results.We developed the 3D FAEM inversion solution based on nonlinear conjugate gradient(NLCG) method, and the gradient of objective function are calculated by adjoint equation. We use quadratic and cubic interpolation with backtracking scheme to accelerate the convergence rate of objective function. The synthetic data example indicate our scheme is correct and validity and compare it with different initial model.The research of this paper has important theoretical and scientific significance not only for understanding the propagation of electromagnetic waves in complex media, but also for improving and perfecting the interpretation and processing of the frequency domain airborne electromagnetic data and guiding the actual production.