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稳定性问题是地震波数值模拟的一个重要问题.基于地震波传播理论,从黏弹介质本构方程出发,对矩形网格下不同黏弹模型波动方程有限差分解的稳定性进行了理论分析,导出了Kelvin-Voigt黏弹模型和Maxwell黏弹模型在任意空间差分精度下稳定性条件的表达式;给出了品质因子Q≥5时的简化式,并通过数值算例验证了理论研究结论的正确性;总结了地震波速度、频率、空间网格大小、差分系数以及品质因子与稳定性条件的关系;通过误差分析给出了近似公式的使用条件.
The stability problem is an important issue in numerical simulation of seismic waves.Based on the theory of seismic wave propagation, from the constitutive equation of viscoelastic medium, the stability of finite difference solutions of wave equation with different viscoelastic model under rectangular grid is theoretically analyzed, and Kelvin -Voigt viscoelastic model and Maxwell viscoelastic model in arbitrary space differential accuracy of the stability of the expression; given the quality factor Q ≥ 5 when the simplified formula, and the numerical examples to verify the theoretical conclusions of the correctness; Summarized the relationship between seismic wave velocity, frequency, space grid size, difference coefficient, quality factor and stability condition; and gave the conditions of using approximate formula by error analysis.