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稳定性问题是数值求解波动方程的基本问题 .文中对三维横向各向同性介质中一阶弹性波方程交错网格高阶差分解法的稳定性进行了分析 ,给出了不同精度差分方程统一的稳定性条件 ,证明了三维TI介质中一阶弹性波方程交错网格高阶差分解法的稳定性由弹性波在X、Y、Z三个方向上的Courant数共同决定 .最后通过几种精度差分方程的稳定性条件 ,说明了这种一阶弹性波方程高阶差分解法具有高精度、高效率的特点 .
The stability problem is the basic problem for the numerical solution of the wave equation.This paper analyzes the stability of the staggered-grid high-order difference method for the first-order elastic wave equation in the three-dimensional transversely isotropic medium, and presents the uniform stability of the differential equation with different precision It is proved that the stability of the staggered-grid high-order difference method for the first-order elastic wave equation in 3D TI media is determined by the Courant numbers of elastic waves in three directions of X, Y and Z. Finally, The stability condition of the first-order elastic wave equation shows that the high-order difference method has high precision and high efficiency.