改进BISQ模型地震波场数值模拟中的边界处理
|
摘要
从改进BISQ模型双相介质所对应的一阶速度—应力运动方程出发,构建2×2N阶交错网格有限差分模拟算法,为了尽可能地减小或消除数值模拟中由人工边界引起的虚假反射,建立完全匹配层(PML)吸收边界的2×2N阶交错网格有限差分算法。详细地讨论了PML吸收边界条件的构建及其有限差分算法的实现。通过MATLAB编程进行波场模拟,将加入PML吸收边界、常规指数衰减吸收边界及未加吸收边界的3种数值模拟结果进行对比,论证PML吸收边界能十分有效地吸收边界反射。
Based on first-order velocity-stress equations of the reformulated BISQ model in double-phase media,the simulation algorithm of finite difference of 2-order time and 2N-order space staggered-grid was built.Meanwhile,in order to minimum effects caused by the artificial boundary in the numerical simulation,the construction of the perfectly matched layer(PML) absorbing boundary condition and the realization of the finite-difference algorithm were discussed in detail.The arithmetic was realized with MATLAB.Compared with the conventional decaying exponential absorbing boundary and the non-absorbing boundary,the PML boundary can more effectively attenuate reflections,which is supported by the wave field modeling.
Based on first-order velocity-stress equations of the reformulated BISQ model in double-phase media,the simulation algorithm of finite difference of 2-order time and 2N-order space staggered-grid was built.Meanwhile,in order to minimum effects caused by the artificial boundary in the numerical simulation,the construction of the perfectly matched layer(PML) absorbing boundary condition and the realization of the finite-difference algorithm were discussed in detail.The arithmetic was realized with MATLAB.Compared with the conventional decaying exponential absorbing boundary and the non-absorbing boundary,the PML boundary can more effectively attenuate reflections,which is supported by the wave field modeling.
引文
[1]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid(Part I):Low-frequency range[J].TheJournal of the Acoustical Society of America,1956,28(2):168-178.
[2]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid(Part II):Higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):179-191.
[3]DVORKIN J,NUR A.Dynamic poroelasticity:A unified modelwith the squirt and the Biot mechanisms[J].Geophysics,1993,58(4):524-533.
[4]DIALLO M S,APPEL E.Acoustic wave propagation insaturated porous media:reformulation of the Biot/Squirt flowtheory[J].Journal of Applied Geophysics,2000,44(4):313-325.
[5]LIU Y,SEN M K.A hybrid scheme for absorbing edgereflections in numerical modeling of wave propagation[J].Geophysics,2010,75(2):A1-A6.
[6]DAI N,VAFIDIS A,KANASEWICH E.Composite absorbingboundaries for the numerical simulation of seismic waves[J].Bulletin of the Seismological Society of America,1994,84(1):185-191.
[7]CLAYTON R,ENGQUIST B.Absorbing boundary conditionsfor acoustic and elastic wave equations[J].Bulletin of theSeismological Society of America,1977,67(6):1529-1540.
[8]ENGQUIST B,MAJDA A.Radiation boundary conditions foracoustic and elastic wave calculations[J].Communications onPure and Applied Mathematics,1979,32(3):313-357.
[9]夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件[J].地球物理学报,2004,47(1):132-136.XIA Fan,DONG Liang-guo,MA Zai-tian.Absorbing boundaryconditions in 3D elastic-wave numerical modeling[J].ChineseJournal of Geophysics,2004,47(1):132-136.
[10]王俊.基于改进BISQ模型的双相介质波场数值模拟方法研究[D].山东:中国石油大学(华东),2009:41-45.WANG Jun.Method study of wavefield numerical simulation intwo-phase medium based on the reformulated BISQ mechanism[D].Shandong:China University of Petroleum(East China),2009:41-45.
[11]CERJAN C,KOSLOFF D,KOSLOFF R,RESHEF M.Anonreflecting boundary condition for discrete acoustic andelastic wave equations[J].Geophysics,1985,50(4):705-708.
[12]BERENGER J P.A perfectly matched layer for the absorption ofelectromagnetic waves[J].Journal of Computational Physics,1994,114(2):185-200.
[13]CHEW W C,LIU Q H.Perfectly matched layers forelastodynamics:a new absorbing boundary condition[J].Journalof Computational Acoustics,1996,4(4):341-359.
[14]LIU Q H,TAO J P.The perfectly matched layer for acousticwaves in absorptive media[J].Journal of the Acoustical Societyof America,1997,102(4):2072-2082.
[15]ZENG Y Q,HE J Q,LIU Q H.The application of the perfectlymatched layer in numerical modeling of wave propagation inporoelastic media[J].Geophysics,2001,66(4):1258-1266.
[16]COLLINO F,TSOGKA C.Application of the perfectly matchedabsorbing layer model to the linear elastodynamic problem inanisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[17]王永刚,邢文军,谢万学,朱兆林.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):19-24.WANG Yong-gang,XING Wen-jun,XIE Wan-xue,ZHUZhao-lin.Study of absorbing boundary condition by perfectlymatched layer[J].Journal of China University of Petroleum:Edition of Natural Science,2007,31(1):19-24.
