| The magnetotelluric(MT)is a significant geophysical exploration method,which is widely used in resource exploration,energy prospecting,deep structure probe and other fields due to its advantages of convenient construction,high exploration efficiency,low cost(compared with seismic exploration)and large exploration depth.The acquisition of geological structure information below the surface,especially deep geological structure information,mainly depends on the interpretation of geophysical observation data.Geophysical forward and inversion is an important means of interpretation of observation data.In the past ten years,great progress has been made in MT three-dimension(3D)inversion theory and its calculation technology based on different forward modeling methods(integral equation,finite difference,finite element,etc.).However,at present,the 3D inversion technology that has been applied in practice is mainly based on the finite difference method.In particular,the 3D interpretation of the measured MT data in China basically adopts the 3D inversion technology based on the finite difference method.Although the 3D finite difference forward modeling method has the advantages of relatively simple implementation and fast calculation,it has great limitations for electromagnetic response simulation of undulating terrain and complex geological structure.Different from the finite difference method,finite element method to simulate rugged topography and complex geologic body has obvious advantages in the respect of electromagnetic response,especially the vector finite element method has been developing rapidly in recent years,due to the vector finite element method can effectively solve the traditional nodes element method exist the problem of spurious solution,has become the main method for complex terrain and complex 3D geological structure electromagnetic response simulation.However,the finite element method also has some shortcomings.The large amount of computation of this method is the main factor that causes the practical process of the 3D MT inversion technology based on the finite element method to lag relatively(compared with the 3D inversion technology based on the finite difference method).It is still a key and difficult point in the application of MT 3D inversion technology to take forward and inversion with topography into consideration of high computational efficiency.In view of this,and for the purpose of practical application,this paper carries out the research of 3D forward and inversion with topography based on vector finite element.In the 3D forward numerical modeling of MT field,the 3D forward algorithm of MT with topography based on vector finite element is developed.Firstly,starting from the governing equation of MT,the large linear equations that satisfy the governing equation are obtained by the vector finite element method.Then,a direct solution method without divergence correction is used to solve the large linear equations corresponding to the vector finite element method,and the MT response of the geoelectric model with topographic is calculated.Finally,the correctness of the 3D forward algorithm in this paper is verified,and the computational efficiency of the direct solution method based on without divergence correction is compared with the iterative solution method with divergence correction in this paper.On this basis,the response of MT field of the 3D geoelectric model with topography is simulated and its influence is analyzed.In terms of 3D inversion of MT,an inversion code of MT with topography based on conjugate gradient(CG)method is presented.In order to avoid directly solving the jacobian matrix in the inversion process,the calculation of the jacobian matrix of 3D MT was studied in detail,and the formula of calculating the partial derivative matrix 3D MT based on the vector finite element was derived.Based on the reciprocal theory,the product of jacobian matrix with a vector and the product of the transpose of jacobian matrix with a vector are turned into the forward problem of two different imaginary field sources,that is,the "quasi-forward" problem.On this basis,the fast 3D forward algorithm implemented in this paper is introduced into the conjugate gradient inversion algorithm,so as to overcome the two difficulties in 3D MT inversion with large storage capacity and long calculation time of jacobian matrix.In order to find out the influence of 3D terrain on the inversion results,the 3D inversion method with topography and the 3D inversion method without topography in this paper were used to invert the synthetic data of different types of pure terrain models,and the results of the two inversion methods were compared.Finally,the inversion experiment is carried out on the synthetic data of the theoretical model with different complexity and noise,so as to verify the validity and reliability of the inversion algorithm in this paper.In the application of 3D MT inversion,the 3D inversion program developed in this paper is used to carry out 3D inversion of two cases of measured MT data with the goal of mineral exploration and geological mapping.Achieve obvious application effect as follows:(1)The 3D fine electrical structure obtained from the interpretation of 3D MT observed data with mineral exploration as the target clearly reflects the geoelectric characteristics of the study area and provides a basis for the exploration of favorable strata and the evaluation of potential mineral resources in the mining area.(2)In the interpretation of 3D MT exploration data aiming at geological mapping,according to 3D electrical structure of underground obtained by the 3D inversion method in this paper,and combined with the geological data of the study area,the 3D geological structure of underground is interpreted,and the spatial distribution characteristics of faults,ground layers and rock masses in the work area are preliminarily identified,which can provide geophysical basis for the 3D geological mapping work in this area.The results show that the 3D MT inversion program in this paper is practical. |
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