Research On Finite-Element Method Based On Unstructured Grids For 3D Magnetotelluric Anisotropic Modeling And Inversion

As an effective geophysical tool based on natural source,magnetotelluric?MT?has been widely used in resource exploration,geological survey and the investigation of earth structures from near surface to upper mantle,especially on research of structures in the deep earth.Conventional 3D MT forward modelling and inversion assume an isotropic model and most of these methods are based on structured meshes.However,electrical anisotropy is often found in the deep earth from MT data and isotropic models can lead to misinterpretations.In such cases,one needs to use an anisotropic model for appropriate and realistic interpretation.In addition,the inversion methods with structured meshes have limited capability to handle complex geological structures and topography in realistic situation.The model accuracy is severely influenced by the quality of mesh.Currently,the study on 3D MT anisotropic forward modeling and inversion over complex terrains and geological structures has not been well studied yet.To overcome this obstacle and promote the interpretation of MT data,I developed a 3D MT forward and inversion method based on unstructured finite-element method for anisotropic media.The main content of this thesis includes3D MT anisotropic modeling,identification of electrical anisotropy from MT data,appropriate strategies for practical anisotropic inversion and interpretation.3D MT anisotropic modeling is the basis for inversions with anisotropic models.An efficient forward algorithm can improve the calculation speed and accuracy of 3D MT modeling,and is one of the most important factors in constructing 3D MT anisotropic inversion.In MT forward modelling,it is important that the geological structures and interfaces in the numerical domains can be modeled as accurately as possible,which can not be efficiently achieved by the conventional structured grids.Unstructured tetrahedral grids enable representing arbitrary structures more accurately with fewer cells compared to regular structured grids,and they allow efficient local refinement.Fortunately,the finite-element method naturally supports unstructured grids.In this thesis,unstructured tetrahedral grids with finite-element method are used for the 3D forward modeling of MT data,which allows for the direct inversion of MT data with topography.It can overcome the defects of regular structured grids such as high computational cost for improving accuracy and difficulty of inverting with topography.In MT numerical experiment section,under the condition of anisotropic media,the influence of different anisotropic parameters on MT responses is analyzed.According the effect of anisotropy to MT apparent resistivity,I have summarized how to identify anisotropy without topography.However,it doesn't work when obvious topography occurs.To solve the problem,I proposed a technique that use the apparent resistivity in polar coordinates system to analyze the anisotropic features,which proved to be a useful way to identify the anisotropy on condition of topography.When one uses artificially refined grids,the accuracy of forward modeling is severely influenced by the quality of the grids,especially for complex geology and topography.In this thesis,I have developed a goal-oriented adaptive unstructured finite-element method for accurate and efficient 3D MT anisotropic modeling,rendering the hard work of artificially refined grids unnecessary.In addition,the anisotropic effect on the adaptive meshes are analyzed,which shows the fact that the grids refinements depends largely on the most conductive components in the horizontal directions.High memory cost and low computational efficiency have limited the practical application of traditional 3D MT inversion.In this thesis,I have used the limited-memory quasi-Newton?L-BFGS?method to perform 3D MT isotropic and anisotropic inversions.This avoids explicitly calculating the Hessian matrices,and greatly reduces the memory requirements.In the L-BFGS method only the objective function and its gradient need to be calculated.I have constructed the objective functional and its gradient with the unstructured grids for isotropic and anisotropic media,respectively.The isotropic inversion experiments show that my inversion method with unstructured grids can achieve good inversion result without carrying out topography correction.The long period MT data from the USArray component of EarthScope project in the United States has been used to test my inversion algorithm.The results were compared with the published results by the WSINV3D code.The comparison was very positive that verified the validity and applicability of my algorithm.In addition,my inversion recovers more detail about the underground structures compared with the published result with structured mesh,which shows the effectiveness of the unstructured mesh for 3D inversion.The results of isotropic inversion for anisotropic data are far beyond the original models,ignoring anisotropic may leads to misinterpretation.Only the anisotropic model can give a reasonable interpretation.Following the 3D MT isotropic inversion algorithm,I have developed a triaxial anisotropic inversion.After that I have proposed an effective strategy for anisotropic inversion for 3D MT data.Firstly,I use the anisotropy identification method I proposed in polar coordinates system to analyze the MT data,which can identify the anisotropic features if anisotropic structures do exist.Secondly,if the data contains anisotropic information,then I do 3D inversions using anisotropic inversion algorithm.Thirdly,the spatial distribution of the anisotropic structure is determined according to the of the distribution anisotropy ratio.Finally,a reasonable 3D anisotropic interpretation in combination with the geological background is carried out.I also verify the effectiveness of my strategy and algorithm via two numerical examples with anisotropic bodies embedded in a flat or topography half space.From the numerical experiments I can draw the conclusions.The unstructured finite-element method with L-BFGS algorithm are effective for 3D MT triaxial anisotropic inversion with topography.In triaxial anisotropic media,^?xand?_y are resolvable,?_z can't be resolvable due to nature of plane wave propagating vertically.In condition of complex geologies with anisotropy,to better recover the real underground electrical structures,one should use anisotropic inversion for MT data.The validity of the anisotropic inversion strategy and algorithm are verified by the Coprod2 and USArray MT data.The inversion of Coprod2 data provides an anisotropic interpretation of the NACP and TOBE anomalies together with a new revealed anomaly.With the inversion of USArray data,a dynamic model of the Cascadia subduction zone is established,which has scientific significance for studying the tectonic stress and motion of the deep earth and the cause of anisotropy.The results of field data inversion can provide a reference to the study of anisotropy in the deep earth.The algorithms addressed in this thesis lay a foundation for 3D MT anisotropic forward modling and inversions,which provides basis for studying the electrical anisotropy of deep earth.In this thesis,I have developed a goal-oriented adaptive finite-element method for 3D MT anisotropic modeling with topography,a noval identification technique of electrical anisotropy from MT data,and an effective strategy for anisotropic inversion for 3D MT data.The achievements have important theoretical and practical value in promoting the level of 3D MT data interpretation.