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采用有限元法精确模拟复杂介质条件下的地震波场,一般采用三角单元,但在节点数相同的情况下,三角单元的计算精度不如矩形单元高,采用三角单元模拟复杂界面时,编制确定结构刚度矩阵非零元素位置的程序也较为麻烦。采用矩形单元离散含有倾斜或起伏界面的地质模型时,无法避免绕射噪声,若加密网格又会增加计算量。为此,本文基于任意四边形单元模拟声波的传播,在倾斜或起伏界面条件下,可以有效避免因离散引起的“阶梯状”界面,在不增加计算量以及内存占用的前提下,有效地消除离散绕射噪声。采用对角的集中质量矩阵代替一致质量矩阵,避免矩阵的求逆运算,从而提高显式有限元法的计算效率;对结构刚度矩阵采用紧凑存储格式,每一行需要存储的元素最多为5个,同时零元素不参与运算,既减少内存的占用,又极大地提高计算效率。
The finite element method is used to accurately simulate the seismic wavefield under complex media conditions. Generally, the triangular elements are used. However, when the number of nodes is the same, the calculation accuracy of the triangular elements is not as high as that of the rectangular elements. When the triangular elements are used to simulate complex interfaces, The procedure for locating non-zero elements in the matrix is also troublesome. When rectangular units are used to discretize geologic models with sloped or undulating interfaces, it is impossible to avoid diffraction noise, which in turn increases computational complexity. Therefore, this paper simulates the propagation of acoustic wave based on arbitrary quadrilateral elements, and effectively avoids “ladder-like” interface due to discreteness under the condition of inclined or undulating interface. Without increasing the amount of computation and memory occupation, Eliminate discrete diffraction noise. The diagonal centralized mass matrix is used instead of the consistent mass matrix to avoid the matrix inversion operation, so as to improve the computational efficiency of the explicit finite element method. For the compact stiffness matrix of the structure, the maximum number of elements to be stored is 5, At the same time zero elements do not participate in computing, both to reduce the memory footprint, but also greatly improve the computational efficiency.