基于紧致交错差分格式的二维声波及黏滞声波方程数值模拟
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P631

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油气资源与勘探技术教育部重点实验室(长江大学)开放基金资助项目,项目编号 K2018-01.


Numerical simulation of two dimensional acoustic and viscous acoustic wave equations based on compact staggered difference scheme
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    摘要:

    针对常规网格差分难以适用于地震波场数值模拟中复杂介质的问题,本文首次将紧致交错有限差分格式应用于粘滞声波方程的数值模拟研究并同声波方程的数值模拟进行了模拟精度、频散关系和稳定性分析等方面的比较。理论研究结果表明:①当差分精度相同时,紧致交错网格所需节点数要少于常规的中心差分和交错差分格式,计算效率更高;②同常规的交错差分与中心差分格式相比,紧致差分的截断误差更小,数值频散也更低,能够适用于粗网格计算;③差分精度相同情况下时进行数值模拟,紧致交错格式的所需要的时间网格更小,稳定性条件也更为严格;④紧致交错差分格式在PML条件下,能够对边界反射进行有效地吸收。最后,对均匀、水平层状介质以及Marmousi模型进行了粘滞声波方程的数值模拟和波场特征分析,实验结果阐述了本文方法对于复杂介质的数值模拟的适应性和有效性,并具有较高的模拟精度及计算效率。

    Abstract:

    To solve the problem of the conventional grid difference scheme is difficult to be applied to the complex medium in the numerical simulation of seismic wave field. This paper utilizes the compact staggered finite difference scheme in the numerical simulation of the viscous acoustic wave equation for the first time. Furthermore, we compared the simulation results with acoustic equations in simulation accuracy, dispersion relation, and stability analysis. The theoretical results illustrated that: ① To achieve the same difference accuracy, the number of nodes required by compact staggered grid is less than conventional central difference and staggered difference schemes. Moreover, the computational efficiency of compact staggered finite difference schemes is higher. ② Compared with the conventional staggered and central difference schemes, the truncation error of the compact difference is minor and with lower numerical dispersion. So it is applicable for coarse grid calculation. ③ Under the same difference accuracy, the time grid size of the compact difference scheme is smaller, and the stability condition is stricter. ④ The Perfect matching layer can effectively absorb boundary reflection using the compact staggered difference scheme . Finally, the numerical simulation of the viscous acoustic wave equation and the analysis of wave field characteristics were conducted on the homogeneous medium model, horizontally layered medium model, and Marmousi model. The experimental results demonstrate the practicability and effectiveness of the proposed method for the numerical simulation of complex media, with high simulation accuracy and computational efficiency.

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邓光校,鲍羽,汪勇. 基于紧致交错差分格式的二维声波及黏滞声波方程数值模拟[J]. 科学技术与工程, 2023, 23(21): 8966-8979.
Deng Guangxiao, Bao Yu, Wang Yong. Numerical simulation of two dimensional acoustic and viscous acoustic wave equations based on compact staggered difference scheme[J]. Science Technology and Engineering,2023,23(21):8966-8979.

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  • 收稿日期:2022-09-22
  • 最后修改日期:2023-06-28
  • 录用日期:2023-01-30
  • 在线发布日期: 2023-07-25
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