声波方程数值模拟矩形网格有限差分系数确定法  

Acoustic wave equation modeling with rectangle grid finite difference operator and its linear time space domain solution

作　　者：梁文全[1] 王彦飞[2] 杨长春[2] 

机构地区：[1]龙岩学院资源工程学院,福建龙岩364000 [2]中国科学院地质与地球物理研究所中国科学院油气资源研究重点实验室,北京100029

出　　处：《石油地球物理勘探》2017年第1期56-62,共7页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目(41325016;91630202);福建省自然科学基金(2016J05104);龙岩学院博士科研启动基金(LB2014010)资助

摘　　要：压制数值频散是有限差分方法的关键问题之一。目前压制数值频散的方法大多假设不同方向空间偏导数的空间步长相同,导致算法精度低,计算效率低。为此,提出使用线性方法压制声波方程矩形网格有限差分算子的数值频散,并进行了稳定性分析、频散分析和数值模拟。通过频散分析和数值模拟,验证了本文方法能够有效压制矩形网格有限差分数值频散,相较于泰勒展开方法和最小二乘方法,线性方法计算有限差分系数的效率更高,可以替代传统的正方形有限差分网格和相应的系数用于声波方程数值延拓。Finite difference methods are widely used in wave equation modeling,reverse time migration,and full waveform inversion.Suppressing the grid dispersion is one of the key points for finite difference approaches.Many current methods determining the finite difference operators assume that the intervals are identical for the spatial partial derivative in different directions.However,to use finite difference operators with different spatial intervals in different directions is more suitable for wave field extrapolation.Therefore,we use a liner method in this paper to determine the finite difference coefficients with rectangle grid.Through dispersion analysis and numerical simulations,the proposed method is proved to be more accurate and efficient.Therefore,the rectangle grid finite difference operator and its linear solution might be applied in wave equation extrapolation instead of conventional methods. © 2017, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.

关 键 词：声波模拟 时间—空间域 有限差分格式 矩形网格 数值频散 

分 类 号：P631[天文地球—地质矿产勘探]