基于辛格式离散奇异褶积微分算子的弹性波场模拟

摘要

本文发展了基于辛格式离散奇异褶积微分算子(SDSCD)的保结构方法模拟弹性波场,求解弹性波动方程时,引入辛差分格式进行时间离散,采用离散奇异褶积微分算子进行空间离散.相比于传统的伪谱方法,该方法提高了计算精度和稳定性.数值结果表明SDSCD方法可以有效地抑制数值频散,为解决大尺度、长时程地震波场模拟问题提供了合适的数值方法.%In this paper, we introduce a structure-preserving method based on symplectic discrete singular convolution differentiator (SDSCD) for simulating elastic wave fields. In the method presented for solving elastic wave equations, physical space is discretized by singular convolution differentiator, whereas a symplectic difference scheme is used for the time discretization. The computational accuracy and stability of this method have been greatly improved compared with traditional pseudo-spectral method. Numerical results suggest the SDSCD algorithm can suppress effectively numerical dispersion, and it is suitable for modeling the large-scale and long-term seismic wave propagation.