含方形凹陷半无限非均匀介质波动问题FDM模拟

FDM Simulation of Wave Motion in a Semi-infinite Inhomogeneous Medium with a Rectangular Depression

摘要:

采用规则网格有限差分方法对二维平面弹性波动方程进行差分离散,得到相应的弹性波动方程的有限差分方程,再将弹性波动方程的差分格式与吸收边界、自由边界的离散形式结合形成弹性波动方程有限差分方程解决问题的主体,将其应用于含方形凹陷半无限非均匀介质的模型中进行数值模拟,得到此离散化模型中不同时刻不同节点的位移值。针对具体算例,运用上述方法结合科学计算软件MATLAB和结果后处理软件DIFEM ISOLINE PLOTER得到不同时刻的水平方向位移等值线图与接收器测量点处的合成位移记录,讨论非均匀介质、吸收边界、方形凹陷等对波动特性的影响。

Abstract:

Using the finite difference method,the two-dimensional elastic wave equation is processed to obtain the finite difference equation.Then,the differential elastic wave equation format is combined with the absorbing boundary and the discrete form of the free boundary.The elastic wave equation finite difference equation is formed to solve the problem.Using the finite difference equation,the displacement on different nodes can be obtained at different times for the rectangle-shaped depression of a semi-infinite inhomogeneous medium.Using the finite difference equation of the two-dimensional elastic wave equation combined with the scientific computation software,MATLAB,and the post-processor software,DIFEM ISOLINE PLOTER,the displacement isoline of the rectangle-shaped depression of the semi-infinite inhomogeneous medium in the x direction can be obtained for different times.The effect of the inhomogeneous media,absorbing boundary,and the rectangle-shaped depression on the wave characteristics is analyzed numerically.