【摘要】 从电偶源三维地电断面可控源电磁法的二次电场边值问题及其变分问题出发,采用任意六面体单元对研究区域进行剖分,并且在单元分析中同时对电导率及二次电场进行三线性插值,实现电导率分块连续变化情况下,基于二次场的可控源电磁三维有限元数值模拟.这个新的可控源电磁三维正演方法可以模拟实际勘探中地下任意形状及电性参数连续变化的复杂模型.理论模型的计算结果表明,均匀大地计算的视电阻率误差和相位误差分别为0.002%和0.0005°.分层连续变化模型的有限元计算结果表明,其与对应的分层均匀模型解析结果有明显差异.三维异常体组合模型以及倾斜异常体等复杂模型的有限元计算结果也有效地反映了异常形态.更多还原

【Abstract】 We focus on the forward problem of controlled source electromagnetic(CSEM)and present a new three-dimensional(3D)finite-element modeling(FEM)algorithm using the secondary field for continuous variation of electrical conductivity within each block.Usually delta sources are used in the governing partial differential equations and the electrical conductivity of each block is assumed to be a constant in traditional FEM for CSEM modeling,which producesnear-field error due to the source singularity and boundary reflections among blocks.On the other hand,the traditional uniform hexahedral grids significantly limit their capacity to handle practical underground structures with complex geometry and continuous variation of electrical conductivity.On the basis of Maxwell′s equations,the electromagnetic field is separated into background field with analytical solution of a layered media and the secondary field caused by anomalous bodies,which is numerically computed by the finite element method,to avoid the source singularity.Firstly,the corresponding variation question of the three-dimension boundary value problem for CSEM is given according to the generalized variational principle.Secondly,the FEM is implemented to solve the variational equation.The computational area is divided into many arbitrary hexahedral element meshes,in which the tri-linear interpolation is performed on the electromagnetic field and conductivity parameter simultaneously to simulate the model with electrical conductivity of continuous variation.Thus the variational equation is converted into a linear equation system,and it is solved to obtain the secondary electric field at each node.In the process,the divergence condition is added to eliminate the spurious solution.Using the relation between the electric fields and the magnetic fields,the secondary magnetic field value of each node is also obtained.In combination with the background field,the total electromagnetic fields of each node can be calculated,resulting in apparent resistivity and impedance phase values on the ground surface.Finally,numerical modeling results for a series of models are carried out to validate the effectiveness of our 3DCSEM finite element algorithm.The result of our method shows 0.002 percent error in apparent resistivity and 0.0005°error in impedance phase for a homogeneous half-space model.The FEM modeling for a continuous multilayer model shows obviously differences in comparison to analytic solutions for its corresponding layered model,which are up to 44.43% for apparent resistivity and 13.27°for impedance phase.For more complicated models,such as the combined model with multiple 3D anomaly bodies or sloping interface anomaly bodies,our FEM method works well and illustrates subsurface structures effectively.A CSEM modeling method is developed using FEM to compute the electromagnetic responses for three-dimensional models.The main feature of our method is that the secondary electrical field is solved by FEM with arbitrary hexahedral element meshing,in which the tri-linear interpolation is performed on the electromagnetic field and conductivity parameter simultaneously.In addition,the divergence condition is used to overcome the spurious solution.Finally the total field is obtained by adding the secondary electrical field to the analytical background field. Numerical experiments show our new three-dimensional CSEM forward modeling algorithm ensures the accuracy of the solution and is able to simulate more complicated model with arbitrarily shaped structures and continuous variation of electrical conductivity.更多还原