基于M-PML边界的Lebedev网格起伏地表正演模拟方法及稳定性分析

贴体网格作为一种"边界拟合网格",能改善传统有限差分处理起伏地表时由阶梯状网格存在所产生的虚假绕射。此外,完全匹配层(PML)技术被证明是一种能够有效消除虚假反射的重要边界条件,但采用自由地表模拟面波时,传统PML易产生不稳定现象。为实现起伏地表自由边界条件下稳定的地震波场模拟,发展一种基于弹性介质的全交错-Lebedev网格有限差分方法,并将边界条件扩展为多轴完全匹配层(M-PML)。在实现算法的基础上,通过模型试算验证新方法的正确性;并对比几种不同完全匹配层技术的稳定性差异,解释PML边界产生不稳定的机制。正演模拟结果表明,M-PML在处理起伏地表面波模拟中有更好的稳定性。

Lebedev grid finite-difference modeling for irregular free-surface and stability analysis based on M-PML boundary condition

Body-fitted grid is usually termed as "boundary conforming grid", which can eliminate artifacts caused by staircase approximation of irregular free surface in classical finite-difference method. In addition, perfectly matched layer (PML) absorbing boundary is approved to be an efficient method to suppress spurious edge reflections. When modeling Rayleigh waves with the existence of free-surface, however, the classical PML algorithm may become unstable. In order to obtain stable seismic wave simulation with an irregular free-surface, this paper proposes a full staggered grid (FSG)-Lebedev grid finite-difference method in elastic media, and extends the boundary condition to multiaxial PML (M-PML). Numerical simulations demonstrate the validity of the proposed method. The stability of the two perfectly matched layer techniques is compared and the instability mechanism of PML is discussed. The numerical results suggest preferred stability of the M-PML technique over the classical PML algorithm.