双相介质瑞雷面波有限差分正演模拟
详细信息 本馆镜像全文    |  推荐本文 | | 获取馆网全文
摘要
为了研究双相介质瑞雷面波的形成机制及传播规律,促进瑞雷面波资料处理方法的发展。文章根据弹性波动方程,采用交错网格有限差分算法,对二维各向同性弹性介质做解析解与数值解的对比,在此基础上,将PML吸收边界条件,改进的镜像法应用于双相介质波动方程中,并作了稳定性分析,对双相介质水平层状、起伏分界面等典型模型瑞雷面波及体波在内的全波场进行研究。结果表明:基于弹性介质解析解与数值解的对比,在误差接受范围内,研究双相介质是可行的;把稍作改进的镜像法应用于双相介质中,能够有效地处理瑞雷面波自由边界问题;通过详细分析双相介质瑞雷面波及体波在内的全波场的信息,对以双相介质为基础的地震波勘探有一定的指导作用。
In order to study the mechanism and propagation of Rayleigh surface wave in biphasic media and promote the development of data-processing method of Rayleigh surface wave,the authors applied finite difference method with staggered grids to simulate the 2D isotropic elastic media based on the elastic wave equation,and made a comparison between the analytical and numerical solutions.On such a basis,the PML absorbing boundary condition and improved image method can be applied to the two-phase medium wave equation to simulate the typical media model including horizontal layer and undulating interface,analyze the full wave information including the Rayleigh surface wave and body wave,and make a stability analysis.The results show that,on the basis of the comparison between the numerical solution and the analytical solution of the elastic media within the acceptable range of the error,the study of biphasic medium is feasible.The slight improvement of the image method can be applied to biphasic media to deal with free boundary condition problem of the Rayleigh surface wave effectively.The detailed analysis of the full wave field information of biphasic media including the Rayleigh surface wave and body wave shows that it has played a guiding role in the seismic exploration on the basis of biphasic media.
引文
[1]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅰ.low-frequency range[J].Journal of the Acoustical Society of America,1956,28(2):168-178.
    [2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.higher frequency range[J].Journal of the Acoustical Society of America,1956,28(2):179-191.
    [3]Biot M A.Generalized theory of acoustic propagation in porous dissipative media[J].Journal of the Acoustical Society of America,1962,34(9A):1254-1261.
    [4]Biot M A.Generalized boundary condition for multiple scatter in acoustic reflection[J].Journal of the Acoustical Society of America,1968,44(6):1616-1622.
    [5]Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms[J].Geophysics,1993,58(4):524-533.
    [6]Dvorkin J,Mavko G,Nur A.Squirt flow in fully saturated rocks[J].Geophysics,1995,60(1):97-106.
    [7]Stoll R D,Bautista E O.Using the Biot theory to establish a baseline geoacoustic model for seafloor sedments[J].Continental Shelf Research,1998,18(14-15):1839-1857.
    [8]Stoll R D.Velocity dispersion in water-saturated granular sediment[J].Journal of the Acoustical Society of America,2002,111(2):785-793.
    [9]杨顶辉,张中杰,滕吉文,等.双相各向异性研究、问题与应用前景[J].地球物理学进展,2000,15(2):7-21.
    [10]Zhu X,Mc Mechan G A.Numerical simulation of seismic responses of poroelastic reservoirs using biot theory[J].Geophysics,1991,56(3):328-339.
    [11]Siamak,Hassanzadeh.Acoustic modeling in fluid-saturated porous media[J].Geophysics,1991,56(4):424-435.
    [12]牛滨华,吴有校,孙春岩.裂隙含流体、气体各向异性介质波场数值模拟[J].长春地质学院学报,1994,24(4):454-460.
    [13]刘仲一,韩其玉.多孔介质声波传播[J].石油大学学报:自然科学版,1994,18(6):30-35.
    [14]Dai N,Vafidis E R,Kanasewich.Wave propagation in heterogeneous,poriusmedia:a velocity-stress,finite-difference method[J].Geophysics,1995,60(2):327-340.
    [15]石玉梅.流体饱和多空隙介质中弹性波运动方程的解—伪谱法[J].西南石油学院学报,1995,17(1):34-37.
    [16]赵成刚,杜修力,崔杰.固体、流体多相孔隙介质中的波动理论及其数值模拟的进展[J].力学进展,1998,28(1):83-92.
    [17]Borge A,Jose M,Carcione.Numerical simulation of the Biot slow wave in water-saturated nivelsteiner sandstone[J].Geophysics,2001,66(3):890-896.
    [18]Stephane G,Michel D.Seismoelectric wave conversions in porous media:Field measurements and transfer function analysis[J].Geophysics,2001,66(5):1417-1430.
    [19]杨宽德,杨顶辉,王书强.基于Biot-Squirt方程的波场模拟[J].地球物理学报,2002,45(6):853-861.
    [20]杨宽德,杨顶辉,王书强.基于横向各向同性BISQ方程的弹性波传播数值模拟[J].地震学报,2002,24(6):599-606.
    [21]孟庆生,何樵登,朱建伟,等.基于BISQ模型双相各向同性介质中地震波数值模拟[J].吉林大学学报:地球科学版,2003,33(2):217-221.
    [22]刘洋,魏修成.双相各向异性介质中弹性波传播有限元方程及数值模拟[J].地震学报,2003,25(2):154-162.
    [23]Liu Y,Li C C.Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method[J].Acta Seismologica Sinica:English Edition,2000,13(2):143-150.
    [24]王东,张海澜,王秀明.部分饱和孔隙岩石中声波传播数值研究[J].地球物理学报,2006,49(2):524-532.
    [25]裴正林.三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报:自然科学版,2006,30(2):16-20.
    [26]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.
    [27]程冰洁,李小凡,徐天吉.非均匀介质中交错网格高阶有限差分数值模拟[J].物探化探计算技术,2006,28(4):294-298.
    [28]Berenger J P.Three-dimensional perfectly matched layer for the absorption of electromagnetic waves[J].Comp.Phys,1996,127:363-379.
    [29]Chew W C,Liu Q H.Perfectly matched layers for elastodynamics:A new absorbing boundary condition[J].Journal of Computational Acoustics,1996,4(4):341-359.
    [30]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elasticdynamic problem in anisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
    [31]Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media[J].Geophysics,2001,66(4):1258-1266.
    [32]Festa G,Nielsen S.PML absorbing boundaries[J].Bull.Seis.Soc.Am.,2003,93(2):891-903.
    [33]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34.
    [34]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):308-315.
    [35]李景叶,陈小宏.TI介质地震波场数值模拟边界条件处理[J].西安石油大学学报:自然科学版,2006,21(4):20-23.
    [36]Aki K,Richards P G.Quantitative seismology:theory and methods[J].W.H.Freeman&Co.San Francisco,1980.
    [37]Mittet R D.Free-surface boundary conditions for elastic staggeredgrid modeling schemes[J].Geophysics,2002,67(5):1616-1623.
    [38]Xu Y X,Xia J H,Miller R D.Numerical investigation of implementation of air-earth boundary by acoustic-elastic boundary approach[J].Geophysics,2007,72(5):147-153.
    [39]马在田,曹景忠,王家林,等.计算地球物理学概论[M].上海:同济大学出版社,1997:20-27.

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