3-D Marine Controlled Source Electromagnetic Forward Modeling Based On Domain Decomposition Method

In the past years,with the urgent need for deep-sea exploration,marine electromagnetic(EM)method has entered a period of rapid development.Many forward algorithms have been developed.However,as the problem becomes more complex,to accurately characterize the variation of the EM field,one needs to discretize the model in fine grids,which can lead to an equations system of millions of unknowns that requires huge memory and computational time.To solve this problem,I apply the non-overlapping domain decomposition method based on vector finite-element(FE)method to the forward modeling of marine controller source electromagnetic(MCSEM)method.The main idea of the domain decomposition method is to decompose the original large model problem into several small ones to reduce the calculation scale and the memory requirements.In this paper,starting from the Maxwell equations in the frequency-domain,the vector Helmholtz equation is derived according to the total field.The mesh of the computational domain is then partitioned using METIS to obtain a certain number of subdomains and the corresponding boundary conditions are established.The governing equation of each subdomain is discretized using the FE method.Next,the subdomains are coupled to obtain a subsystem with reduced order.After solving the subsystem,the EM field in each subdomain can be obtained.In this paper,the theoretical foundation and implementation process of solving the MCSEM problem based on the domain decomposition method are described in detail,and the new application of the domain decomposition method in the MCSEM is given.The specific technical details are addressed as follows:(1)Theoretical basic of 3D EM forward modeling based on the total field using FE method.Due to the complex topography of the submarine sedimentary environment,to effectively simulate the actual geological conditions,this paper uses the total field method combined with unstructured tetrahedral grids to establish the governing equation for each subdomain.The FE method is used to discretize the governing equations to obtain the forward problem of each subdomain.(2)Coupling and solving strategy for subdomain problems based on domain decomposition method.The boundary conditions between the subdomains are used to couple the subdomains to form an order reduced problem.It is pointed out that iterative method based on the Krylov subspace method(such as the generalized minimum residual method)are more suitable for solving this problem,and the parallelization strategy of the domain decomposition method is given.(3)Analysis of numerical examples.The domain decomposition method based on the FE method is applied to the MCSEM forward modeling in the frequency-domain.The accuracy of the algorithm is verified by comparison with 1D semi-analytical results.I further analyze the effects of different transmission frequencies and air conductivities on the number of iterations of the iterative solver,which shows that the algorithm has good stability.Finally,the complex seabed geological model is simulated and the corresponding EM characteristics of the MCSEM are analyzed,as well as the computing resources required for the algorithm when dealing with problems of different scales are addressed.The numerical results show that the algorithm developed here is an effective method for the MCSEM forward modeling that can deal with large-scale problems.