CAJ | 학술논문

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.
은정성문제시지진파수치모의적일개중요문제. 기우지진파전파이론, 종점탄개질본구방정출발, 대구형망격하불동점탄모형파동방정유한차분해적은정성진행료이론분석, 도출료Kelvin-Voigt점탄모형화Maxwell점탄모형재임의공간차분정도하은정성조건적표체식; 급출료품질인자Q≥5시적간화식, 병통과수치산례험증료이론연구결론적정학성; 총결료지진파속도、빈솔、공간망격대소、차분계수이급품질인자여은정성조건적관계; 통과오차분석급출료근사공식적사용조건.
The stability problem is a very important aspect in seismic wave numerical simulation. 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.