基于波动方程有限差分数值模拟及FCT消频散分析  

Finite Difference Numerical Simulation of Wave Equation and Its Dispersion Analysis of FCT Elimination

作　　者：赵威 李伟波 桂志先[1] 周游[1] 于晓东 ZHAO Wei;LI Weibo;GUI Zhixian;ZHOU You;YU Xiaodong(Key Laboratory of Exploration Technologies for Oil and Gas Resources, Ministry of Education, Yangtze University, Wuhan, Hubei 430100, China)

机构地区：[1]长江大学油气资源与勘探技术教育部重点实验室,湖北武汉430100

出　　处：《中国锰业》2018年第2期187-191,共5页China Manganese Industry

摘　　要：随着地震勘探与开发的不断进行,正演数值模拟仍然扮演着重要的角色。在基于波动方程的有限差分数值模拟过程中,往往会由于网格离散化而不可避免地产生数值频散现象。而数值频散一般会给模拟结果带来严重影响,因此减弱或消除这种频散问题显得尤为必要。在前人的研究前提下,基于各向同性介质(均匀介质、层状介质)的地震波方程采用交错网格有限差分进行数值模拟,并引进通量校正传输的方法(FCT)来进行对比分析数值频散问题。通过对不同情况下波场快照的分析对比,可以得到该方法可以有效的消除(网格离散)数值频散现象,特别对于采样间隔较大的网格模拟尤为突出,可以大大改善数值模拟的结果,是一种有效的消频散技术。With the continuous development of seismic exploration and development,numerical simulation still plays an important role. In the process of finite difference numerical simulation based on wave equation,numerical dispersion is often caused by grid discretization. However,numerical dispersion can have a serious effect on the simulation results. So,it is necessary to weaken or eliminate this problem. On the premise of forefathers＇ research,this article is based on isotropic medium（ homogeneous medium,layered media）,the seismic wave equation of the staggered grid finite difference numerical simulation,and the introduction of flux correction method of transport（ FCT has grown） for comparison and analysis the numerical dispersion. Through the analysis of wave field snapshot under different conditions,we can get the method to effectively eliminate the（ discrete） grid numerical dispersion phenomenon. Especially for sampling interval especially larger grid simulation,it can greatly improve the result of numerical simulation,as is a kind of effective dispersion elimination technique.

关 键 词：正演模拟 波动方程 交错网格 有限差分 FCT频散分析 

分 类 号：P631.4[天文地球—地质矿产勘探]