Comparison of different free-surface boundary conditions for Rayleigh waves finite-difference modeling
Yuan Shichuan1, Song Xianhai1,2, Cai Wei1, Hu Ying1, Lu Peng1
1. Institute of Geophysics and Geomatics, China University of Geosciences(Wuhan), Wuhan, Hubei 430074, China; 2. Hubei Subsurface Multi-scale Imaging Key Laboratory, Wuhan, Hubei 430074, China
Abstract:The free-surface boundary condition is a key factor of Rayleigh waves modeling.Under the condition of two-dimensional isotropic elastic medium and based on standard staggered-grid high-order finite difference algorithm,we simulate numerically the four most used free-surface boundary conditions:the stress image method (SIM),the modified stress image method (MSIM),the transversely isotropic medium substitution approach (MS),and the acoustic-elastic boundary approach (AEA).We compare their snapshot,waveform curves,and dispersion curves in a homogeneous half-space model.Under the same conditions,snapshots generated by four methods obey laws of physics.Their fit errors of analytical solutions and numerical solutions decrease with the increase of the grid subdivision.The stability and the numerical simulation accuracy of the SIM and AEA are significantly higher than that of MSIM and MS.For simple models,SIM and AEA achieve results with higher precision than the other two.However,AEA obtains the best results,which means it is the most suitable for the Rayleigh waves modeling.
Xia J H,Miller R D,Park C B.Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves.Geophysics,1999,64(3):691-700.
[2]
Park C B,Miller R D,Xia J H.Multichannel analysis of surface waves (MASW).Geophysics,1999,64(3):800-808.
[3]
董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856-864.Dong Liangguo,Ma Zaitian,Cao Jingzhong.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation.Chinese Journal of Geophysics,2000,43(6):856-864.
[4]
周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567-573.Zhou Zhusheng,Liu Xiliang,Xiong Xiaoyu.Finite difference modelling of Rayleigh surface wave in elastic media.Chinese Journal of Geophysics,2007,50(2):567-573.
[5]
熊章强,张大洲,秦臻等.瑞雷波数值模拟中的边界条件及模拟实例分析.中南大学学报(自然科学版),2008,39(4):824-830.Xiong Zhangqiang,Zhang Dazhou,Qin Zheng et al.Boundary conditions and case analysis of numerical modeling of Rayleigh wave.Journal of Central South University (Science and Technology Edition),2008,39(4):824-830.
[6]
邵广周,李庆春,吴华.基于波场数值模拟的瑞利波频散曲线特征及各模式能量分布.石油地球物理勘探,2015,50(2):306-315.Shao Guangzhou,Li Qingchun,Wu Hua.Dispersion curves and mode energy distribution of Rayleigh wave based on wavefield numerical simulation.OGP,2015,50(2):306-315.
杜启振,白清云,李宾.横向各向同性介质优化差分系数法地震波场数值模拟.石油地球物理勘探,2010,45(2):170-176.Du Qizhen,Bai Qingyun,Li Bin.Optimized difference coefficient method seismic wave field numerical simulation in vertical transverse isotropic medium.OGP,2010,45(2):170-176.
[9]
Wang L M,Luo Y H,Xu Y X.Numerical investigation of Rayleigh-wave propagation on topography surface.Journal of Applied Geophysics,2012,86(11):88-97.
[10]
高静怀,何洋洋,马逸尘.黏弹性与弹性介质中Rayleigh面波特性对比研究.地球物理学报,2012,55(1):207-218.Gao Jinghuai,He Yangyang,Ma Yichen.Comparison of the Rayleigh wave in elastic and viscoelastic media.Chinese Journal of Geophysics,2012,55(1):207-218.
[11]
杨宇,黄建平,雷建设等.Lebedev网格黏弹性介质起伏地表正演模拟.石油地球物理勘探,2016,51(4):698-706.Yang Yu,Huang Jianping,Lei Jianshe et al.Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface.OGP,2016,51(4):698-706.
