Numerical Simulation Of Electromagnetic Field Based On Finitespectral Element Method

Magnetotelluric sounding is a geophysical exploration method of natural sources,which is widely used in mineral resources exploration,geological survey,environmental and water resources survey,and deep earth structure and other research.Numerical simulation is of great significance for theoretical research,exploration design and data processing interpretation of magnetotelluric.The commonly used numerical simulation methods include finite difference method,integral equation method,finite element method,finite volume method,spectral element method and so on.The finite difference method and the integral equation method are difficult to deal with Complex electrical models.The convergence of finite element method requires the coordination of nodes between elements,which makes local mesh encryption difficult.Finite element method is the process specification and can simulate complex geological body,the spectral element method has high precision characteristics,in order to improve the accuracy and efficiency of magnetotelluric numerical simulation,the finite element-spectral element method is introduced into the field of magnetotelluric sounding,a finite element method dealing with complex structure model of flexibility and high precision and exponential convergence of spectral method.In this paper,the numerical simulation of low frequency plane wave electromagnetic field based on finite element-spectral element method,Starting from Maxwell's equations in frequency domain,The partial differential equation satisfied by two-dimensional magnetotelluric forward modeling and the boundary value problem satisfied by twodimensional medium magnetotelluric field are derived in detail.Based on the Galerkin weighted allowance method,the calculation area is discretized,the spectral element method is used to solve the interface between the abnormal body and the medium,and the background region is solved by finite element method.Gauss-Lobatto-Legendre(GLL)orthogonal polynomials are used to interpolate basis functions for unknown quantities(electromagnetic field values)at interpolation nodes,In addition,the GLL numerical integration is adopted and the integral matrix is assembled to form a large sparse symmetric linear system of equations.Finally,the coefficient matrix is compressed and stored,and the stable double conjugate gradient algorithm is used to solve the linear equations of large sparse coefficients.The electromagnetic field distribution is obtained,and the two-dimensional finite element-spectral element method numerical simulation of magnetotelluric is realized.An international standard model COMMEMI2D-0?COMMEMI2D-1 is calculated in numerical experiments to verify the effectiveness and accuracy of the algorithm.Comparison with Finite Element Method,Compared with the finite element method,the results not only show that the algorithm has higher calculation accuracy and efficiency,but also improve the numerical simulation results of electromagnetic field in low frequency region.Through the design of complex geoelectric models,the validity and flexibility of the finite element-spectral element method applied to magnetotelluric forward modeling are demonstrated,and the magnetotelluric response characteristics of these typical models under TE and TM excitation modes are further analyzed,which provides reference and guiding significance for practical work.