Title

Numerical simulation of 2D seismic wavefield using fifth-point eighth-order super compact difference scheme

单位

(1.油气资源与勘探技术教育部重点实验室(长江大学),湖北武汉430100;2.中石化重庆涪陵页岩气勘探开发有限公司,重庆408014)

Organization

(1.Key Laboratory of Exploration Technologies for Oil and Gas Resources,Ministry of Education,Yangtze University,Wuhan 430100,China;2.Sinopec Chongqing Fuling Shale Gas Exploration and Production Corporation,Chongqing 408014,China)

摘要

首先将迎风机制引入五点八阶超紧致有限差分(CCD8)格式,得到五点七阶迎风超紧致(UCCD7)格式,并对两种格式进行数值频散分析和精度分析;其次建立了二阶声波方程的位移场时间四阶离散格式,将五点CCD8格式和五点UCCD7格式分别应用于位移场空间导数的求取,并分析这两种格式的稳定性条件;最后基于PML边界条件,将上述两种格式分别应用于声波方程的均匀介质、水平层状介质及Marmousi模型的数值模拟和波场特征分析及对比。研究结果表明:相较于普通紧致差分,五点CCD8格式具有小截断误差、高模拟精度、低数值频散、高稳定性、所需网格点数少的优点;引入迎风机制后,声波方程的五点UCCD7格式稳定性得到进一步提高;模型试算的结果验证了五点CCD8格式适用于复杂介质的数值模拟,模拟精度和计算效率都高。

Abstract

In this study the fifth-point eighth-order combined compact difference scheme (CCD8) and fifth-point seventh-order upwind combined compact difference scheme (UCCD7) were used in a numerical simulation based on acoustic and elastic wave equations.Based on Taylor series expansion and acoustic wave equation,a fourth-order discrete scheme for the displacement field was established.The CCD8 and UCCD7 were used to calculate the spatial derivative of the displacement field,and the accuracy,dispersion,and stability of the two schemes were analyzed.Finally,using the PML boundary conditions,the two formats were tested on uniform medium,horizontal layered medium,and Marmousi model.The results showed that compared with normal compact difference,CCD8 has smaller truncation error,higher simulation precision,lower numerical dispersion,higher stability,and requires fewer grid points;the introduction of windward mechanism could improve the stability of CCD7.The numerical simulation results verified that the CCD8 scheme and UCCD7 scheme are practical and effective.

关键词：

五点八阶超紧致差分; 五点七阶迎风超紧致差分; 数值模拟; 数值频散; 稳定性条件 ;

Keywords:

fifth-point eighth-order combined compact difference scheme; fifth-point seventh-order
upwind super combined compact difference scheme; numerical simulation; numerical
dispersion; stability condition ;

基金项目

国家自然科学基金项目(41504102)和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(K2017-24)共同资助。

DOI

10.3969/j.issn.1000-1441.2019.02.003

二维地震波场的五点八阶超紧致有限差分数值模拟