一阶声波方程时间四阶精度差分格式的伪谱法求解  

Pseudo spectrum method of first-order acoustic wave equation finite-difference schemes with fourth-order time difference accuracy

作　　者：唐怀谷 何兵寿[1] 

机构地区：[1]中国海洋大学海底科学与探测技术教育部重点实验室,山东青岛266100

出　　处：《石油地球物理勘探》2017年第1期71-80,共10页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目(41174087);"863"项目(2013AA064201)资助

摘　　要：在地震波场数值模拟中,伪谱法不产生由空间网格离散引起的数值频散,而常规伪谱法用于求解时间二阶精度差分格式时,则会受到时间差分精度较低的影响而产生数值频散。本文基于一阶声波方程,提出将差分格式的时间差分精度增至四阶,并利用伪谱法求解,从而在避免由空间网格离散引起的数值频散的同时,降低由时间网格离散引起的数值频散。此外,与时间二阶精度差分格式伪谱法相比,时间四阶精度差分格式伪谱法的稳定性条件更为宽松,进而可通过增大时间网格步长提高计算效率。In seismic numerical simulation,pseudo spectrum method is unaffected by numerical dispersion results from difference of space derivative.However,the regular pseudo spectrum method is applied in difference scheme with second-order accuracy of time difference,which means the method is still affected by numerical dispersion result from time difference with low accuracy.We prove that finite-difference schemes with fourth-order accuracy of time difference can suppress dispersion result from time difference.Furthermore,stability condition is looser when pseudo spectrum method applied in finite-difference schemes with fourth-order accuracy of time difference than in finite-difference schemes with second-order accuracy of time difference,which means calculation efficiency can be improved by enlarging time step. © 2017, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.

关 键 词：一阶声波方程 数值模拟 伪谱法 时间高阶差分格式 数值频散 稳定性条件 

分 类 号：P631[天文地球—地质矿产勘探]