非均匀弹性介质中旋转交错网格有限差分与任意高阶间断有限元地震波场模拟方法研究
详细信息 本馆镜像全文    |  推荐本文 | | 获取馆网全文
摘要
复杂介质中的地震波数值模拟对于地震勘探非常重要.实际应用中经常遇到介质参数剧烈变化的情况,必须选择合适的数值方法进行正演,使波场模拟精度和计算效率满足要求.本文研究了旋转交错网格有限差分法与任意高阶间断有限元法在非均匀弹性介质中波场模拟的精度与计算效率,分析了界面两侧介质参数相对变化量以及界面倾角对上述两种方法数值模拟结果的影响.对于水平界面,界面两侧介质参数一定范围内的改变对旋转交错网格有限差分法的振幅精度和相位精度没有影响;在介质参数存在强反差的情况下,任意高阶间断有限元法需要使用高阶多项式基函数来达到较高的相位精度.有限元法的相位精度优于有限差分法,但需要更多的计算量.对于倾斜界面,当单位波长内含有14个网格点时,界面倾角的变化对旋转交错网格有限差分法的振幅精度及相位精度没有影响,且其精度与任意高阶间断有限元法的精度相接近.
Numerical modeling of seismic wavefield in complex media plays an important role in exploration geophysics.In some seismic numerical applications we have to simulate wave propagation with sharp medium discontinuities.The rotated staggered grid(RSG) finite difference(FD) method and the arbitrary high-order derivatives discontinuous Galerkin(ADER-DG) finite element(FE) method are both developed to solve the problem of strong material heterogeneities.In this paper we compared the RSG FD scheme with the ADER-DG FE scheme on their behaviors at high contrast discontinuities.We simulate wave propagation in two models,one is a two-layer model with flat interface,and the other with a dipping interface.In the first model,when we change the ratio of the material parameters in the first layer to the parameters in second layer,the envelop and phase misfits of the RSG FD scheme change little;the ADER-DG FE scheme needs to use a high-order polynomial basis functions to get small phase misfits with strong material heterogeneities.The FE scheme has advantage over the FD method on phase misfits,but it needs a high CPU effort.In the second model,when we change the angle of the dipping interface,the envelop and phase misfits of the RSG FD scheme change little with 14 grid points per wavelength according to the dominant frequency.
引文
Berg P,If F,Nielsen P,et al.1994.Analytical reference solutions:Advanced seismic Modeling[A].Helbig K,ed.Modeling the Earth for Oil Exploration[M].Pergamon Press,421-427.
    Cohen G,Fauqueux S.2000.Mixed finite elements with masslumping for the transient wave equation[J].Journal of Computational Acoustics,8(1):171-188.
    Cao J,Gai Z X,Zhang J,et al.2004.A comparative study on seismic wave methods for multi-layered media with irregular interfaces Part 1:irregular topography problem[J].Chinese J.Geophys.(in Chinese),47(3):495-503.
    Dormy E,Tarantola A.1995.Numerical simulation of elastic wave propagation using a finite volume method[J].Journal of Geophysical Research,100(B2):2123-2133.
    Dong L G,Ma Z T,Cao J Z,et al.2000.A staggered-grid highorder difference method of one-order elastic wave equation[J].Chinese J.Geophys.(in Chinese),43(3):411-419.
    Fornberg B.1998.A practical guide to pseudospectral methods[M]:Cambridge:Cambridge University Press.
    He Y F,Sun W J,Fu L Y.2013.Comparison of boundary element method and finite-difference method for simulating seismic wave propagation in complex media[J].Progress in Geophys.(in Chinese),28(2):664-678,doi:10.6038/pg20130215.
    Kaser M,Dumbser M.2006.An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes-I.The two-dimensional isotropic case with external source terms[J].Geophysical Journal International,166(2):855-877.
    Kaser M,Hermann M,de la Puente J.2008.Quantitative accuracy analysis of the discontinuous Galerkin method for seismic wave propagation[J].Geophys.J.Int.,173(3):990-999
    Kelly K R,Ward R W,Treitel S,et al.1976.Synthetic seismograms;a finite-difference approach[J].Geophysics,41(1):2-27.
