谱元法波场模拟中网格质量影响的量化分析

Quantitative Analysis of Mesh Quality Impact on Spectral Element Method-based Wavefield Forward Modeling

本文旨在量化分析网格质量对谱元法波场正演模拟精度与收敛性的影响。研究首先通过理论计算,明确了网格歪斜度对拉格朗日多项式插值近似误差的影响,结果显示当网格歪斜度增加时,插值误差显著增大。在此基础上,对六种不同网格歪斜度的地质模型进行了谱元法地震波场正演模拟实验,实验结果显示:当网格剖分的歪斜度大于0.8时,模拟精度不受影响;歪斜度降至0.6时,吸收边界波场模拟开始出现不稳定;而歪斜度进一步降低至0.4及以下时,波场正演模拟出现严重不收敛现象。这些量化结果直接证明了网格质量对谱元法波场正演模拟的重要性,为网格质量评价和波场正演模拟精度、效率稳定性之间建立了可量化分析的桥梁,同时为优化网格剖分策略提供了科学依据。

The paper aims to quantitatively analyze the impact of mesh quality on the accuracy and convergence of spectral-element method(SEM)wavefield forward modeling.Theoretical calculations first clarified the influence of mesh skewness on the approximation error of Lagrange polynomial interpolation,revealing a significant increase in interpolation error with increasing mesh skewness.Subsequently,SEM seismic wavefield forward modeling experiments were conducted on six geological models with varying mesh skewness.The results indicate that when mesh skewness exceedes 0.8,simulation accuracy remaines unaffected;at a skewness of 0.6,simulation instability emerges in the absorbing boundary wavefield;and when skewness further decreases to 0.4 or less,severe non-convergence occurres in the wavefield forward simulation.These quantified results directly demonstrate the significance of mesh quality in SEM wavefield forward modeling,establishing a quantifiable bridge between mesh quality evaluation and accuracy,efficiency,and stability of forward modeling.Additionally,they provide a scientific basis for optimizing mesh generation strategies.