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交错网格有限差分方法已经被广泛应用到数值模拟和地震波传播的研究中.传统交错网格有限差分方法中,一阶空间导数的高阶差分系数是通过Taylor级数展开求取的,这种表示空间导数的方法会导致数值频散的产生.本文针对时间二阶空间十阶交错网格有限差分算法,采用最小二乘法通过改变积分区间求取一系列一阶空间导数的差分系数,分析该差分系数和传统方法求取的差分系数的频散关系.选取效果最佳的最小二乘法进行数值模拟,并与传统方法相比较.数值频散分析和弹性波场模拟分析表明:介质弹性参数和离散参数相同的情况下,采用最佳积分区间的最小二乘法更能有效地压制数值频散,比Taylor级数展开法具有更高的数值模拟精度.
The staggered-grid finite difference method has been widely used in numerical simulation and seismic wave propagation.In the traditional finite difference method of staggered-grid method, the higher-order difference coefficients of first-order spatial derivatives are obtained by Taylor series expansion The method of representing the spatial derivative leads to the generation of numerical dispersion.In this paper, for the finite difference algorithm of 10-order staggered grid in the second-order space, the difference coefficient of a series of first-order spatial derivatives is obtained by changing the integral interval by the least squares method. The difference coefficient and the traditional method to obtain the dispersion coefficient of the dispersion relationship.The best choice of the least squares method for numerical simulation, and compared with the traditional method.Modial dispersion analysis and elastic wave field simulation shows that: the medium elastic parameters and In the case of the same discrete parameters, the least-squares method of the best integration interval can suppress the numerical dispersion more effectively, and has higher numerical simulation accuracy than the Taylor series expansion method.