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3-D time-domain electromagnetic modeling based on multi-resolution grid with application to geomagnetically induced currents
Physics of the Earth and Planetary Interiors ( IF 2.3 ) Pub Date : 2021-01-15 , DOI: 10.1016/j.pepi.2021.106651
Jingyu Gao , Maxim Smirnov , Maria Smirnova , Gary Egbert

Time-domain electromagnetic modeling in 3-D requires the solution of partial differential equations discretized on a grid. The finer grid resolution is usually required to describe rapid variations of the electromagnetic field in the near-surface, where the source and small-scale anomalies present. Since the electromagnetic field diffuses in the lossy medium, its variations become smoother with depth. The conventional finite-difference modeling approach using the staggered grid extends the fine grid resolution (needed for shallow layers) to all depths. It results in over-discretization of the problem and redundant computational costs. Here, we apply the multi-resolution (MR) grid approach to the time-domain electromagnetic modeling (TDEM). The MR grid allows us to decrease the grid resolution with depth and consequently reduce the number of degrees of freedom without compromising the accuracy of the solution. We implement a way of treating the loop source in TDEM modeling such that the definition of the source term is based on the Biot-Savart law; this allows separation of the loop source from the grid, making the source simulation more flexible.

To verify our new TDEM modeling, we perform several synthetic tests. We also apply the algorithm to model the geomagnetically induced electric field (GIE). Such modeling is an essential part of estimating hazards caused by geomagnetically induced currents (GIC). In contrast to frequency-domain modeling primarily used in previous studies, the time-domain GIE modeling allows us to consider the time variability of the source in the ionosphere in real-time.

For more realistic simulations, we use a large-scale 3-D resistivity model of Fennoscandia. An example of the MR grid GIE modeling highlights the areas of high GIE contrasts and shows that the real inhomogeneous 3-D resistivity distribution and realistic source geometry are necessary for a better estimation of GIC.



中文翻译:

基于多分辨率网格的3D时域电磁建模及其在地磁感应电流中的应用

在3-D中进行时域电磁建模需要解决离散化在网格上的偏微分方程。通常需要更精细的网格分辨率来描述近表面电磁场的快速变化,其中存在源和小范围异常现象。由于电磁场在有损介质中扩散,因此其变化随深度而变得更平滑。使用交错网格的常规有限差分建模方法将精细的网格分辨率(浅层需要)扩展到所有深度。这会导致问题过于分散,并导致冗余的计算成本。在这里,我们将多分辨率(MR)网格方法应用于时域电磁建模(TDEM)。MR网格使我们能够随着深度降低网格分辨率,从而减少自由度的数量,而不会影响解决方案的准确性。我们在TDEM建模中实现了一种处理循环源的方法,以使源项的定义基于Biot-Savart法则;这样可以将环路源与网格分开,从而使源仿真更加灵活。

为了验证我们新的TDEM建模,我们执行了一些综合测试。我们还将算法应用于地磁感应电场(GIE)的建模。这种建模是估算由地磁感应电流(GIC)引起的危害的重要部分。与以前的研究中主要使用的频域建模相反,时域GIE建模使我们能够实时考虑电离层中源的时间变化。

为了进行更真实的仿真,我们使用芬诺斯堪迪亚的大型3-D电阻率模型。MR网格GIE建模的示例突出显示了高GIE对比度的区域,并显示了真实的非均匀3-D电阻率分布和真实的源几何形状对于更好地估计GIC必不可少。

更新日期:2021-02-11
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