Spectral-element method with arbitrary hexahedron meshes for time-domain 3D airborne electromagnetic forward modeling
Spectral-element method with arbitrary hexahedron meshes for time-domain 3D airborne electromagnetic forward modeling
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用于时域 3D 机载电磁正演建模的任意六面体网格谱元法
DOI：
10.1190/geo2018-0231.1
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发表时间：
2019-01
期刊：
影响因子：
3.3
通讯作者：
Cai Jing
中科院分区：
文献类型：
--
作者：
Huang Xin;Yin Changchun;Farquharson Colin G.;Cao Xiaoyue;Zhang Bo;Huang Wei;Cai Jing
三维时域机载电磁（AEM）建模的主流数值方法，如有限差分法（FDTD）或有限元法（FETD），已经相当成熟。然而，这些方法在处理复杂地质构造的能力和依赖于地球模型的高质量网格划分方面存在局限性。在空间离散化的混合阶谱元方法和时间离散化的后向欧拉方法的基础上，提出了一种时域谱元方法。混合阶SE方法可以提高多项式的阶数并抑制伪解，从而提供准确的结果。BE法是一种无条件稳定的技术，没有时间步长限制。为了处理AEM发射环附近场的快速变化，我们将二次场与一次场分开，只模拟二次场，并提前计算一次场。为了得到块对角质量矩阵，从而使待解方程组中非零元素的个数最小化，我们应用了降阶高斯-洛巴托-勒让德积分技术。然后对方程组采用直接求解器，从而可以有效地处理多个AEM源。为了验证SETD算法的准确性，我们将结果与层状地球模型的半解析解进行了比较。在此基础上，分析了采用变形物理网格对不同三维模型的建模精度和效率，并与三维FETD代码的结果进行了比较，进一步展示了SETD对AEM正演建模的灵活性。
Mainstream numerical methods for 3D time-domain airborne electromagnetic (AEM) modeling, such as the finite-difference (FDTD) or finite-element (FETD) methods, are quite mature. However, these methods have limitations in terms of their ability to handle complex geologic structures and their dependence on quality meshing of the earth model. We have developed a time-domain spectral-element (SETD) method based on the mixed-order spectral-element (SE) approach for space discretization and the backward Euler (BE) approach for time discretization. The mixed-order SE approach can contribute an accurate result by increasing the order of polynomials and suppress spurious solutions. The BE method is an unconditionally stable technique without limitations on time steps. To deal with the rapid variation of the fields close to the AEM transmitting loop, we separate a secondary field from the primary field and simulate the secondary field only, for which the primary field is calculated in advance. To obtain a block diagonal mass matrix and hence minimize the number of nonzero elements in the system of equations to be solved, we apply Gauss-Lobatto-Legendre integral techniques of reduced order. A direct solver is then adopted for the system of equations, which allows for efficient treatment of the multiple AEM sources. To check the accuracy of our SETD algorithm, we compare our results with the semianalytical solution for a layered earth model. Then, we analyze the modeling accuracy and efficiency for different 3D models using deformed physical meshes and compare them against results from 3D FETD codes, to further show the flexibility of SETD for AEM forward modeling.
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影响因子：
2.8
作者：
C. Schwarzbach;Ralph-Uwe Börner;K. Spitzer
通讯作者：
C. Schwarzbach;Ralph-Uwe Börner;K. Spitzer
DOI：
10.1109/tmtt.2005.860502
发表时间：
2006-01
影响因子：
4.3
作者：
Joon-Ho Lee;Tian Xiao;Qing Huo Liu
通讯作者：
Joon-Ho Lee;Tian Xiao;Qing Huo Liu
3-D Maxwell 特征值问题的混合谱元法
DOI：
10.4208/cicp.230113.140814a
发表时间：
2015-01
影响因子：
4.3
作者：
Liu Na;Eduardo Tobon Luis;Zhao Yanmin;Tang Yifa;Liu Qing Huo
通讯作者：
Liu Qing Huo
DOI：
10.1007/s11430-007-6016-z
发表时间：
2007
期刊：
Science in China Series D: Earth Sciences
影响因子：
--
作者：
Bolin Wu;Chiyang Liu;Jianqiang Wang
通讯作者：
Bolin Wu;Chiyang Liu;Jianqiang Wang
影响因子：
3.3
作者：
D. Oldenburg;E. Haber;R. Shekhtman
通讯作者：
D. Oldenburg;E. Haber;R. Shekhtman