Starting with the model of the Biot two-phase media theory,the authors set up the 2D/3C velocity-stress elastic wave equation of the two-phase isotropic media and the finite difference time domain scheme through deduction.The wave field simulation is based on the two-phase homogeneous and inhomogeneous isotropic media using the traditional staggered-grid method and the rotated staggered-grid method.The results show that the rotated staggered grid difference scheme performs perfectly for the two-phase isotropic media.A comparison between rotated stagger-grid and traditional stagger-grid demonstrates that the finite difference algorithm of rotating staggered-grid is more stable and can avoid errors caused by interpolation,and hence the rotated staggered-grid difference scheme is a numerical simulation of seismic wave field method with a strong effectiveness.
林朋, 卢勇旭. 传统和旋转交错网格有限差分在双相介质中的模拟对比[J]. 物探与化探, 2016, 40(1): 203-208.
LIN Peng, LU Yong-Xu. The simulation contrast in the two-phase media between the traditional and rotated staggered grid. Geophysical and Geochemical Exploration, 2016, 40(1): 203-208.
[1] Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid,I:Low-frequency range[J].The Journal of the Acoustic Society of America,1956a,28:168-178.[2] Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid,Ⅱ:High-frequency range[J].The Journal of the Acoustic Society of America,1956b,28:179-191.[3] Biot M A.Mechanics of deformations and acoustic propagation in porous media[J].J Appl Phys,1962a,33:1482-1498.[4] Schmitt P D.Acoustic multipole logging in the transversely isotropic poroelastic formations[J].The Journal of the Acoustic Society of America,1989,86(6):2397-2421.[5] Crampin S,Yedlin M.Shear-wave singularities of wave propagation in anisotropic media[J].J Geophys,1981,49:43-46.[6] 王尚旭.双相介质中弹性波问题有限元数值解和AVO问题[D].北京:中国石油大学(北京),1990.[7] 牟永光,裴正林.三维复杂地震数值模拟[M].北京:石油工业出版社,2005.[8] 刘洋,李承楚.双相各向异性介质中弹性波传播特征研究[J].地震学报,1999,21(4):367-373.[9] 杨顶辉.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,2002,45(4):575-583.[10] 裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J].石油物探,2005,44(4):308-316.[11] 裴正林.双相各向异性介质弹性波传播交错网格高阶有限差分法模拟[J].石油地球物理勘探,2006,41(2):137-143.[12] 孙卫涛,杨慧珠.双相各向异性介质弹性波场有限差分正演模拟[J].固体力学学报,2004,25(1):21-28.[13] 孙瑞艳.TTI介质旋转交错网格有限差分及其组合边界条件[D].东营:中国石油大学(华东),2010.[14] Saenger E. H,Gold N,Shapiro S A.Modeling the propagation of elastic waves using a modified finite-difference grid[J].Wave Motion,2010,31:77-92.[15] 王亚妮,李长江,李庆春.旋转交错网格VTI介质波场模拟与波场分解[J].物探化探计算技术,2015,37(2):198-202.[16] 李长江,李庆春,王亚妮.旋转交错网格TTI介质波场模拟与波场分解[J].物探与化探,2015,39(3):553-557.[17] Bohlen T,Saenger E H.Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves[J].Geophysical Prospecting,1995,43(6):805-829.