可控源电磁场三维自适应矢量有限元正演模拟

本文实现了可控源电磁(CSEM)场三维自适应矢量有限元正演算法,该算法采用非结构四面体单元进行三维网格剖分,能够真实模拟地形起伏和复杂电性异常体.采用一次场和二次场分离的方式计算电磁场响应,能够有效解决有限元模拟中的源点奇异性,提高场源附近电磁场数值精度,其中一次场利用CSEM一维正演算法解析求得,二次场采用矢量有限元方法求得.并利用基于后验误差估计的自适应网格细化算法指导网格细化,以减少人为设计网格导致的误差.通过一维和三维模型的数值模拟,验证了本文算法的有效性:一维模型有限元解与解析解吻合得很好,电磁场振幅相对误差在1%左右,相位差整体小于1°;三维模型有限元解与有限体积解吻合得也很好.模拟了一个含三维倾斜板状异常体的可控源电磁响应,表明了本文算法模拟复杂地电结构电磁场的能力和有效性.

Adaptive edge finite element modeling of the 3D CSEM field on unstructured grids

We present a 3D finite-element (FE) algorithm for the CSEM forward problem based on the secondary field formulation. In this method, the electric fields are approximated by edge elements rather than nodal elements,so that spurious solutions can be eliminated. The computational domain is subdivided into unstructured tetrahedral elements, which allows using complex model geometries including bathymetry and tilted electrical interfaces. To further improve the accuracy of the FE solution, adaptive grid refinement guided by an a posteriori error estimator is performed iteratively. To demonstrate the performance of the presented algorithm, we first benchmark FE solutions against analytical solutions for the 1D canonical model, and show that the errors of FE solutions decrease rapidly at the first few grid refinement iterations, and after 10 refinement iterations a highly accurate solution is achieved, with the relative amplitude error of electromagnetic fields close to 1 percent and the error in phase less than 1°. Then we compare FE solutions and finite volume (FV) solutions for the 3D canonical model, yielding an excellent agreement with each other. Finally, forward responses of a slightly complicated model in which a 3D sloping conductor is presented is adequately modeled by the FE algorithm proposed in this paper. The synthetic numerical examples indicate that the presented FE algorithm is very effective, well suitable to handle complex models with unstructured meshes employed, and highly precise modeling results can be obtained by performing the adaptive grid refinement.