双相各向异性介质中偶数阶精度有限差分数值模拟

摘要

To improve the accuracy of the conventional finite-difference method, finite-difference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any even-order accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.%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.