论文标题
使用高阶差异时间域方法在不均匀网格上使用高阶差异时域方法受控的源电磁建模
Controlled-source electromagnetic modelling using high order finite-difference time-domain method on a nonuniform grid
论文作者
论文摘要
在地球中传播的3D低频电磁场的模拟在计算上很昂贵。我们在非均匀网格上提出了一个虚拟的波域高阶有限差分时间域（FDTD）建模方法，以计算频率域3D受控的源电磁（CSEM）数据。该方法克服了在不均匀网格上的传统二阶交错网格有限差方案中广泛存在的不一致问题，并通过任意高阶方案实现了高精度。可以通过使用有效算法反转Vandermonde矩阵系统来准确计算自适应节点间距的有限差分系数。建立了适用于非均匀网格的通用稳定性条件，揭示了时间步长和这些有限差异系数的依赖性。使用固定点迭代的递归方案旨在确定产生最佳非均匀网格的拉伸因子。我们方法中的网格拉伸减少了离散化中所需的网格点数，这使其比具有密集采样均匀网格的标准高阶FDTD更有效。当网格沿着深度伸展而无需水平拉伸时，就可以观察到我们方法的更好准确性，而不是在垂直和水平方向上拉伸。我们方法的效率和准确性由数值示例证明。
Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute frequency-domain 3D controlled-source electromagnetic (CSEM) data. The method overcomes the inconsistency issue widely present in the conventional 2nd order staggered grid finite difference scheme over nonuniform grid, achieving high accuracy with arbitrarily high order scheme. The finite-difference coefficients adaptive to the node spacings, can be accurately computed by inverting a Vandermonde matrix system using efficient algorithm. A generic stability condition applicable to nonuniform grids is established, revealing the dependence of the time step and these finite-difference coefficients. A recursion scheme using fixed point iterations is designed to determine the stretching factor to generate the optimal nonuniform grid. The grid stretching in our method reduces the number of grid points required in the discretization, making it more efficient than the standard high-order FDTD with a densely sampled uniform grid. Instead of stretching in both vertical and horizontal directions, better accuracy of our method is observed when the grid is stretched along the depth without horizontal stretching. The efficiency and accuracy of our method are demonstrated by numerical examples.
