3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids
3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids
复制标题
DOI：
10.1190/geo2013-0172.1
复制
发表时间：
2014-07-01
期刊：
影响因子：
3.3
通讯作者：
Farquharson, Colin G.
中科院分区：
文献类型：
--
作者：
Ansari, Seyedmasoud;Farquharson, Colin G.
提出了三维电磁频域正演问题的有限元解法。该方法将电场分解为亥姆霍兹方程和电荷守恒方程中的矢量势和标量势。向量势和标量势分别使用边缘元基函数和节点元基函数。进行这种分解的目的是为了满足电场的切向分量和电流密度的法向分量在元素间边界上的连续性，从而找到问题的有效解决方案。将计算域细分为非结构化四面体单元。采用加权残差法的伽辽金变体对方程组进行离散化，将近似向量势和标量势作为稀疏线性系统的未知数。采用带不完全LU预条件的广义最小残差求解器对系统进行了迭代求解。通过5个算例对求解方法进行了验证。在第一个和第二个例子中，将均匀半空间表面上的小偶极子产生的场与其相应的解析解进行了比较。第三个算例与积分方程法在低导电性半空间中埋有导电块的长接地线源模型上的计算结果进行了比较。第四个示例涉及验证大电导率对比的方法，其中磁偶极子发射器-接收器对在浸入盐水的石墨立方体上移动。数值方法的解与该情景的物理尺度模型的数据很好地吻合。最后一个算例验证了埋在海洋导电沉积物中的电阻盘模型的解。对于所有的例子，使用电位的解的收敛速度明显快于使用电场的解。
We present a finite-element solution to the 3D electromagnetic forward-modeling problem in the frequency domain. The method is based on decomposing the electric field into vector and scalar potentials in the Helmholtz equation and in the equation of conservation of charge. Edge element and nodal element basis functions were used, respectively, for the vector and scalar potentials. This decomposition was performed with the intention of satisfying the continuity of the tangential component of the electric field and the normal component of the current density across the interelement boundaries, therefore finding an efficient solution to the problem. The computational domain was subdivided into unstructured tetrahedral elements. The system of equations was discretized using the Galerkin variant of the weighted residuals method, with the approximated vector and scalar potentials as the unknowns of a sparse linear system. A generalized minimum residual solver with an incomplete LU preconditioner was used to iteratively solve the system. The solution method was validated using five examples. In the first and second examples, the fields generated by small dipoles on the surface of a homogeneous half-space were compared against their corresponding analytic solutions. The third example provided a comparison with the results from an integral equation method for a long grounded wire source on a model with a conductive block buried in a less conductive half-space. The fourth example concerned verifying the method for a large conductivity contrast where a magnetic dipole transmitter-receiver pair moves over a graphite cube immersed in brine. Solutions from the numerical approach were in good agreement with the data from physical scale modeling of this scenario. The last example verified the solution for a resistive disk model buried in marine conductive sediments. For all examples, convergence of the solution that used potentials were significantly quicker than that using the electric field.