[12]
张煜,徐义贤,夏江海等.含流体孔隙介质中面波的传播特性及应用.地球物理学报,2015,58(8):2759-2778.Zhang Yu,Xu Yixian,Xia Jianghai et al.Characteristics and application of surface wave propagation in fluid-filled porous media.Chinese Journal of Geophy-sics,2015,58(8):2759-2778.
[13]
Yuan S Y,Wang S X,Sun W J et al.Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation.Exploration Geophysics,2014,45(2):94-104.
[14]
裴正林.任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟.石油地球物理勘探,2004,39(6):629-634.Pei Zhenglin.Staggered-grid high-order finite-difference numerical simulation of elastic wave equation for any irregular surface.OGP,2004,39(6):629-634.
[15]
Bohlen T,Saenger E H.Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves.Geophysics,2006,71(4):T109-T115.
[16]
Aki K,Richards P G.Quantitative Seismology:Theory and Methods.W H Freeman,New York,1980.
[17]
Levander A R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,53(11):1425-1436.
[18]
Robertsson J O A.A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography.Geophysics,1996,61(6):1921-1934.
[19]
Crase E.High-order (space and time) finite-difference modeling of the elastic wave equation.SEG Technical Program Expanded Abstracts,1990,9:987-991.
[20]
Hestholm S,Ruud B O.3-D finite-difference elastic wave modeling including surface topography.Geophysical Prospecting,1994,42(5):371-390.
[21]
Kosloff D,Kessler D,Filho A Q et al.Solution of the equations of dynamic elasticity by a Chebychev spectral method.Geophysics,1990,55(6):734-748.
[22]
王秀明,张海澜.用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法.中国科学G辑,2004,34(5):481-493.Wang Xiuming,Zhang Hailan.Modeling the seismic wave in the media with irregular free interface by the finite-difference method.Science in China (Series G),2004,34(5):481-493.
[23]
Boore D.Finite difference methods for seismic wave propagation in heterogeneous materials//Methods in Computational Physics:Advances in Research and Applications,Academic Press,London,1972,11:1-37.
[24]
Zahradnik J,Priolo E.Heterogeneous formulations of elastodynamic equations and finite-difference schemes.Geophysical Journal International,1995,120(3):663-676.
[25]
Graves R W.Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences.Bulletin of Seismological Society of America,1996,86(4):1091-1106.
[26]
Mittet R.Free-surface boundary conditions for elastic staggered-grid modeling schemes.Geophysics,2002,67(5):1616-1623.
[27]
Xu Y,Xia J,Miller R D.Numerical investigation of implementation of air-earth boundary by acoustic-elastic boundary approach.Geophysics,2007,72(5):SM147-SM153.
[28]
王周,李朝晖,龙桂华等.求解弹性波有限差分法中自由边界处理方法的对比.工程力学,2012,29(4):77-83.Wang Zhou,Li Chaohui,Long Guihua et al.Comparison among implementations of free-surface boundary in elastic wave simulation using the finite-difference method.Engineering Mechanics,2012,29(4):77-83.
[29]
Berg P,If F,Nielsen P et al.Analytical reference solutions,Advanced seismic modeling//Modeling the Earth for Oil Exploration (Helbig K Ed).Pergamon Press,New York,1994,421-427.
[30]
凡友华,刘家琦,肖柏勋.计算瑞利波频散曲线的快速矢量传递算法.湖南大学学报(自然科学版),2002,29(5):25-30.Fan Youhua,Liu Jiaqi,Xiao Boxun.Fast vector-transfer algorithm for computation of Rayleigh wave dispersion curves.Journal of Hunan University (Natural Sciences Edition),2002,29(5):25-30.
[31]
Luo Y H,Xia J H,Miller R D et al.Rayleigh-wave dispersive energy imaging using a high-resolution linear Radon transform.Pure and Applied Geophysics,2008,165(5):903-922.
[32]
夏江海,高玲利,潘雨迪等.高频面波方法的若干新进展.地球物理学报,2015,58(8):2591-2605.Xia Jianghai,Gao Lingli,Pan Yudi et al.New findings in high-frequency surface wave method.Chinese Journal of Geophysics,2015,58(8):2591-2605.