3D Time Domain Airborne EM Forward Modeling Based On Spectral-Element-Time-Domain(SETD) Method

With the fast development of national economy,the existing mineral resources can't meet the needs.As an important branch of exploration geophysics,airborne electromagnetic(AEM)method is widely used in mineral resource exploration,environmental and engineering surveys,groundwater exploration and geothermal surveys.All these are due to its advantages such as fast exploration speed,high efficiency,and the ground staffs do not need to enter the survey area.In order to obtain the underground three-dimensional(3D)electrical structural features,3D inversion has received widespread attention.The inversion requires the support of 3D forward modeling.Therefore,the development of high-precision and efficient 3D forward modeling is particularly important.In this thesis I use the time-domain spectral element(SETD)method based on the Gauss-Lobatto-Chebyshev(GLC)polynomial to study the 3D forward simulation of the time-domain airborne electromagnetic(ATEM)responses.Compared with the traditional finite-element(FE)or finite-difference(FD)method,the spectral element(SE)method includes both the flexible segmentation features and high precision characteristics.Therefore,the spectral element method can achieve the flexible segmentation for anomalous bodies and accurate numerical results.In order to complete the 3D forward EM simulation based on SETD method,firstly,I derive the vector Helmholtz equation(control equation)for the secondary electric field and total electric field based on the time-domain Maxwell equations.Secondly,I use GLC vector interpolation basis function to spectrally expand the electric and magnetic field values in cells.Thirdly,the Galerkin method and the backward differential are used to discrete the spatial parameter and time derivative of the governing equation,respectively.Further,a large linear equation is formed that is solved by a direct solver.Finally,the ATEM responses at the receiving point are obtained by interpolation.In this thesis,I explain the basic principles of the GLC SETD method and the ATEM 3D forward simulation theory,complete the accuracy verification,and analyze the response characteristics of typical ATEM models.It includes the following aspects:(1)I derive the Helmholtz equation based on the secondary field separation method and the total field method,respectively.First,the calculation area is divided into several small units,and the GLC high-order vector interpolation basis functions are used to perform spectral approximation of the true solution.The Galerkin method and the backward difference are used to discrete Helmholtz equation.At the end,we use a direct solver to solve the large linear equations system and the interpolation basis function to obtain the ATEM responses at the receiving point.(2)I introduce the construction method of GLC higher-order vector interpolation basis function.First,I explain the transformation relationship between the physical unit and the reference unit,and construct a higher-order vector interpolation basis function in the reference unit.Since the GLC polynomial has an analytical expression,the mass matrix and stiffness matrix can be analytically derived,thereby ensuring the calculation accuracy of 3D forward simulation.(3)I complete the accuracy verification,and summarize the forward modeling principle for SETD method.In this thesis,the SETD method is applied to ATEM 3D forward simulation.The 3D forward simulation solution of the layered model is compared with the one-dimensional analytical solution,which verifies the reliability of the algorithm in this paper.Analyzing the error and efficiency of 3D forward modeling solution based on the secondary field separation and the total field method,I conclude that if the same calculation accuracy is guaranteed,the forward simulation based on the second field separation method is more efficient.And it is verified that the numerical simulation accuracy can be improved by increasing the order of the spectral element normal vector interpolation basis function or refining the mesh.(4)I analyze the EM response characteristics of typical models in ATEM.The numerical simulation results show that the application of the SETD method to ATEM 3D forward simulation has certain guiding significance for actual production in airborne EM.