二维粘弹介质五点八阶超紧致有限差分声波方程数值模拟

本文首次将五点八阶超紧致有限差分格式(CCD8)用于粘弹介质声波方程的数值模拟中。此文根据泰勒级数展开粘滞声波方程,建立了位移场时间二阶离散格式,将CCD8用于对位移场空间导数的求取。然后,对CCD8格式进行稳定性研究,频散的压制效果对比分析,及截断误差对比。将CCD8格式运用于均匀介质模型以及水平层状介质模型中进行数值模拟,最后运用于对Marmousi模型的数值模拟中。研究结果表明：(1)CCD8与普通八阶紧致差分相比,具有更小的截断误差、更高的模拟精度以及低数值频散的优势；(2)CCD8具有较高稳定性；(3)采用完全匹配层(PML)对人工边界进行处理后对均匀介质、含有层状介质以及Marmousi模型进行粘弹声波方程的数值模拟,发现模拟效果不错,从而验证了方法的实用性和有效。

Numerical Simulation Of 2D Viscoelastic Acoustic Wave Equation Used Five Point Eight Order Combined Compact Difference Scheme

The numerical simulation of seismic wave field has important significance in the study of the nature of seismic wave propagation. In this paper, the five point eight order combined compact difference scheme is used in the numerical simulation of viscoelastic acoustic wave equation. According to the Taylor series expansion, the two-order discrete scheme of the viscoelastic acoustic equation is established, then CCD8 are used to calculate the spatial derivative of the displacement field. Then analyze CCD8 stability, use Fourier method for suppressing effect of dispersion contrast analysis, and analyze truncation error. At last,CCD8 are used for numerical simulation in homogeneous medium model and horizontally layered medium model and Marmousi model. The results show that: (1)CCD8 has the advantages of smaller truncation error and higher simulation precision and low numerical dispersion than normal order compact difference;(2)CCD8 with high stability;(3) Based on the processing of artificial boundary reflection using perfectly matched layer boundary condition, the numerical simulation and wave field analysis of viscoelastic acoustic wave equation are carried out using homogeneous medium model, horizontally layered medium model and Marmousi model show that the seismic wave field is clear, which verified the practicability and validity of CCD8.