    Kristekova M,Kristek J,Moczo P,et al.2006.Misfit criteria for quantitative comparison of seismograms[J].Bulletin of the Seismological Society of America,96(5):1836-1850.
    Kummer B,Behle A,Dorau F.1987.Hybrid modeling of elasticwave propagation in two-dimensional laterally inhomogenous media[J].Geophysics,52(6):765-771.
    Liu H L,Chen K Y,Yang W.et al.2010.Numerical modelling of P-and S-wave field separation with high-order staggered-grid finite-difference scheme[J].Progress in Geophys.(in Chinese),25(3):877-884,doi:10.3969/j.issn.1004-2903.2010.03.021.
    Muir F,DellingerJ,Etgen J,et al.1992.Modeling elastic fields across irregular boundaries[J].Geophysics,57(9):1189.
    Moczo P,Krislek J,Vavrycuk V,et al.2002.3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities[J].Bulletin of the Seismological Society of America,92(8):3042-3066.
    Moczo P,Kristek J,Galis M,et al.2011.3-D finite-difference,finite-element,discontinuous-Galerkin and spectral-element schemes analysed for their accuracy with respect to P-wave to Swave speed ratio[J].Geophysical Journal International,187(3):1645-1667.
    Patera A T.1984.A spectral element method for fluid dynamics:laminar flow in a channel expansion[J].Journal of Computational Physics,54(3):468-488.
    Pi H M,Jiang X Y,Liu C,et al.2009.Three methods of wave equation forward modeling and comparision[J].Progress in Geophys.(in Chinese),24(2):391-397,doi:10.3969/j.issn.1004-2903.2009.02.004.
    Podgornova O,Lisitsa V.2010.Accuracy analysis of finitedifference staggered-grid numerical schemes for elastic-elastic and fluid-elastic interfaces[C].//80th Annual Meeting,Society of Exploration Geophysicists.Expanded Abstracts,3087-3091
    Saenger E H,Gold N,Shapiro S A.2000.Modeling the propagation of elastic waves using a modified finite-difference grid[J].Wave Motion,31(1):77-92.
    Tessmer E.1995.3-D seismic modelling of general material anisotropy in the presence of the free surface by a Chebyshev spectral method[J].Geophysical Journal International,121(2):557-575.
    Virieux J.1984.SH-wave propagation in heterogeneous media;velocity-stress finite-difference method[J].Geophysics,49(11):1933-1942.
    Yin W,Yin X Y,Wu G C,et al.2006.The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation[J].Chinese J.Geophys.(in Chinese),49(2):561-568,doi:10.3321/j.issn:0001-5733.2006.02.032.
    Zahradnik J,Moczo P,Hron F.1993.Testing four elastic finitedifference schemes for behavior at discontinuities[J].Bulletin of the Seismological Society of America,83(1):107-129.
    曹军,盖增喜,张坚,等.2004.用于不规则界面多层介质的地震波方法比较研究:不规则地形问题[J].地球物理学报,47(3):495-503.
    董良国,马在田,曹景忠,等.2000.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,43(3):411-419.
    何彦峰,孙伟家,符力耘.2013.复杂介质地震波传播模拟中边界元法与有限差分法的比较研究[J].地球物理学进展,28(2):664-678,doi:10.6038/pg20130215.
    刘洪林,陈可洋,杨微,等.2010.高阶交错网格有限差分法纵横波波场分离数值模拟[J].地球物理学进展,25(3):877-884.doi:10.3969/j.issn.1004-2903.2010.03.021.
    皮红梅,蒋先艺,刘财,等.2009.波动方程数值模拟的三种方法及对比[J].地球物理学进展,24(2):391-397,doi:10.3969/j.issn.1004-2903.2009.02.004.
    殷文,印兴耀,吴国忱,等.2006.高精度频率域弹性波方程有限差分方法及波场模拟[J].地球物理学报,49(2):561-568,doi:10.3321/j.issn:0001-5733.2006.02.032.

版权所有:© 2021 中国地质图书馆 中国地质调查局地学文献中心