【摘要】 本文实现了海洋可控源电磁三维矢量有限元数值模拟.由于采用非结构四面体单元进行三维网格剖分,该方法可以模拟复杂电性异常体和海底地形.一维模型的数值模拟结果表明,电场实、虚部均与解析解吻合得相当好,计算误差基本小于1%.二维模型的计算结果与已有的二维自适应非结构有限元模拟结果吻合很好.带地形模型的数值模拟结果显示,海底地形对电场影响很大,有可能掩盖海底油气藏产生的异常.更多还原

【Abstract】 Nodal finite element(FE)has become a popular numerical method in computational geo-electromagnetics since 1970 s.However,the zero-divergence property of the electromagnetic field and the discontinuity of the normal component of the electrical field harass the elegant implementation of nodal FE.The former brings in the spurious solution in the simulation while the latter makes it impossible for regular nodal FE to solve electromagnetic field directly.This paper focuses on 3Dforward modeling of marine controlled-source electromagnetics(CSEM)with an electrical dipole source,using vector finite element method on unstructured tetrahedral grids which can simulate complicated geometry and submarine topography without spurious solution.The curl-curl electrical field full-wave equation,which is derived from Maxwell′s equations,is used as the governing equation in our marine CSEM simulation.Somerfeld radiation operator is chosen as the boundary condition on the truncated boundary.By applying the generalized variational principle to the boundary value problem of the electrical field,the equivalent variational problem is obtained. Unstructured tetrahedral grids are employed for spatial discretization in the 3D calculation domain using a non-commercial mesh generator Gmsh.Nédélec type vector basis functions are adopted for the interpolation of the electrical field withineach tetrahedral element. These basis functions are divergence-free intrinsically and they guarantee the continuity of the tangential field component when crossing the interface between two different media.Unlike the nodal FE,the unknowns are assigned to the edges of the elements rather than the nodes.Substituting the electrical field by the interpolation,a system of linear equations is constructed.We solve the system of linear equations with a direct solver.A 1Dstratified air-sea-sediment model is designed for the validation of our 3Dvector FE algorithm.We output the numerical solution of the electrical field of 0.01 Hz,0.1Hz and 1.0Hz with three measurement configurations:inline,broadside and a 45-degree angle between the survey line and the dipole source direction.The comparison between the analytical and numerical solution shows that the relative error are less than 1%for most cases when the observation points are a few hundred meters away from the source.The CSEM response of a 2Dair-sea-sedimentbasement model with a horst type interface between the sediment and basement layers is then compared with the numerical solution of the well-known 2DFE algorithm MARE2 DCSEM and it shows high consistency between the 2Dand 3Dnumerical solutions.The influence of submarine topography to CSEM response is also studied. The simulation indicates that submarine topography has significant impact on the electrical field in marine CSEM.The existence of submarine topography may cover the anomalous signal induced by oil reservoir.Finally,the CSEM response to a 3D reservoir model covered by complicated submarine topography and fluctuant stratum interface is simulated and the results show that the complicated topography makes unsmooth changes to the MVO(Magnitude Versus Offset)curve.We develop a 3D marine CSEM simulation algorithm using vector FE on unstructured meshes.The main advantages of vector FE we use in marine CSEM over regular nodal FE are:(1)no divergence correction is needed because of the vector basis functions are divergence-free;(2)the electrical field is solved directly without worrying about the discontinuity of the normal component of the electrical field.On the other hand,unstructured tetrahedral grids can easily handle complicated submarine topography and refined reservoir structures.The comparisons with1 Danalytical solution and 2D numerical solution show high accuracy of our algorithm.The simulations also show that submarine topography may be an important contributor to the uncertainties of CSEM MVO anomalies.更多还原