[18]赵海波,王秀明,王东,陈浩.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报,2007,50(2):581-591.ZHAO Hai-bo,WANG Xiu-ming,WANG Dong,CHEN Hao.Applications of the boundary absorption using a perfectlymatched layer for elastic wave simulation in poroelastic media[J].Chinese Journal of Geophysics,2007,50(2):581-591.
[19]熊章强,张大洲,秦臻,周文斌.瑞雷波数值模拟中的边界条件处理及模拟实例分析[J].中南大学学报:自然科学版,2008,39(4):824-830.XIONG Zhang-qiang,ZHANG Da-zhou,QIN Zheng,ZHOUWen-bin.Boundary conditions and case analysis of numericalmodeling of Rayleigh wave[J].Journal of Central SouthUniversity:Science and Technology,2008,39(4):824-830.
[20]李宁.完美匹配层理论及其在地震波场数值模拟中的应用[D].哈尔滨:中国地震局工程力学研究所,2006:46-49.LI Ning.The theory and the application of perfectly matchedlayer in the seismic wave simulation[D].Harbin:Institute ofEngineering Mechanics,China Earthquake Administration,2006:46-49.
[2]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid(Part II):Higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):179-191.
[3]DVORKIN J,NUR A.Dynamic poroelasticity:A unified modelwith the squirt and the Biot mechanisms[J].Geophysics,1993,58(4):524-533.
[4]DIALLO M S,APPEL E.Acoustic wave propagation insaturated porous media:reformulation of the Biot/Squirt flowtheory[J].Journal of Applied Geophysics,2000,44(4):313-325.
[5]LIU Y,SEN M K.A hybrid scheme for absorbing edgereflections in numerical modeling of wave propagation[J].Geophysics,2010,75(2):A1-A6.
[6]DAI N,VAFIDIS A,KANASEWICH E.Composite absorbingboundaries for the numerical simulation of seismic waves[J].Bulletin of the Seismological Society of America,1994,84(1):185-191.
[7]CLAYTON R,ENGQUIST B.Absorbing boundary conditionsfor acoustic and elastic wave equations[J].Bulletin of theSeismological Society of America,1977,67(6):1529-1540.
[8]ENGQUIST B,MAJDA A.Radiation boundary conditions foracoustic and elastic wave calculations[J].Communications onPure and Applied Mathematics,1979,32(3):313-357.
[9]夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件[J].地球物理学报,2004,47(1):132-136.XIA Fan,DONG Liang-guo,MA Zai-tian.Absorbing boundaryconditions in 3D elastic-wave numerical modeling[J].ChineseJournal of Geophysics,2004,47(1):132-136.
[10]王俊.基于改进BISQ模型的双相介质波场数值模拟方法研究[D].山东:中国石油大学(华东),2009:41-45.WANG Jun.Method study of wavefield numerical simulation intwo-phase medium based on the reformulated BISQ mechanism[D].Shandong:China University of Petroleum(East China),2009:41-45.
[11]CERJAN C,KOSLOFF D,KOSLOFF R,RESHEF M.Anonreflecting boundary condition for discrete acoustic andelastic wave equations[J].Geophysics,1985,50(4):705-708.
[12]BERENGER J P.A perfectly matched layer for the absorption ofelectromagnetic waves[J].Journal of Computational Physics,1994,114(2):185-200.
[13]CHEW W C,LIU Q H.Perfectly matched layers forelastodynamics:a new absorbing boundary condition[J].Journalof Computational Acoustics,1996,4(4):341-359.
[14]LIU Q H,TAO J P.The perfectly matched layer for acousticwaves in absorptive media[J].Journal of the Acoustical Societyof America,1997,102(4):2072-2082.
[15]ZENG Y Q,HE J Q,LIU Q H.The application of the perfectlymatched layer in numerical modeling of wave propagation inporoelastic media[J].Geophysics,2001,66(4):1258-1266.
[16]COLLINO F,TSOGKA C.Application of the perfectly matchedabsorbing layer model to the linear elastodynamic problem inanisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[17]王永刚,邢文军,谢万学,朱兆林.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):19-24.WANG Yong-gang,XING Wen-jun,XIE Wan-xue,ZHUZhao-lin.Study of absorbing boundary condition by perfectlymatched layer[J].Journal of China University of Petroleum:Edition of Natural Science,2007,31(1):19-24.
[18]赵海波,王秀明,王东,陈浩.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报,2007,50(2):581-591.ZHAO Hai-bo,WANG Xiu-ming,WANG Dong,CHEN Hao.Applications of the boundary absorption using a perfectlymatched layer for elastic wave simulation in poroelastic media[J].Chinese Journal of Geophysics,2007,50(2):581-591.
[19]熊章强,张大洲,秦臻,周文斌.瑞雷波数值模拟中的边界条件处理及模拟实例分析[J].中南大学学报:自然科学版,2008,39(4):824-830.XIONG Zhang-qiang,ZHANG Da-zhou,QIN Zheng,ZHOUWen-bin.Boundary conditions and case analysis of numericalmodeling of Rayleigh wave[J].Journal of Central SouthUniversity:Science and Technology,2008,39(4):824-830.
[20]李宁.完美匹配层理论及其在地震波场数值模拟中的应用[D].哈尔滨:中国地震局工程力学研究所,2006:46-49.LI Ning.The theory and the application of perfectly matchedlayer in the seismic wave simulation[D].Harbin:Institute ofEngineering Mechanics,China Earthquake Administration,2006:46-49.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心