Two-dimensional Forward Modeling Of Magnetotelluric Based On The Spectral Element Method

The magnetotelluric method(also known as magnetotelluric sounding method,referred to as "MT")is a geophysical exploration method using the natural alternating electromagnetic field as the field source to detect the underground electrical structure.It is widely used in the fields of energy exploration,mineral prospecting,geological survey,earthquake prediction and engineering geology.In recent years,with the progress of numerical algorithm,the improvement of data acquisition system and the rapid development of high-performance computer,It greatly promoted the development of the electromagnetic numerical simulation technology,appeared a variety of highly efficient numerical algorithm,effectively improve the speed and precision of the numerical simulation.Spectral element method,as a new numerical method,has been developed rapidly in recent decades.In order to improve the accuracy and efficiency of numerical simulation of MT,spectral element method is introduced into the field of MT sounding in this paper.Spectral element method is a numerical simulation method combining finite element method and spectral method.It has the flexibility of finite element method to deal with complex structure model and the high precision and exponential convergence of spectral method,which makes spectral element method widely used in the fields of fluid mechanics,dynamics,acoustics and seismic wave field.In recent years,spectral element method has been applied to numerical simulation of Marine controllable source electromagnetism,but no scholars have applied spectral element method to numerical simulation of magnetotelluric field,so this paper applies spectral element method to 2D forward modeling of magnetotelluric field.The theoretical basis of the spectral element method has been introduced in this paper,starting from the maxwell's equations of frequency domain,MT 2D forward modeling was deduced in detail the meet by the partial differential equation and two-dimensional magnetotelluric places for medium boundary value problem,based on the Galerkin weighted residual method,the solving domain with rectangular element subdivision,cell of an unknown quantity(value)of electromagnetic field in the interpolation node interpolation basis function selects Gauss-Lobatto-Legendre(GLL)orthogonal polynomial,form a large-scale system of linear equations using numerical integral GLL finally,Combined with boundary conditions,the electromagnetic field distribution was obtained by solving the linear equationsdirectly with Intel Pardiso solver,and the simulation of the magnetotelluric two-dimensional spectral element method was realized.In order to test the reliability of the proposed algorithm and program,the layered model and the international standard COMMEMI 2D-1 model are given in the calculation examples for comparative verification.In the example of layered model,the reliability and stability of the spectral element algorithm program are demonstrated by comparing the one-dimensional analytical solution and SEM numerical simulation results.In COMMEMI 2D-1 model,the simulation results of spectral element method and integral equation method are almost the same,the curve shape of the algorithm results in this paper is consistent with that of the standard model,which verifies the effectiveness of this algorithm in MT numerical simulation.