The Research On MT Tipper Finite Element Forward Modelling And MT Sparsity-Constrained Inversion

Magnetotelluric(MT)sounding methods,which is a geophysical survey methods by using natural alternating electromagnetic fields as field sources,have long been an important application in geophysical prospecting and basic research of large-scale structures of the crust and upper mantle.The traditional magnetotelluric sounding method quantitatively studies the underground electrical structure through apparent resistivity and phase parameters.However,the high resolution of the dumper data for the anomalous lateral boundary makes the tipper data also an important interpretation parameter in the MT survey.In addition,in the study of magnetotelluric inversion,smooth regularization constraint inversion is the most common method of inversion,but this type of method has the problem of abnormal artifacts when dealing with abnormal regions in deep regions.However,using the regularization constraints of the L1 norm can overcome this drawback to some extent.In view of the above two points,this paper mainly studies numerical simulations of two-dimensional and three-dimensional magnetotelluric tipper,analyzes and discusses the influence of various factors on the response of the tipper.Besides,this paper studies the sparsity-constrained inversion of two-dimensional magnetotellurics based on wavelet transform,and compares and discusses respective characteristics of sparsity-constrained inversion and smooth inversion.In the forward modeling of two-dimensional magnetotellurics,based on the idea of the finite element weighted residual method,form Maxwell's equations of the TE model,a forward numerical simulation study of two-dimensional magnetotelluric tipper was carried out.Compared to the traditional rectangular subdividing unit,the triangular subdivided unit can simulate various complex terrains and the cryptographic processing in the key research area can bring about a higher precision solution.Firstly,the tipper response of the electrical models with two high-and low-impedance anomalies were simulated.The characteristics of the tipper data and apparent resistivity parameters in the magnetotelluric sounding were compared and analyzed.The results show that the data of the tipper have higher horizontal resolution.On this basis,because the Z-tipper electromagnetic method(ZTEM)in the frequency domain combines the characteristics of the aero-electromagnetic method and the tipper data,it is suitable for detecting the boundary position of anomalies at a certain depth,thus simulating the ZTEM tipper of the simulated tunnel model.The sub-response,and analysis of the influence of factors such as line height,anomaly depth,topography,magnetic permeability anomaly,and noise error on the ZTEM tipper response further deepened the understanding of the characteristics of the tipper response.In the forward modeling of three-dimensional magnetotelluric tipper,the ZTEM method is used to perform vector finite element forward numerical simulation of three-dimensional ZTEM tipper vector from the Maxwell's equations using unstructured tetrahedral elements.At the same time,through the calculation and test of the tunnel model,the effects of factors such as the height of the survey line,the anomaly depth,topography,magnetic permeability anomaly,and noise error on the ZTEM tipper response are quantitatively analyzed.Finally,for the single anomaly model and the compound anomaly body model,the use of the tipper parameters can well reflect the characteristics of the horizontal distribution of the target anomaly,and realizes the recognition of the horizontal position of the simple and complex electric model target body by the rake.It lays the foundation for studying the ZTEM method and ZTEM inversion.In the two-dimensional magnetotelluric sparsity-constrained inversion,the inversion process of the underground electric structure obtained from the magnetotelluric observation data is a nonlinear ill-posed problem,so the smoothness constraint is widely used to estimate the regularized solution.In this paper,based on the theory of compressive sensing algorithm,an inversion method based on wavelet basis function for sparse model is proposed.The objective function of the inversion is that minimizes the data residuals of the L2 norm and the Li norm of a model penalty.The accuracy and validity of the sparsity-constrained inversion of two-dimensional magnetotellurics are proved by the inversion experiments of high and low resistance anomalous bodies and fault geoelectric models.