波动方程有限差分法中的频散与假频分析  

Analysis on dispersion and alias in finite-difference solution of wave equation.

作　　者：孙成禹[1] 宫同举[1] 张玉亮[1] 张文颖[1] 

机构地区：[1]中国石油大学地球资源与信息学院,山东省东营市257061

出　　处：《石油地球物理勘探》2009年第1期43-48,共6页Oil Geophysical Prospecting

基　　金：国家973计划(2007CB209605);国家863计划(2007AA060502)资助课题

摘　　要：波动方程有限差分运算中不可避免地会出现数值频散现象,从而严重干扰了波场正演模拟结果。通过对波动方程有限差分解法中频散问题的理论研究,并就空间采样间隔、传播距离及速度因素等对频散的影响进行了定量分析,指出了由频散导致的假频现象及其主要特点,并利用数值算例和模型正演验证了研究结论:①频散使得高频分量传播速度变慢,而零频率分量的传播速度等于地层真实速度;②在抑制频散方面,采用8阶精度差分格式能够达到精度与效率的统一,使用震源子波的峰值频率对应的波长内不应少于7个采样点;③离散差分使得折叠频率降低,对于低速地层,应特别注意对频散的压制和防止假频产生。The finite-difference operation of wave equation appears inevitably the phenomenon of numeric dispersion, seriously interfering forward simulation results of wavefield. Through theoretical study of dispersion issue in finite-difference solution of wave equation and quantitative analysis on the influence of spatial sampling interval, propagating distance and velocity on dispersion, the paper pointed out the alias phenomenon resulted from dispersion and main characters and proved the studied conclusions by numeric case and model forward simulation: the dispersion makes the velocity of high-frequency component become slow and propagating velocity of zero-frequency component equals to the true velocity of strata; in aspect of suppression of dispersion, using 8th-order precision finite-difference format can reach the unification of precision with efficiency and it should not less 7 samples within the wavelength relative to used peak frequency of source wavelet; discrete difference makes folding frequency ahead and it should pay more attention to suppression of dispersion and prevention of alias production for the strata with lower velocity.

关 键 词：波动方程 有限差分 频散 折叠频率 假频 

分 类 号：P631.4[天文地球—地质矿产勘探] TN011[天文地球—地质学]