Study on the Stability of Finite Difference Solution of Visco-Elastic Wave Equations

• 责任者：Sun Chengyu (College of Geo-Resource and Information ; China University of Petroleum ; Qingdao 266555 ; China) ; Xiao Yunfei
• 刊名：Acta Seismologica Sinica
• 出版年：2010
• 卷期：32(2)
• 关键词：弹性波 ; elastic waves ; 波动方程 ; wave equation
• 页码：p.147-156
• 图表：3 illus., 1 table, 16 refs.
• 分类号：0500
• issnNo：ISSN0253-3782
• isbnNo：CN11-2021/P

Based on the theory of seismic waves and constitutive relations of visco-elastic models, the stability problem of finite difference scheme with rectangular grids for two visco-elastic models is analyzed. Expressions of stability condition under arbitrary spatial accuracy for Kelvin-Voigt and Maxwell models are derived. With an approximation of medium quality factor Q≥5, a simplified expression is developed and some digital models are given to show the validity of theoretical results. Influence of velocity, frequency, size of grid, differential coefficients, as well as quality factor, on the stability condition is summarized. Finally, the working condition of the simplified stability expression is given by means of its error analysis.