论文标题

精确的2.5D频域雷达波使用加权差异操作员建模

Accurate 2.5D frequency domain radar waves modelling using weighted-averaging difference operators

论文作者

Bernard, Doyon, Bernard, Giroux

论文摘要

在频域中建模雷达波传播在完全波形倒置中吸引人,因为它允许降低问题的非线性,降低数据空间的维度,更好地描述衰减以及有效处理多个来源。此外,当可以在一个水平维度中假定物理属性不变时,执行2.5D建模很有趣,因为与3D情况相比,它可以减少巨大的计算要求。在2.5D中,可以使用有限差异方法在空间中的两个方向上传播波,并在第三方向上执行空间傅立叶变换,以获得完整的三维解决方案。使用简单的中央有限差分实现,可以获得空间中的二阶精度,并且每次波长最多需要20个网格点才能准确模拟电磁波。如此大量的网格点会影响与频域建模相关的存储需求。我们提出了一种高精度算法,以通过2.5D中的有限差异来求解频域电磁波方程。该算法依靠9分模板来构建加权平均数值操作员。选择权重以最大程度地减少数值分散和各向异性,从而使网格单元大小的要求放松,从而使计算成本降低了约3.6倍,而中央有限差分差异方法。这种新的算法可减少数值误差,而无需增加矩阵系统的数值带宽,并且可以轻松地将其转移到3D频域建模。

Modelling radar wave propagation in frequency domain is appealing in full waveform inversion because it allows decreasing the non-linearity of the problem, decreasing the dimension of the data space, better description of attenuation, and handling efficiently multiple sources. Besides, performing 2.5D modelling is interesting when physical properties can be assumed invariant in one horizontal dimension because it allows reducing drastically computation requirements compared to the 3D case. In 2.5D, finite-difference methods can be used to propagate the wave in two directions in space and a spatial Fourier transform is performed in the third direction to get a full three dimensional solution. With a simple central finite-difference implementation, second order accuracy in space is obtained and up to twenty grid points per wavelength are necessary to accurately simulate electromagnetic waves. Such a large number of grid points will impact on the storage requirement associated with frequency domain modelling. We propose a high accuracy algorithm to solve the frequency domain electromagnetic wave equation by finite-differences in 2.5D. The algorithm relies on a nine-point stencil to build weighted-averaging numerical operators. The weights are chosen to minimize numerical dispersion and anisotropy, which allows relaxing the requirements on grid cell size and thus decreases computational costs by a factor of about 3.6 compared to the central finite-difference method. This new algorithm reduces the numerical error without increasing the numerical bandwidth of the matrix system to solve, and can be easily transposed to 3D frequency domain modelling.

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