地震波数值模拟中优化的通量校正传输方法
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摘要
为了有效提高地震波正演数值模拟精度,提出了一种优化的通量校正传输方法,即在每一步时间递推过程中,沿坐标轴方向和对角线方向均引入通量校正参数进行波场校正处理,以高频散的均匀介质地震模拟波场为例,研究对比了不同中心网格有限差分近似阶数、传统的FCT方法和优化的FCT方法校正得到的地震波场效果。数值计算结果表明,传统的FCT方法容易产生虚假波场,而优化的FCT方法可以削弱或消除这些假波动,并指出结合高差分阶数和应用优化的FCT方法可以更好地提高数值模拟记录的信噪比。
In order to improve forward numerical simulation precision of seismic wave,this paper puts forward an optimized flux-corrected transport method,the flux corrected parameters are introduced along the coordinate and diagonal directions at each step of the numerical iteration to correct the wave field,and takes the seismic wave field simulation with high-dispersion as example,and compares the corrected seismic wave results among different centered-grid finite-difference approximating order and conventional FCT method and optimized FCT scheme.The numerical results show that: conventional FCT method can easily introduce false wave field which could be reduced or removed by the proposed method.At the same time,the author points out numerical precision of the records can be greatly improved by combining the methods of high-order difference and optimized FCT scheme together.
In order to improve forward numerical simulation precision of seismic wave,this paper puts forward an optimized flux-corrected transport method,the flux corrected parameters are introduced along the coordinate and diagonal directions at each step of the numerical iteration to correct the wave field,and takes the seismic wave field simulation with high-dispersion as example,and compares the corrected seismic wave results among different centered-grid finite-difference approximating order and conventional FCT method and optimized FCT scheme.The numerical results show that: conventional FCT method can easily introduce false wave field which could be reduced or removed by the proposed method.At the same time,the author points out numerical precision of the records can be greatly improved by combining the methods of high-order difference and optimized FCT scheme together.
引文
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[43]朱生旺,魏修成.波动方程非规则网格任意阶精度差分法正演[J].石油地球物理勘探,2005,40(2):149-153.
[44]孟凡顺,李清仁,张绍亮,等.非均匀各向同性介质中声波传播的盒式积分法模拟[J].大庆石油地质与开发,2005,24(5):99-102.
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[54]陈可洋.完全匹配层吸收边界条件研究[J].石油物探,2010,49(5):472-477.
[55]陈可洋.声波和弹性波叠后逆时深度偏移[J].天然气勘探与开发,2010,33(3):20-21,49.
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[2]牟永光.储层地球物理学[M].北京:石油工业出版社,1996.
[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[J].地球物理学报,2000,43(6):856-864.
[4]Higdon R L.Absorbing boundary conditions for elastic waves[J].Geophysics,1991,56(2):231-241.
[5]Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophysics,1978,42(6):1 099-1 110.
[6]Liao Z P,Wong H L,Yang B P,et al.A transmitting boundary for transient wave analysis[J].Scientia Sinica(SeriesA),1984,27(10):1 063-1 076.
[7]杨微,陈可洋.加权吸收边界条件的优化设计[J].石油物探,2009,48(3):244-246.
[8]陈可洋,杨微.优化的三维地震波旁轴近似吸收边界条件[J].勘探地球物理进展,2009,32(3):179-181,206.
[9]李文杰,魏修成,刘洋.声波正演中一种新的边界条件-双重吸收边界条件[J].石油物探,2004,6:32-35.
[10]Berenger J P,A perfectly matched layer for the absorption of electromagnetic waves[J].J Comput.Phys,1994,11(4):185-200.
[11]陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79.
[12]Hastings F D,Schneider J B,Broschat S L,Application of the perfectly matched layer(PML)absorbing boundary condition to e-lastic wave propagation[J].Journal Acoustical Society of America,1996,100(5):3 061-3 069.
[13]陈明阳,于荣金.色散媒质中的理想匹配层吸收边界及其误差分析[J].光学学报,2002,22(4):50-55.
[14]邢丽.地震声波数值模拟中的吸收边界条件[J].上海第二工业大学学报,2006.23(4):16-22.
[15]朱兆林,马在田.各向异性介质中二阶弹性波方程模拟PML吸收边界条件[J].大地测量与地球动力学,2007.27(5):50-53.
[16]陈可洋.边界吸收中镶边法的评价[J].中国科学院研究生院学报,2010,27(2):170-175.
[17]张显文,韩立国,黄玲,等.基于递归积分的复频移PML弹性波方程交错网格高阶差分法[J].地球物理学报,2009,52(7):1 800-1 807.
