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采用任意偶数阶精度有限差分数值模拟方法,可以提高传统有限差分方法的精度。本文首先介绍了由泰勒级数展开得到的计算任意阶导数的任意偶数阶精度有限差分方法;然后,将此方法应用于双相各向异性介质中地震波传播数值模拟中。数值模拟结果表明,模拟精度随着差分精度阶数的提高而提高;为了平衡计算精度和计算效率之间的关系,得到合适的阶数、网格大小和时间步长是比较重要的;通过模拟观测到了四类波、震源点的静态模式、SV波波面尖角、反射波和透射波等。
Using any even-order finite-difference numerical simulation method can improve the accuracy of the traditional finite-difference method. In this paper, we firstly introduce the finite difference method of any even-order precision obtained from the expansion of Taylor series to calculate arbitrary order derivatives. Then, this method is applied to the numerical simulation of seismic wave propagation in two-phase anisotropic media. Numerical simulation results show that the simulation accuracy increases with the increase of the order of differential precision. In order to balance the accuracy of calculation with the calculation efficiency, it is more important to get the appropriate order, grid size and time step. Four types of wave were observed, the static mode of the source point, the sharp angle of the SV wave surface, the reflected wave and the transmitted wave.