Elastic wave modelling in 3D heterogeneous media: 3D grid method
Elastic wave modelling in 3D heterogeneous media: 3D grid method
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DOI：
10.1046/j.1365-246x.2002.01743.x
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发表时间：
2002-09
影响因子：
2.8
通讯作者：
Z. Jianfeng;Liu Tielin
中科院分区：
文献类型：
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作者：
Z. Jianfeng;Liu Tielin
本文提出了一种新的三维非均匀介质中弹性波模拟的数值方法，本文称之为三维网格法。这项工作是对二维非均匀介质中P-SV波传播的二维网格法的推广。与有限元数值网格离散化方法类似，该格式灵活地结合了表面地形和曲面界面，并且自然地满足了三维地形的自由面边界条件。该算法是在紧凑交错网格格式的基础上发展而来的，它不像传统的有限差分方法那样满足每个节点的弹性动力学微分方程组，而是在每个节点上采用积分平衡的方法来求解。该格式的计算量和内存需求与同阶有限差分方法大致相同。本文提出了一种四面体和平行六面体混合网格法，并详细讨论了四面体网格法和平行六面体网格法的数值离散和稳定性准则。用三维Lamb问题的解析解和半球形弹坑绕射的边界方法对所提出的方法进行了验证。文中还给出了表面带有半柱形沟槽的弹性半空间和三维平面分层模型中面波传播的算例。
SUMMARY We present a new numerical technique for elastic wave modelling in 3D heterogeneous media with surface topography, which is called the 3D grid method in this paper. This work is an extension of the 2D grid method that models P-SV wave propagation in 2D heterogeneous media. Similar to the finite-element method in the discretization of a numerical mesh, the proposed scheme is flexible in incorporating surface topography and curved interfaces; moreover it satisfies the free-surface boundary conditions of 3D topography naturally. The algorithm, developed from a parsimonious staggered-grid scheme, solves the problem using integral equilibrium around each node, instead of satisfying elastodynamic differential equations at each node as in the conventional finite-difference method. The computational cost and memory requirements for the proposed scheme are approximately the same as those used by the same order finite-difference method. In this paper, a mixed tetrahedral and parallelepiped grid method is presented; and the numerical dispersion and stability criteria on the tetrahedral grid method and parallelepiped grid method are discussed in detail. The proposed scheme is successfully tested against an analytical solution for the 3D Lamb problem and a solution of the boundary method for the diffraction of a hemispherical crater. Moreover, examples of surface-wave propagation in an elastic half-space with a semi-cylindrical trench on the surface and 3D plane-layered model are presented.