摘要
首次将五点八阶超紧致有限差分格式(CCD8)用于黏弹介质声波方程的数值模拟中,并对该格式进行了频散分析和精度分析,与普通紧致差分格式进行比较。随后,根据泰勒级数展开黏滞声波方程,建立了位移场时间二阶离散格式,将CCD8用于对位移场空间导数的求取,且对CCD8格式进行稳定性研究。最后将CCD8格式运用于均匀介质模型以及水平层状介质模型以及Marmousi模型的数值模拟和波场特征分析及对比中。研究结果表明:①CCD8与CD8相比,具有更小的截断误差、更高的模拟精度以及低数值频散的优点;②CCD8具有较高稳定性;③采用完全匹配层(perfectly matched layer,PML)对人工边界进行处理后对均匀介质、水平层状介质以及Marmousi模型进行黏滞声波方程的数值模拟,发现模拟效果不错,从而验证了CCD8的实用性和有效性性。
The five point eight order combined compact difference scheme is used in the numerical simulation of viscoelastic acoustic wave equation.According to the Taylor series expansion,the two-order discrete scheme of the viscoelastic acoustic equation is established,then CCD8 are used to calculate the spatial derivative of the displacement field.And stability of the CCD8 are analyzed.At last,CCD8 are used for numerical simulation in homogeneous medium model and horizontally layered medium model and Marmousi model.The results show that:①CCD8 has the advantages of smaller truncation error and higher simulation precision and lower numerical dispersion than CD8;②CCD8 has high stability;③Based on the processing of artificial boundary reflection using perfectly matched layer boundary condition,the numerical simulation and wave field analysis of viscoelastic acoustic wave equation are carried out using homogeneous medium model,horizontally layered medium model and Marmousi model show that the seismic wave field is clear,which verified the practicability and validity of CCD8.
作者
周诚尧
汪勇
桂志先
于晓东
ZHOU Cheng-yao;WANG Yong;GUI Zhi-xian1];YU Xiao-dong(Key Laboratory of Exploration Technologies for Oil and Gas Resources,Ministry of Education,Yangtze University 1,Wuhan 430100,China)
出处
《科学技术与工程》
北大核心
2020年第1期54-63,共10页
Science Technology and Engineering
基金
国家自然科学基金(41504102)
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(K2018-01)
关键词
五点八阶超紧致差分
黏弹介质声波方程
数值频散
稳定性条件
数值模拟
five point eight order combined compact difference scheme
viscoelastic media
acoustic wave equation
numerical simulation
numerical dispersion
stability condition
