准规则网格高阶有限差分法非均质弹性波波场模拟
|
摘要
为精确描述弹性波在非均匀介质中的传播,本文提出一种准规则网格高阶有限差分地震正演模拟方法。该法是将位移分量交错排列,做中心差分运算,在数学上等价于交错网格法,并给出了震源加载方法、边界条件和稳定性条件。与传统交错网格法和规则网格法相比,该方法在模拟精度和稳定性方面与交错网格法相同且优于传统规则网格法;而从内存占用上,相较于交错网格,二维时内存占用减少了60%,三维时减少了66.7%。利用层状模型验证了方法的模拟精度;利用复杂的Marmousi-2模型说明了方法的适用性和稳定性。
In this paper,we propose a quasi-regular grid high-order finite-difference seismic forward modeling to accurately describe elastic wave propagation in heterogeneous media.The quasi-regular grid strategy is to stagger the displacement component of the elastic wave equation and make a new center difference operator for displacement,while the simulation accuracy and stability are the same as those of the staggered grid.But the memory usage of the quasi-regular grid is reduced by 60% in 2 D and66.7%in 3 Dcompared to the staggered grid.Then the equivalence between the quasi-regular grid and staggered grid is mathematically demonstrated,and the source loading,boundary conditions and stability are analyzed.A numerical test is carried out on a layered model to validate the accuracy of the quasiregular grid method by comparing with staggered grid and regular grid methods.Finally,a test on Marmousi-2 model proves the applicability and stability of the proposed method.
In this paper,we propose a quasi-regular grid high-order finite-difference seismic forward modeling to accurately describe elastic wave propagation in heterogeneous media.The quasi-regular grid strategy is to stagger the displacement component of the elastic wave equation and make a new center difference operator for displacement,while the simulation accuracy and stability are the same as those of the staggered grid.But the memory usage of the quasi-regular grid is reduced by 60% in 2 D and66.7%in 3 Dcompared to the staggered grid.Then the equivalence between the quasi-regular grid and staggered grid is mathematically demonstrated,and the source loading,boundary conditions and stability are analyzed.A numerical test is carried out on a layered model to validate the accuracy of the quasiregular grid method by comparing with staggered grid and regular grid methods.Finally,a test on Marmousi-2 model proves the applicability and stability of the proposed method.
引文
[1] Song X,Fomel S.Fourier finite-difference wave pro-pagation[J].Geophysics,2011,76(5):T123-T129.
[2] Alkhalifah T.Residual extrapolation operators for efficient wavefield construction[J].Geophysical Journal International,2013,193(2):1027-1034.
[3] Pestana R C,Stoffa P L.Time evolution of the wave equation using rapid expansion method[J].Geophy-sics,2010,75(4):T121-T131.
[4] Tessmer E.Using the rapid expansion method for accurate time-stepping in modeling and reverse-time migration[J].Geophysics,2011,76(4):S177-S185.
[5] Fomel S,Ying L,Song X.Seismic wave extrapolation using low rank symbol approximation[J].Geophysical Prospecting,2013,61(3):526-536.
[6] Wu Z,Alkhalifah T.The optimized expansion based low-rank method for wavefield extrapolation[J].Geophysics,2014,79(2):T51-T60.
[7] Fang G,Fomel S,Du Q,et al.Low rank seismic-wave extrapolation on a staggered grid[J].Geophysics,2014,79(3):T157-T168.
[8] Kelly K R,Ward R W,Treitel S,et al.Synthetic seismograms:A finite-difference approach[J].Geophy-sics,1976,41(1):2-27.
[9] Robertsson J O A,Blanch J O,Symes W W,et al.Galerkin-wavelet modeling of wave propagation:Optimal finite-difference stencil design[J].Mathematical and Computer Modelling,1994,19(1):31-38.
[10] Robertsson J O A,Blanch J O,Symes W W.Visco-elastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456.
[11] Alterman Z,Karal Jr F C.Propagation of elastic waves in layered media by finite difference methods[J].Bu-lletin of the Seismological Society of America,1968,58(1):367-398.
