The Edge Finite Element And Coupled Potentials Finite Volume Method For3D CSEM Modeling In The Frequency Domain

With gradually increasing energy demand and developed techniques,marine electromagnetic methods have gained extensive attention in the oil and gas exploration industry over the past decade. Although the data of3D seismic reflection can provide high precision of geological structure information and instructions of oil and gas construction,different characteristics of rock properties may produce the same characteristics of AVO.So,seismic can not effectively improve the success rate of reservoir drilling.By analyzing related data, when the pore structure contains higher oil gas and hydrate and shows a high different resistivity relative to the surrounding rock, the resistivity often has a difference of more than50times.By a significant difference in electrical, electromagnetic prospecting method is sensitive to the reaction of the reservoir. To solve problems of large amount of calculation and the multiple field source emission and low number of induction in MCSEM, this article has studied the3D MCSEM based on the adaptive edge finite element algorithm with a scalable parallel and the coulomb-gauged finite volume method(FVM) of coupled vector-scalar potential.We discussed the MCSEM observation device parameters effect on abnormal response and reservoir monitoring by means of MCSEM.1.On account of scalable parallel vector finite element algorithm of three-dimensional MCSEM,In order to eliminate the singularity problem in the source point field,we divide the electric field into the primary and the secondary field before calculation.The primary field is solved by analytical methods, the second order partial differential equations of the second field is discreted by the method of vector finite element.h-adaptive refine is a iterative process of numerical solution calculation, estimating residual posterior error,refining/coarsening mesh and recalculating, consequently making errors distribute on the almost mesh.Thus on the premise of saving computational resources, the calculation accuracy can be improved.2.We use METIS software package to decompose the mesh. The global mesh is divided into many local mesh,data between the local mesh is only associated with the units on the boundary of the adjacent local mesh in order to ensure the data communication is the least during the parallel computing between each process.3.In three dimensional EM problems, when the matrix is discreted by the Maxwell equation,the condition number is usually large.when using Krylov subspace methods solve the equation,it is difficult to make the equation converge fastly during constructing an efficient precondition.In addition, the marine electromagnetic method usually adopts the way of multi-source measuring.The stiffness matrix is determined by a certain frequency and a certain model,so changing the field source will only change the right hand items of equation.If iterative method is used to solve the problem, the amounts of calculation will increase with the increasing of the right hand items.The direct method has a great advantage over the iterative method. In this paper, the method of parallel Multifrontal based on MUMPS is adopted.4.In the three-dimensional marine electromagnetic numerical simulation,the frequenciy is often relatively low.No matter the three dimensional finite element method or finite volume method is adopted, it can eventually lead to be ill conditioned equation which is discreted by the numerical algorithm.To solve the low number of induction,this paper establishes a kind of three dimensional finite volume algorithm based on coupled scalar-vector potential.Maxwell’s equations can be converted to meet the coupling potential Helmholtz equation of coulomb gauge.Using Yee’s staggered grid form large sparse complex coefficient of linear equation.By making use of distribution characteristics obtained in the discretization process of non-zero elements in the large sparse matrix, the row format compression method (CSR)is adopted to compresse and store the discrete equation coefficient matrix in order to save the storage space of the computer.To effectively reduce the condition number of coefficient matrix and improve iteration speed of Krylov subspace, the minimum residual method of incomplete LU decomposition preprocessing (SQMR) is adopted to solve large complex coefficient equations.5.Based on the three dimensional finite volume algorithm of coupling potential,we discuss the corresponding abnormal response by changing the parameters of MCSEM observation,and study the feasibility of reservoir monitoring in the bottom of the sea.The results show that the advantages of edge finite element method are that it can accurately describe the complex geological body and improve simulation accuracy. Compared with vector finite element method,finite volume method is more suitable for simply electric model, because it can reduce the amount of calculation and improve the computational efficiency. In this paper, calculation results of the vector finite element algorithm for multiple source problem have the advantages of high speed and precision.The coupled potential finite volume method can still keep high convergence speed and satisfactory numerical results at a lower frequency.These two kinds of algorithms provide a good foundation for further observation system design and inverse calculation.