3D Anisotropic Forward Modeling For Time-domain Marine CSEM Based On Unstructured Finite-element And Rational Krylov Subspace Method

With the progress of the equipment and technology for marine exploration in China,the exploration of marine resources has become an important strategy in recent years.After many years of development,the theory and techniques of the marine controlled-source electromagnetic method(CSEM)have been mature.As a research hotspot,the forward modeling and inversion of the 3D marine CSEM method have set up a relatively complete theoretical basis and technical means.However,the research on the modeling of electrical anisotropy was still limited to the frequency-domain method,and the related research on the 3D marine EM method in time-domain was either based on isotropic or transverse isotropic models.But there was still a blank in the study of arbitrary anisotropic models based on the 3D marine CSEM method in the time-domain.Compared with the frequency-domain method,the time-domain EM method can finish a full-wave EM observation by transmitting once.Through the analysis of the EM signal of different time channels,the seabed structure can be effectively detected.Moreover,the time-domain EM method can effectively suppress the airwave in shallow water,rendering this method an important tool in marine exploration.Different from the terrestrial environment,the submarine sedimentary strata,oil reservoirs,and submarine metal orebodies are generally anisotropic.Therefore,it is urgent to develop the technology of data processing and interpretation for anisotropic models.As the basis of inversion and interpretation,the accuracy and efficiency of forward modeling for arbitrarily anisotropic models is vital.Compared with the other methods,the unstructured finite-element method can better simulate the undulating topography and complex geological structures of the seabed,and the local refining technology of tetrahedral mesh has been more mature.By refining the electrical interface and the area where the receivers and transmitters are located,the accuracy of forward simulation can be greatly improved.However,with the improvement of the calculation accuracy,the number of grids increases simultaneously,which can lead to high requirements for the efficiency of the algorithm.Therefore,this paper use the vector finite-element method based on the unstructured grid to simulate the EM responses of the three-dimensional(3D)marine CSEM method for arbitrarily anisotropic models,and the rational Krylov subspace method is combined to improve the modeling efficiency.This paper then analyze the EM responses in the time-domain for different anisotropic parameters and identify the anisotropic characteristics of different models.The main research contents are as follows:(1)Three-dimensional vector finite-element method for anisotropic time-domain modeling based on unstructured meshes.For a better reflection of the anisotropic characteristics of the model,the unstructured grid was used to locally refining the anisotropic medium,and the power-off observation mode was adopted to study the 3D marine CSEM responses of the total field for anisotropic models in the time-domain.(2)Solution to the time-domain EM method based on rational Krylov subspace method.Based on the governing equation of the finite-element method for the electric field,the expression of the EM solution vector in the time-domain is derived.The effective approximation of matrix exponential function and vector product in the rational Krylov subspace is found to solve the electric field vector,which avoids the time step discretization in conventional methods like the backward Euler method.(3)Analysis of numerical results for typical examples.In this thesis,the accuracy of the algorithm is verified by comparing the 3D time-domain CSEM responses based on the rational Krylov method with the one-dimensional semi-analytical solutions,and the efficiency of the algorithm is demonstrated by comparing it with the backward Euler method.Then,by simulating the EM responses for the models with different anisotropic parameters and analyzing the influence of anisotropic parameters on the distribution of electric field and current,the relationship between the anisotropic characteristics and the distribution of electric field and current is established.Besides,this paper also analyze the results of a magnetic and an electrical transmitting source.The comparison shows that the time-domain EM responses obtained by this algorithm are sensitive to the anisotropic characteristics of seabed sediments and ore bodies,including their trend and inclination.(4)Identification of anisotropic characteristics.Via circular observations,the data generated by a group of orthogonal sources are collected,the apparent resistivity is calculated and drawn in the polar coordinate system,and the anisotropic characteristics of the underground model can be identified by observing the polar diagram.The relative size,inclination,and trend of the anisotropic conductivity axes are successfully identified.The identification effects of the electrical and the magnetic transmitting source are further compared.This provides important support to the future marine CSEM data inversion and interpretation.