[12] Boore D M.Finite difference methods for seismic wave propagation in heterogeneous materials[J].Methods in Computational Physics,1972,11:1-37.
[13] Madariaga R.Dynamics of an expanding circular fault[J].Bulletin of the Seismological Society of America,1976,66(3):639-666.
[14] Virieux J.SH-wave propagation in heterogeneous media:Velocity-stress finite-difference method[J].Geophysics,1984,49(11):1933-1942.
[15] Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):1203-1216.
[16] Levander A R.Fourth-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425-1436.
[17] Graves R W.Simulating seismic wave propagation in 3D elastic media using staggered-grid finite diffe-rences[J].Bulletin of the Seismological Society of America,1996,86(4):1091-1106.
[18] Moczo P,Kristek J,Halada L.3D fourth-order staggered-grid finite-difference schemes:Stability and grid dispersion[J].Bulletin of the Seismological Society of America,2000,90(3):587-603.
[19] Kristek J,Moczo P,Galis M.Stable discontinuous staggered grid in the finite-difference modelling of seismic motion[J].Geophysical Journal International,2010,183(3):1401-1407.
[20] 刘洋,李承楚,牟永光.任意偶数阶精度有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):1-10.LIU Yang,LI Chengchu,MOU Yongguang.Finite-difference numerical modeling of any even-order accuracy[J].Oil Geophysical Prospecting,1998,33(1):1-10.
[21] 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.DONG Liangguo,MA Zaitian,CAO Jingzhong.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(6):856-864.
[22] 殷文,印兴耀,吴国忱,等.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,2006,49(2):561-568.YIN Wen,YIN Xingyao,WU Guochen,et al.The method of finite difference of high precision on elastic wave equations in the frequency domain and wavefield simulation[J].Chinese Journal of Geophysics,2006,49(2):561-568.
[23] 杨庆节,刘财,耿美霞,等.交错网格任意阶导数有限差分格式及差分系数推导[J].吉林大学学报(地球科学版),2014,44(1):375-385.YANG Qingjie,LIU Cai,GENG Meixia,et al.Staggered grid finite difference scheme and coefficients deduction of any number of derivatives[J].Journal of Jilin University(Earth Science Edition),2014,44(1):375-385.
[24] 杜启振,郭成锋,公绪飞.VTI介质纯P波混合法正演模拟及稳定性分析[J].地球物理学报,2015,58(4):1290-1304.DU Qizhen,GUO Chengfeng,GONG Xufei.Hybrid PS/FD numerical simulation and stability analysis of pure P-wave propagation in VTI media[J].Chinese Journal of Geophysics,2015,58(4):1290-1304.
[25] 黄金强,李振春,黄建平,等.TTI介质Lebedev网格高阶有限差分正演模拟及波型分离[J].石油地球物理勘探,2017,52(5):915-927.HUANG Jinqiang,LI Zhenchun,HUANG Jianping,et al.Lebedev grid high-order finite-difference mode-ling and elastic wave-mode separation for TTI media[J].Oil Geophysical Prospecting,2017,52(5):915-927.
[26] 高正辉,孙建国,孙章庆,等.基于完全匹配层构建新方法的2.5维声波近似方程数值模拟[J].石油地球物理勘探,2016,51(6):1128-1133.GAO Zhenghui,SUN Jianguo,SUN Zhangqing,et al.2.5D acoustic approximate equation numerical simulation with a new construction method of the perfect matched layer[J].Oil Geophysical Prospecting,2016,51(6):1128-1133.
[27] 梁文全,王彦飞,杨长春.声波方程数值模拟矩形网格有限差分系数确定法[J].石油地球物理勘探,2017,52(1):56-62.LIANG Wenquan,WANG Yanfei,YANG Changchun.Acoustic wave equation modeling with rectangle grid finite difference operator and its linear time space domain solution[J].Oil Geophysical Prospecting,2017,52(1):56-62.
[28] Di Bartolo L,Dors C,Mansur W J.A new family offinite-difference schemes to solve the heterogeneous acoustic wave equation[J].Geophysics,2012,77(5):T187-T199.
[29] Dablain M A.The application of high-order differencing to the scalar wave equation[J].Geophysics,1986,51(1):54-66.
