A staggered-grid convolutional differentiator for elastic wave modelling
A staggered-grid convolutional differentiator for elastic wave modelling
复制标题
用于弹性波建模的交错网格卷积微分器
DOI：
10.1016/j.jcp.2015.08.017
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发表时间：
2015-11
影响因子：
4.1
通讯作者：
Fu Li-Yun
中科院分区：
文献类型：
--
作者：
Sun Weijia;Zhou Binzhong;Fu Li-Yun
控制偏微分方程中导数的计算是物理波传播数值模拟研究的热点之一。本文通过对一阶导数算子的带限谱进行傅里叶逆变换，导出了一阶速度-应力弹性波方程的交错网格卷积微分器（CD）。锥形窗口函数用于截断无限交错网格CD模板。截断CD算子几乎与解析解一样精确，并且与有限差分（FD）方法一样有效。在波浪模拟中，窗函数的选择将影响CD算子的精度。我们通过最小化导数的谱误差并与普通的Hanning窗函数进行比较来寻找不同阶CD算子的最佳高斯窗函数。结果表明，对于同一CD算子，最优高斯窗函数与Hanning窗函数相似。我们研究了不同阶数的窗口CD算子和交错网格FD方法的精度。与传统的交错网格FD方法相比，短交错网格CD算子可以达到与长FD算子相当的精度，且计算成本更低。例如，8阶交错网格CD算子可以实现与16阶交错网格FD算法相同的精度，但所需的计算资源和时间为一半。从均匀模型和地壳波导模型的数值例子被用来说明的CD运营商的优越性比传统的交错网格FD运营商的波传播的模拟。
The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.
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影响因子：
5.2
作者：
Yi Luo;G. Schuster
通讯作者：
Yi Luo;G. Schuster
影响因子：
3
作者：
D. Komatitsch;J. Vilotte
通讯作者：
D. Komatitsch;J. Vilotte
影响因子：
0.9
作者：
J. Virieux
通讯作者：
J. Virieux
影响因子：
3.3
作者：
FORNBERG, B
通讯作者：
FORNBERG, B
DOI：
--
发表时间：
2014-06
期刊：
--
影响因子：
--
作者：
P. Moczo;J. Kristek;M. Galis
通讯作者：
P. Moczo;J. Kristek;M. Galis