A Fourth Order Accurate SH-Wave Staggered Grid Finite-difference Algorithm with Variable Grid Size and VGR-Stress Imaging Technique
A Fourth Order Accurate SH-Wave Staggered Grid Finite-difference Algorithm with Variable Grid Size and VGR-Stress Imaging Technique
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DOI：
10.1007/s00024-008-0298-8
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发表时间：
2008-02
影响因子：
2
通讯作者：
J. Narayan;Sanjay Kumar
中科院分区：
文献类型：
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作者：
J. Narayan;Sanjay Kumar
本文提出了一种实现平面自由表面边界条件的新方法。它基于在自由表面边界条件的显式计算过程中自由表面上方的垂直网格尺寸的减小。这项技术与众所周知的应力成像技术非常相似。VGR-应力成像技术是为这种新的自由表面边界条件(VGR代表“垂直网格尺寸缩小”)而提出的。为了研究VGR应力成像技术的性能，将其应用于一种新开发的时间精度为二阶、空间精度为四阶的变网格交错网格SH波有限差分(FD)算法。结果表明，如果采用应力成像技术作为自由面边界条件，第一土层的有效厚度(ETH)将比指定厚度(ATH)减小一半。各种数值实验的定性和定量结果表明，VGR应力成像技术优于应力成像技术，因为它避免了由于使用跨自由表面的应力分量图像而引起的厚度差异。在迭代数值实验的基础上，确定了变网格条件下FD格式的稳定性条件，即每个最短波长至少需要5~6个网格点才能避免网格色散。当最大网格间距比达到12.5或更高时，并不影响(2，4)SH波算法的精度。与均匀网格相比，对于特定的盆地边缘模型，计算内存和计算时间分别减少了10.46和5.38倍，反映了新FD算法的有效性。
This article presents a new approach for the implementation of a planar-free surface boundary condition. It is based on a vertical grid-size reduction above the free surface during the explicit computation of a free surface boundary condition. This technique is very much similar to the well-known stress imaging technique. VGR-stress imaging technique name is proposed for this new free surface boundary condition (VGR stands for ‘vertical grid-size reduction’). To study the performance of the proposed VGR-stress imaging technique, it was implemented in a newly developed second order accurate in time and fourth-order accurate in space (2, 4) staggered grid SH-wave finite-difference (FD) algorithm with variable grid size. It was confirmed that the effective thickness (ETH) of first soil layer becomes less by one-half of vertical grid size than the assigned thickness (ATH), if stress imaging technique is used as a free surface boundary condition. The qualitative and quantitative results of various numerical experiments revealed that the proposed VGR-stress imaging technique is better than the stress imaging technique since it is free from the thickness discrepancy arising due to the use of images of stress components across the free surface. On the basis of iterative numerical experiments, it was confirmed that the stability condition for this FD scheme with variable grid size isIt was also inferred that at least five to six grid points per shortest wavelength are required to avoid the grid dispersion. The maximum grid-spacing ratio up to 12.5 or even more did not affect the accuracy of (2,4) SH-wave algorithm. The obtained reduction of 10.46 and 5.38 folds in the requirement of computational memory and time for a particular basin-edge model, as compared with the homogeneous grid size, reflects the efficacy of the new FD algorithm.