[30] 李青阳,吴国忱,梁展源.基于PML边界的时间高阶伪谱法弹性波场模拟[J].地球物理学进展,2018,33(1):228-235.LI Qingyang,WU Guochen,LIANG Zhanyuan.Time domain high-order pseudo spectral method based on PML boundary for elastic wavefield simulation[J].Progress in Geophysics,2018,33(1):228-235.
[31] 吴建鲁,吴国忱,王伟,等.基于等效交错网格的流固耦合介质地震波模拟[J].石油地球物理勘探,2018,53(2):272-279.WU Jianlu,WU Guochen,WANG Wei,et al.Seismic forward modeling in fluid-solid media based on equi-valent staggered grid scheme[J].Oil Geophysical Prospecting,2018,53(2):272-279.
[32] Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophy-sics,2012,43(6):155-165.
[33] Clayton R,Engquist B.Absorbing boundary condi-tions for acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,67(6):1529-1540.
[34] Cerjan C,Dan K,Kosloff R,et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[35] Berenger J P.A perfectly matched layer for the ab-sorption of electromagnetic waves[J].Physics of Plasmas,1994,114(2):185-200.
[2] Alkhalifah T.Residual extrapolation operators for efficient wavefield construction[J].Geophysical Journal International,2013,193(2):1027-1034.
[3] Pestana R C,Stoffa P L.Time evolution of the wave equation using rapid expansion method[J].Geophy-sics,2010,75(4):T121-T131.
[4] Tessmer E.Using the rapid expansion method for accurate time-stepping in modeling and reverse-time migration[J].Geophysics,2011,76(4):S177-S185.
[5] Fomel S,Ying L,Song X.Seismic wave extrapolation using low rank symbol approximation[J].Geophysical Prospecting,2013,61(3):526-536.
[6] Wu Z,Alkhalifah T.The optimized expansion based low-rank method for wavefield extrapolation[J].Geophysics,2014,79(2):T51-T60.
[7] Fang G,Fomel S,Du Q,et al.Low rank seismic-wave extrapolation on a staggered grid[J].Geophysics,2014,79(3):T157-T168.
[8] Kelly K R,Ward R W,Treitel S,et al.Synthetic seismograms:A finite-difference approach[J].Geophy-sics,1976,41(1):2-27.
[9] Robertsson J O A,Blanch J O,Symes W W,et al.Galerkin-wavelet modeling of wave propagation:Optimal finite-difference stencil design[J].Mathematical and Computer Modelling,1994,19(1):31-38.
[10] Robertsson J O A,Blanch J O,Symes W W.Visco-elastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456.
[11] Alterman Z,Karal Jr F C.Propagation of elastic waves in layered media by finite difference methods[J].Bu-lletin of the Seismological Society of America,1968,58(1):367-398.
[12] Boore D M.Finite difference methods for seismic wave propagation in heterogeneous materials[J].Methods in Computational Physics,1972,11:1-37.
[13] Madariaga R.Dynamics of an expanding circular fault[J].Bulletin of the Seismological Society of America,1976,66(3):639-666.
[14] Virieux J.SH-wave propagation in heterogeneous media:Velocity-stress finite-difference method[J].Geophysics,1984,49(11):1933-1942.
[15] Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):1203-1216.
[16] Levander A R.Fourth-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425-1436.
[17] Graves R W.Simulating seismic wave propagation in 3D elastic media using staggered-grid finite diffe-rences[J].Bulletin of the Seismological Society of America,1996,86(4):1091-1106.
[18] Moczo P,Kristek J,Halada L.3D fourth-order staggered-grid finite-difference schemes:Stability and grid dispersion[J].Bulletin of the Seismological Society of America,2000,90(3):587-603.
[19] Kristek J,Moczo P,Galis M.Stable discontinuous staggered grid in the finite-difference modelling of seismic motion[J].Geophysical Journal International,2010,183(3):1401-1407.
[20] 刘洋,李承楚,牟永光.任意偶数阶精度有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):1-10.LIU Yang,LI Chengchu,MOU Yongguang.Finite-difference numerical modeling of any even-order accuracy[J].Oil Geophysical Prospecting,1998,33(1):1-10.
