Adaptive Finite Element Magnetotelluric Anisotropic Forward Modeling Based In High-order Interpolation

The Magnetotelluric Sounding(MT)is a geophysical exploration method that uses natural alternating electromagnetic fields to study underground geological structures.Because of its large depth of exploration and not influence without high resistance shielding,correspondingly the low-resistance reaction is sensitive,and low cost of construction(relative to seismic exploration)and many other advantages.It has been widely used in petroleum,minerals,engineering and other fields,and has achieved good exploration results.One of the current assumptions of magnetotelluric sounding is that the underground medium is homogeneously isotropic,but in the actual exploration process,the situation is very complex,the surface is often not horizontal and underground geological structure is anisotropic,such as thin layer interaction and metamorphic rock formation.Its resistivity distribution changes in changes in all directions,when the electric and magnetic fields are not vertical.If it still uses the traditional method to deal with the same sex,you will get a wrong understanding.In view of the above problems,this paper mainly studies the response characteristics of magnetotelluric physical field in different media,and carries out the forward calculation of MT through the more mature finite element numerical simulation method.Using finite element polynomial cubic interpolation technique combined with adaptive finite element algorithm to improve the speed and accuracy of forward modeling.In addition,the unstructured triangular meshing technique is applied to the undulating terrain and complex geological models to effectively solve the simulation error caused by the traditional quadrilateral segmentation which can not fit the curve edge well.Combining the above techniques,to simulate the propagation media,respectively.Discussing the effects of undulating topography and complex geological structures on apparent resistivity and impedance phase of TE polarization mode and TM polarization mode,and the angle between the axial orientation and the electrical principal axis on apparent resistivity and impedance phase is also discussed in anisotropy.This paper starts from the Maxwell equations,Firstly The partial differential equations of satisfying magnetotellurics in isotropic should be deduced and Further deduce the equations in anisotropy.Then the corresponding variational problem is derived by Galerkin weighted residual method,and forward modeling using the object-oriented adaptive finite element method.First,executing forward calculation from a coarse grid,and the posterior error estimation is used to control whether the target performs mesh encryption.This method doesn't require initial fine mesh,and it also avoids the increase of calculation caused by global refinement and greatly improves the calculation efficiency.Adaptive finite element algorithm program developed using the more popular Python programming language.Use dolfin library in finite element analysis and numpy and matplotlib library for matrix operations and data visualization.In order to verify the correctness of the adaptive finite element program,this paper uses the calculation results published by the predecessors and the algorithm of this paper to test the finite element program in this paper.After completing the program varication,The undulating terrain model,COMMEMI-2D1 model and several famous two-dimensional anisotropic models are simulated respectively,and the influence of different media on the electromagnetic field of the earth is discussed.