Three-dimensional Anisotropic Finitie Element Modeling And Inversion Of Magnetotelluric Data

As an important geophysical method,the magnetotelluric method(MT)is widely used in many fields such as mineral resource exploration,geothermal resource exploration,and deep earth structure detection.With the gradual penetration of electromagnetic exploration into complex geological structures and the increasing demand for fine exploration,high-precision three-dimensional(3D)electromagnetic exploration has gradually become a research hotspot.The refined interpretation of largescale magnetotelluric data requires the development of efficient and stable 3D modeling and inversion algorithms.Traditional 3D modeling and inversion algorithms are based on the assumption of isotropic media,and the electrical anisotropy of strata has been gradually confirmed since the 1960 s.A lot of studies have proved that electrical anisotropy has a great influence on magnetotelluric exploration.Neglecting or inappropriate handling of electrical anisotropy is considered a significant source of error in the analysis and interpretation of electromagnetic data.In areas with complex geological structures,MT data show strong anisotropy characteristics,and it is difficult for algorithms based on isotropy to fit such data.Therefore,it is urgent to develop 3D anisotropic modeling and inversion algorithms.The high-precision 3D modeling algorithm is the basis of the inversion algorithm,and the accuracy and speed of the modeling algorithm will have a great impact on the efficiency of the inversion algorithm.Therefore,this thesis first develops a modeling algorithm based on vector finite element method for 3D MT data in anisotropic media,and the formulation is based on the electric field governing equation.In order to speed up the iterative solution and reduce the running time of the electric field discrete system,two optimization strategies are discussed based on the realization of the modeling algorithm.One is to implement the divergence correction technology in the modeling calculation process,which can significantly speed up the iterative solution process.The other is to apply the rational Krylov subspace model order reduction technique to the electric field discrete system,which can significantly reduce the multi-frequency modeling calculation time.The direct solution based on electric field governing equation consumes a huge amount of memory when the number of calculation area subdivision elements is large.Discretization of the governing equation of potential filed using the finite element method becomes another option of modeling algorithm.Therefore,this thesis also develops a modeling algorithm based on nodal finite element of 3D MT data in anisotropic media,and the formulation is based on the potential field governing equation.Numerical experiments show that the iterative solution of the potential field discrete system has a good convergence in a wide frequency range,which overcomes the slow convergence of the electric field discrete system at low frequencies.Inversion algorithm plays a central role in the interpretation of electromagnetic data.From the view of numerical calculation,the inversion method can be regarded as an optimization algorithm in essence.The choice of the optimization algorithm has a significant impact on the efficiency of the inversion.In this thesis,a Gauss-Newton(GN)method with an approximate quadratic convergence rate is used to minimize the objective functional.The results of traditional smooth inversion are often continuously diffused,in order to obtain inversion results with clearer boundaries and higher resolution.In this thesis,the minimum support gradient(MSG)model constraint is applied to the 3D inversion of magnetotelluric data for the first time,and a 3D isotropic inversion algorithm of MT based on the MSG model constraint is developed.The developed algorithm is applied to the synthetic data of two theoretical models,and the inversion results of the minimum norm(MN)model constraint,the flattest model(FM)constraint and the minimum support gradient(MSG)model constraint are compared.The inversion results show that the inversion based on the MSG model constraint can improve the resolution of anomalies and obtain a clearer geoelectric interface.In addition,it is also proved inversion of MSG model constraint is not sensitive to the focusing factor,and a relatively stable inversion result can be obtained for a wide range of focusing factors.In order to further prove the application effect of the developed algorithm on the field data,the Gauss-Newton inversion algorithm based on the MSG model constraint was applied to the long-period data of the USArray of the Earth Scope project in the United States.It is proved that the developed inversion program still has good applicability to the measured magnetotelluric data.When the isotropic model is used to fit the data with obvious electrical anisotropy characteristics,deviation or even wrong geological information is often generated.In order to better interpret the data containing electrical anisotropy information,this thesis develops the 3D axial anisotropic GN inversion algorithm of MT data based on realization of the 3D isotropic inversion algorithm.The validity and correctness of the inversion algorithm are verified by a series of numerical experiments of two examples.Numerical test results show that using the isotropic inversion code to fit anisotropic data,deviation and even false geological structures appear,a more reliable geoelectric structure can be obtained by using the axial anisotropic inversion.