[21] 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.DONG Liangguo,MA Zaitian,CAO Jingzhong.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(6):856-864.
[22] 殷文,印兴耀,吴国忱,等.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,2006,49(2):561-568.YIN Wen,YIN Xingyao,WU Guochen,et al.The method of finite difference of high precision on elastic wave equations in the frequency domain and wavefield simulation[J].Chinese Journal of Geophysics,2006,49(2):561-568.
[23] 杨庆节,刘财,耿美霞,等.交错网格任意阶导数有限差分格式及差分系数推导[J].吉林大学学报(地球科学版),2014,44(1):375-385.YANG Qingjie,LIU Cai,GENG Meixia,et al.Staggered grid finite difference scheme and coefficients deduction of any number of derivatives[J].Journal of Jilin University(Earth Science Edition),2014,44(1):375-385.
[24] 杜启振,郭成锋,公绪飞.VTI介质纯P波混合法正演模拟及稳定性分析[J].地球物理学报,2015,58(4):1290-1304.DU Qizhen,GUO Chengfeng,GONG Xufei.Hybrid PS/FD numerical simulation and stability analysis of pure P-wave propagation in VTI media[J].Chinese Journal of Geophysics,2015,58(4):1290-1304.
[25] 黄金强,李振春,黄建平,等.TTI介质Lebedev网格高阶有限差分正演模拟及波型分离[J].石油地球物理勘探,2017,52(5):915-927.HUANG Jinqiang,LI Zhenchun,HUANG Jianping,et al.Lebedev grid high-order finite-difference mode-ling and elastic wave-mode separation for TTI media[J].Oil Geophysical Prospecting,2017,52(5):915-927.
[26] 高正辉,孙建国,孙章庆,等.基于完全匹配层构建新方法的2.5维声波近似方程数值模拟[J].石油地球物理勘探,2016,51(6):1128-1133.GAO Zhenghui,SUN Jianguo,SUN Zhangqing,et al.2.5D acoustic approximate equation numerical simulation with a new construction method of the perfect matched layer[J].Oil Geophysical Prospecting,2016,51(6):1128-1133.
[27] 梁文全,王彦飞,杨长春.声波方程数值模拟矩形网格有限差分系数确定法[J].石油地球物理勘探,2017,52(1):56-62.LIANG Wenquan,WANG Yanfei,YANG Changchun.Acoustic wave equation modeling with rectangle grid finite difference operator and its linear time space domain solution[J].Oil Geophysical Prospecting,2017,52(1):56-62.
[28] Di Bartolo L,Dors C,Mansur W J.A new family offinite-difference schemes to solve the heterogeneous acoustic wave equation[J].Geophysics,2012,77(5):T187-T199.
[29] Dablain M A.The application of high-order differencing to the scalar wave equation[J].Geophysics,1986,51(1):54-66.
[30] 李青阳,吴国忱,梁展源.基于PML边界的时间高阶伪谱法弹性波场模拟[J].地球物理学进展,2018,33(1):228-235.LI Qingyang,WU Guochen,LIANG Zhanyuan.Time domain high-order pseudo spectral method based on PML boundary for elastic wavefield simulation[J].Progress in Geophysics,2018,33(1):228-235.
[31] 吴建鲁,吴国忱,王伟,等.基于等效交错网格的流固耦合介质地震波模拟[J].石油地球物理勘探,2018,53(2):272-279.WU Jianlu,WU Guochen,WANG Wei,et al.Seismic forward modeling in fluid-solid media based on equi-valent staggered grid scheme[J].Oil Geophysical Prospecting,2018,53(2):272-279.
[32] Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophy-sics,2012,43(6):155-165.
[33] Clayton R,Engquist B.Absorbing boundary condi-tions for acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,67(6):1529-1540.
[34] Cerjan C,Dan K,Kosloff R,et al.A nonreflecting boundary condition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[35] Berenger J P.A perfectly matched layer for the ab-sorption of electromagnetic waves[J].Physics of Plasmas,1994,114(2):185-200.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |