任意偶数阶精度交错网格声波方程数值模拟

Numerical Modeling of Acoustic Wave Equation base on Staggered-grid any Even-order Accurate

以波动理论为理论基础,利用泰勒级数展开推导出了一阶应力-速度声波方程组的空间任意偶数阶精度交错网格差分格式。选用衰减边界条件,进行了边界效果对比及差分精度选取测试。结果表明差分精度越高,频散越弱,数值模拟的效果越好。应用空间八阶、时间二阶精度差分格式,实现了各向同性介质模型的声波方程数值模拟。正演模拟结果可以清晰地反映出声波波场中波传播的运动学和动力学特征,可推广应用于三维声波高精度波场正演模拟中。

Based on the wave theory,starting from the establishment of one-order stress-velocity wave equation,even-order accurate difference schemes of any order derivatives can be derived from the expansion of Taylor series. There are many kinds of boundary conditions and the damping boundary condition was used here. The effectiveness of boundary condition was compared and the best difference accuracy was tested at the same time. The results show that the higher accuracy of difference brings less frequency dispersion and better numerical modeling effect. Choosing temporal second order accuracy and a eighth order spatial accuracy,the numerical modeling of one-order stress-velocity wave equation in isotropic medium was achieved. The characters of dynamics and kinematics of wave in acoustic wave-field can be reflected from the results,for which it can be extended to three-dimensional scalar acoustic high-precision forward numerical simulation.