[18]Cerjan C,Kosloff D,Kosloff R,et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[19]邵振海,洪伟,周健义.透射边界条件的统一理论[J].中国科学(E辑),2002,30(1):64-69.
[20]颜力.频域吸收边界条件的构造理论[J].信息与电子工程,2003,1(1):31-36.
[21]罗大清,吴律,宋炜.加权方向校正及插值预测吸收边界条件的三维波动方程叠前数值模拟[J].石油地球物理勘探,1999,34(3):275-284.
[22]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟[J].中国海洋大学学报,2005,35(1):43-48.
[23]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[J].石油地球物理勘探,2004,39(6):629-634.
[24]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478.
[25]王秀明,张海澜,王东.利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播[J].地球物理学报,2003,46(6):842-849.
[26]陈可洋,杨微,刘洪林,等.二阶弹性波动方程高精度交错网格波场分离数值模拟[J].物探与化探,2009,33(6):700-704.
[27]裴正林,牟永光.非均匀介质地震波传播交错网格高阶有限差分法模拟[J].石油大学学报,2003,27(6):17-21.
[28]周辉,刘斌,徐世浙,等.二维各向异性介质中三分量波动方程有限元法模拟[J].青岛海洋大学学报,2000,30(4):688-672.
[29]Semblat J F,Brioist J J.Efficiency of higher order finite elements for the analysis of seismic wave propagation[J].Journal ofSound and Vibration,2000,231(2):460-467.
[30]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.
[31]Gazdag J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(6):854-859.
[32]Kosloff D D,Baysal E,Forward modeling by a Fourier method.[J].Geophysics,1982,47(10):1 402-1 421.
[33]Forberg B,The pseudospectral method:Comparisons with finite difference for the elastic wave equation[J].Geophysics,1987.52(4):483-501.
[34]傅旦丹,何樵登.正交各向异性介质地震弹性波场的伪谱法正演模拟[J].石油物探,2001,40(3):8-14.
[35]马永旺,詹正彬,顾汉明.伪谱法地震波传播数值模拟[J].石油物探,2001,40(2):42-48.
[36]缪林昌.井间地震Hartley变换法正演模拟与偏移[J].石油物探,1994,33(4):70-77.
[37]Saatcilar P,Ergintav S,Canitez N.The use of the Hartley transform in Geophysical application[J],Geophysics,1990,55(10):1 488-1 495.
[38]孙建国.王雪秋.利用有限正弦和有限余弦变换模拟地震波场:声波方程[J].吉林大学学报(地球科学版),2006,36(1):108-112.
[39]Zhou B,GREENHALGHS.Seismic scalar wave equation modeling by a convolutional differentiator[J].Bulletin of the Seismo-logical Society of America,1992,82(1):289-303.
[40]Zhou B,GREEHALGH S A,ZHE J.Numerical seismogram computations for inhomogeneous media using a short,variablelength convolutional differentiator[J].Geophysical Prospecting,1993,41(6):751-766.
[41]张中杰,腾吉文,杨顶辉.声波与弹性波数值模拟中的褶积微分算子法[J].地震学报,1996,18(1):63-69.
[42]程冰洁,李小凡.2.5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,28(4):1099-1105.
[43]朱生旺,魏修成.波动方程非规则网格任意阶精度差分法正演[J].石油地球物理勘探,2005,40(2):149-153.
[44]孟凡顺,李清仁,张绍亮,等.非均匀各向同性介质中声波传播的盒式积分法模拟[J].大庆石油地质与开发,2005,24(5):99-102.
[45]张厚柱,张宇,孙正.高维波动方程数值模拟的隐式分裂有限差分格式[J].石油物探,2007,46(6):595-597.
[46]裴正林.地震波标量方程的小波自适应网格优先差分数值模拟[J].石油地球物理勘探,2005,40(3):267-272.
[47]陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236.
[48]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现[J].地球物理学报,2002,45(5):533-545.
[49]陈可洋.地震波数值模拟中差分近似的各向异性分析[J].石油物探,2010,49(1):19-22.
[50]董良国,李培明.地震波传播数值模拟中的频散问题[J].天然气工业,2004,24(6):53-56.
[51]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略[J].地球物理学进展,2005,20(1):58-65.
[52]宁刚,熊章强,陈持.波动方程有限差分正演模拟误差来源分析[J].物探与化探,2008,32(2):203-206.
[53]陈可洋.宽频双程走时计算方法及其波场照明分析[J].勘探地球物理进展,2010,33(4):270-274.
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