二维弹性波频率域17点差分格式及正演模拟  

A 17-point difference scheme for 2D frequency-domain elastic wave and modeling

作　　者：岳晓鹏[1,2] 白超英[1] 岳崇旺[1] 

机构地区：[1]长安大学地质工程与测绘学院,陕西西安710064 [2]许昌学院数学与统计学院,河南许昌461000

出　　处：《物探与化探》2017年第2期299-305,共7页Geophysical and Geochemical Exploration

基　　金：国家青年自然科学基金(41504090);中央高校基金(310826161021)

摘　　要：为优化二维各向同性介质中弹性波频率域正演时阻抗矩阵的结构,减小正演所需内存,提高正演效率,在25点差分格式的基础上进行适当的简化,得到了二维弹性波频率域17点差分格式。该格式重新计算了弹性波中偏微分项和加速项的差分算子,减少了计算过程中的网格节点需求,构造了优化阻抗矩阵后的频率域正演矩阵方程;推导了纵波和横波相速度的频散公式,给出了不同泊松比条件下的频散曲线,得到了相速度误差控制范围±1%时每一横波波长内网格数需求。通过对比频散曲线和数值模拟时得到的波场快照及检波点处U、V分量,验证了17点差分格式与25点差分格式相比,具有稍严格的网格间距需求、相当的计算精度、略少的计算时间和更小的阻抗矩阵带宽等特点。The 2D elastic wave frequency domain 17-point difference scheme is obtained based on the simplified 25-point difference scheme so as to optimize the structure of impedance matrix,reduce required memory and improve efficiency in 2D isotropic media forward.This scheme recalculates partial differential operators in the elastic wave equation,reduces the grid node in calculation process,and constructs the forward matrix equation with optimized impedance matrix. The P-wave and S-wave velocity dispersion formulae are derived,the dispersion curves of different Poisson＇s ratio are given,and the grid number requirement in each horizontal wave length is given with phase velocity error range being ±1%.The frequency dispersion curve and numerical simulation of the wave field snapshots and seismic records show that the 17-point difference scheme has slightly strict grid spacing requirements,similar accuracy,slightly less computation time and smaller impedance matrix bandwidth in comparison with 25-point difference scheme.

关 键 词：弹性波方程 有限差分 频率域 数值模拟 

分 类 号：P631.4[天文地球—地质矿产勘探]