王周, 李朝晖, 龙桂华, 高琴, 赵家福. 求解弹性波有限差分法中自由边界处理方法的对比[J]. 工程力学, 2012, 29(4): 77-83.
引用本文: 王周, 李朝晖, 龙桂华, 高琴, 赵家福. 求解弹性波有限差分法中自由边界处理方法的对比[J]. 工程力学, 2012, 29(4): 77-83.
WANG Zhou, LI Zhao-hui, LONG Gui-hua, GAO Qin, ZHAO Jia-fu. COMPARISON AMONG IMPLEMENTATIONS OF FREE-SURFACE BOUNDARY IN ELASTIC WAVE SIMULATION USING THE FINITE-DIFFERENCE METHOD[J]. Engineering Mechanics, 2012, 29(4): 77-83.
Citation: WANG Zhou, LI Zhao-hui, LONG Gui-hua, GAO Qin, ZHAO Jia-fu. COMPARISON AMONG IMPLEMENTATIONS OF FREE-SURFACE BOUNDARY IN ELASTIC WAVE SIMULATION USING THE FINITE-DIFFERENCE METHOD[J]. Engineering Mechanics, 2012, 29(4): 77-83.

求解弹性波有限差分法中自由边界处理方法的对比

COMPARISON AMONG IMPLEMENTATIONS OF FREE-SURFACE BOUNDARY IN ELASTIC WAVE SIMULATION USING THE FINITE-DIFFERENCE METHOD

  • 摘要: 自由边界条件在计算方法中的数值表征是地震波模拟中的一个重要内容,表征的有效性直接关系到所得波场能否代表地表介质特性的真实响应。该文评估了交错网格有限差分法中5 种常用自由边界处理方法:直接法、应力镜像法、改进应力镜像法、横向各向同性介质替换法和声学边界替换法,并与有限元法模拟结果进行了对比,波形曲线直观比较及波幅比与相关系数定量比较显示横向各向同性介质替换法与有限法模拟结果一致性最好。进一步的层状介质模型弹性波数值模拟结果表明:横向各向同性介质替换法的精度和可靠性最高,能真实表征地表介质中的地震波传播。

     

    Abstract: Representation of free-surface boundary condition in numerical calculations is an important aspect for seismic wave simulation. The effectiveness of numerical representation directly relates to whether the wave field can represent the true response of free-surface medium characteristics. Five common implementations of free-surface boundary used in the staggered-grid finite-difference method were evaluated, including the direct method, the stress image method, the improved stress image method, the transversely isotropic medium approach and the acoustic-elastic boundary approach, and a comparison with the finite-element method was also conducted. Simulation results of the transversely isotropic medium approach and the finite-element method are consistent best in visual comparison of waveform curve and quantitative comparison of amplitude ratio and correlation coefficient. Further numerical simulation results of elastic wave in layered medium model show that the transversely isotropic medium approach is the most accurate and reliable one which could represent seismic wave propagation in free-surface medium.

     

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