custEM: Customizable finite-element simulation of complex controlled-source electromagnetic data
custEM: Customizable finite-element simulation of complex controlled-source electromagnetic data
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DOI：
10.1190/geo2018-0208.1
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发表时间：
2019-03
期刊：
影响因子：
3.3
通讯作者：
R. Rochlitz;N. Skibbe;T. Günther
中科院分区：
文献类型：
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作者：
R. Rochlitz;N. Skibbe;T. Günther
我们开发了开源工具箱 custEM（可定制电磁建模），用于模拟复杂的 3D 受控源电磁 (CSEM) 问题。它基于开源有限元库 FEniCS，支持四面体网格、多重处理、高阶多项式和各向异性。我们使用多种有限元方法来求解时谐麦克斯韦方程，该方程基于总电场或二次电场以及测量电势公式。此外，我们还开发了二次磁场公式，如果仅需要磁场，则显示出卓越的性能。使用 Nédélec 基函数，我们将网格边缘的电流密度稳健地纳入总场公式中。后者能够在考虑地形的情况下对 CSEM 问题进行建模。我们使用 pyhed 库评估半解析一维分层地球解决方案，支持偶极子或环路源的任意配置以进行二次场计算。所有系统矩阵均已修改为对称矩阵，并与直接求解器 MUMPS 并行求解。除了有限元内核之外，还实施了网格生成、插值和可视化模块来简化和自动化建模工作流程。我们通过四个示例证明了 custEM 的功能，包括针对分析解决方案的验证、所有实施方法的交叉验证以及具有 3D 地形的模型的结果。面向对象的实现允许进行可定制的修改和添加，或者仅使用专为特殊任务（例如网格生成或矩阵组装）设计的子模块。因此，该工具箱适合与其他代码进行交叉验证，并作为开发 3D 反演例程的基础。
We have developed the open-source toolbox custEM (customizable electromagnetic modeling) for the simulation of complex 3D controlled-source electromagnetic (CSEM) problems. It is based on the open-source finite-element library FEniCS, which supports tetrahedral meshes, multiprocessing, higher order polynomials, and anisotropy. We use multiple finite-element approaches to solve the time-harmonic Maxwell equations, which are based on total or secondary electric field and gauged potential formulations. In addition, we develop a secondary magnetic field formulation, showing superior performance if only magnetic fields are required. Using Nédélec basis functions, we robustly incorporate the current density on the edges of the mesh for the total field formulations. The latter enable modeling of CSEM problems taking topography into account. We evaluate semianalytical 1D layered-earth solutions with the pyhed library, supporting arbitrary configurations of dipole or loop sources for secondary field calculations. All system matrices have been modified to be symmetric and solved in parallel with the direct solver MUMPS. Aside from the finite-element kernel, mesh generation, interpolation, and visualization modules have been implemented to simplify and automate the modeling workflow. We prove the capability of custEM, including validation against analytic-solutions, crossvalidation of all implemented approaches, and results for a model with 3D topography with four examples. The object-oriented implementation allows for customizable modifications and additions or to use only submodules designed for special tasks, such as mesh generation or matrix assembly. Therefore, the toolbox is suitable for crossvalidation with other codes and as the basis for developing 3D inversion routines.