3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids
3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids
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DOI：
10.1093/gji/ggx358
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发表时间：
2017-11-01
影响因子：
2.8
通讯作者：
Farquharson, C. G.
中科院分区：
文献类型：
--
作者：
Jahandari, H.;Farquharson, C. G.
与常规结构化网格相比，非结构化网格可以更准确地表示任意结构，并且使用更少的单元。与直线网格相比，这些网格也允许更有效的细化。在本研究中，四面体网格用于大地电磁数据的反演，这允许在模型中直接包含地形，使用基于线框的地质模型约束反演，并在观测站进行局部改进。采用最小结构迭代模型空间高斯-牛顿算法进行优化。采用迭代求解器求解高斯-牛顿法向方程组的每一步，并利用伪正演问题计算求解器所需的灵敏度矩阵向量积。该方法减少了显式形成Hessian或Jacobian矩阵的需要，从而大大减少了所需的计算内存。正演问题采用基于边缘的有限元方法，并使用稀疏直接求解器求解。该求解器允许在高斯-牛顿迭代中对类似的伪正演问题进行矩阵分解，从而极大地减少了计算时间。给出了两个示例来展示该算法的能力：第一个示例使用基准模型，而第二个示例表示具有地形和硫化物矿床的现实地质环境。反转的数据是全张量阻抗和磁传递函数矢量。反演结果充分恢复了模型并再现了数据，表明了非结构化网格在复杂和现实的大地电磁学反演场景中的有效性。第一个示例还用于通过与数据空间对应方法的比较来演示所提出的模型空间方法的计算效率。
Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.