二维弹性波频率域15点差分格式及正演模拟  

15-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] YUE Xiao-peng;BAI Chao-ying;YUE Chong-wang(College of Geology Engineering and Geomatics, Chang＇ an University, Xi＇ an 710064, China;School of Mathematics and Statistics, Xuchang University, Henan Xuchang 461000, China)

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

出　　处：《地球物理学进展》2017年第5期2132-2139,共8页Progress in Geophysics

基　　金：国家科技重大专项子课题(2011ZX05024-001-03);国家青年科学自然科学基金(41504090);中央高校基金(310826161021)联合资助

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15点差分格式.利用该格式重新计算了弹性波方程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简单模型数值模拟时得到的波场快照、检波点处速度分量及单炮记录,验证了15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、更少的计算时间和更小的阻抗矩阵带宽等特点.最后,利用复杂模型数值模拟对本方法的适应性进行了验证.The 2 D elastic wave frequency domain 15-point difference scheme is obtained based on the simplified 25-point difference scheme,to optimize the structure of impedance matrix,to reduce required memory and to improve efficiency in 2 D isotropic media forward. This scheme recalculates partial differential operators in the elastic wave equation,reduces the grid node in calculation process, constructs the forward matrix equation with optimized impedance matrix. The P-wave and S-wave velocity dispersion formulas are derived,the dispersion curves of different Poisson＇s ratio are given,the grid number requirement in each horizontal wave length are given with phase velocity error range± 1%. The dispersion curves and the wave field snapshots,seismic records and single-shot record of simple model show that,the 15 point difference scheme have slightly strict grid spacing requirements,and similar accuracy,smaller computation time and smaller impedance matrix bandwidth, compared with 25-point difference scheme. Finally,the applicability of the proposed method is verified by numerical simulations of complex models.

关 键 词：弹性波方程 有限差分 频率域 频散曲线 数值模拟 

分 类 号：P631[天文地球—地质矿产勘探]