Three-dimensonal Inversion Of Frequency-domain CSEM Data Using Vector-based Finite Element Method

The controlled-source electromagnetic(CSEM)mostly utilizes the artificial source which generates current flows to accurately reconstruct the electrical conductivity distribution in the subsurface.Compared to the natural-source-based magnetotelluric(MT)geophysical method,the CSEM method has stronger anti-interference ability and compared to the gravity and magnetic prospecting method,the CSEM method usually results in higher resolution results.The CSEM method is now widely used in the exploration of resources in a variety of complex environments.With the continuous improvements of the CSEM exploration equipment,the CSEM exploration can better adapt to the complex environment,and the scale of the observation data obtained is getting larger.To get the sophisticated interpretation of large-scale CSEM data,we should develop efficient,reliable,and stable 3D inversion methods,which have important theoretical and practical significance.High-precision 3D forward modeling is the basis of 3D inversion algorithm,and it is the most time-consuming part of the process for 3D inversion.To form an efficient and reliable 3D inversion algorithm,this paper first develops an efficient and reliable 3D forward modeling algorithm.In order to simulate the complex geological structure,the vector-based finite element method with irregular structured grid and unstructured grid is used to study the CSEM forward modeling problem.We solve the forward modeling problem efficiently with MKL Paradiso parallel direct solver.Considering the fact that the forward modeling is frequency independent,the algorithm is further parallelized over frequencies to speed up the modeling and inversion process.Thus,a multi-level parallel solution strategy based on direct solver and frequency is formed.The inversion process is equivalent to getting the optimization solution of the objective function.In this paper,the Gauss-Newton optimization method with approximate quadratic convergence is adopted.Conventionally,the inversion results usually depend a lot on the initial inversion model.To solve the above problem,a new roughness method for the irregular structured grid and unstructured grid is proposed.Based on the proposed roughness method,the CSEM 3D inversion algorithms using vector-based FE method with the irregular structured and unstructured grid are developed.By comparing the inversion results of several complex land CSEM models with different initial models,the effectiveness and stability of the two inversion algorithms based on the proposed roughness matrix are verified,furthermore,the newly developed methods are proved to be less dependent on the initial models.Different marine reservoir models with topography were applied to the study,which validated the proposed two inversion schemes can handle complex marine CSEM models well.These synthetic studies proved the proposed CSEM 3D inversion schemes are of great theoretical and practical significance and can be applied to the sophisticated interpretation of large-scale CSEM data and pre-drilling reservoir prediction.Considering the inherent defect of the CSEM method,the resolution of CSEM inversion results is usually limited compared to the seismic.The conventional inversion methods usually result in continuously distributed images,and the boundaries for different physical properties are usually blurry,which may generate difficulties in the data interpretation.To obtain clearer boundary information and higher resolution inversion results of the CSEM method,the multinary transform was introduced to the inversion of CSEM data,and the inversion scheme with multinary transform is called multinary inversion.The multinary inversions based on irregular structured and unstructured grids are developed,respectively.Complex land CSEM synthetic models and marine synthetic CSEM models with complex geometry were applied to validate the proposed CSEM 3D multinary inversion algorithms.By comparing the inversion results of the conventional,focusing and the multinary inversion methods,we proved the effectiveness of the multinary inversion method in depicting the sharp boundaries of different physical properties,improving the resolution of the CSEM inversion method,and further,the comparison in some extend validated the multinary inversion can overcome the insensitivity to the high resistivity of the CSEM method.Furthermore,to validate the proposed methods can also be used to the field CSEM data,the proposed inversion methods based on unstructured grids are used to study the field CSEM data of the medium-size silver-lead-zinc mine in Gansu province,China.By comparing the results of the inversion methods with the geological map and the drilling data,the effectiveness and stability of the inversion schemes were validated.The comparison further showed the multinary inversion can show an explicit advantage in depicting different geophysical structural properties.This field data study presented that the proposed inversion methods can also be well used in field data.These studies showed the developed inversion methods have theoretical and practical significance,and could be widely used for the study of the deep earth structure and the exploration of all kinds of resources.The innovation of this study is mainly reflected in the following two aspects:(1)a roughness matrix calculation strategy that is suitable for the hexahedral mesh and tetrahedral mesh is proposed,by integrating the calculation strategy with the vector-based FE method and Gauss-newton optimization scheme,the maximum smoothness inversion methods are developed,which are proposed to be efficient,reliable,stable and are less dependent on the initial models;(2)the multinary transform function is first introduced to the EM inversion,based on which the multinary inversion methods for the hexahedral and tetrahedral grids are developed.The results of the multinary inversion methods are with higher resolution and clearer boundary.