交错网格在伪谱法弹性波场数值模拟中的应用
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摘要
为消除伪谱法弹性地震波场数值模拟中因数值计算产生的干扰伪波,分析了伪谱法弹性波场数值计算产生干扰伪波的原因,提出在伪谱法弹性波场数值模拟时引入交错网格,采用中心网格和交错网格联合计算的方式(即:采用交错网格计算一阶导数,采用中心网格计算二阶导数)来克服波场计算过程中的数值振荡现象。模型计算结果表明,该方法可以有效消除伪谱法模拟波场中的干扰伪波,使波场计算值稳定、准确、可靠。
In order to eliminate the interfere pseudo-wave caused by numerical computation in the elastic wavefield modeling by pseudo-spectral method,we analyzed the reasons leading to the phenomena,and introduced staggered grids into elastic wavefield modeling by pseudo-spectral method.The numerical oscillation in wavefield modeling is overcome by joint computation of central grids and staggered grids(first-order spatial derivative is calculated by staggered grids and second-order spatial derivative is calculated by central grids).Model testing result indicates that the method can effectively remove the interfere pseudo-wave and make the modeling result stable,accurate and reliable.
In order to eliminate the interfere pseudo-wave caused by numerical computation in the elastic wavefield modeling by pseudo-spectral method,we analyzed the reasons leading to the phenomena,and introduced staggered grids into elastic wavefield modeling by pseudo-spectral method.The numerical oscillation in wavefield modeling is overcome by joint computation of central grids and staggered grids(first-order spatial derivative is calculated by staggered grids and second-order spatial derivative is calculated by central grids).Model testing result indicates that the method can effectively remove the interfere pseudo-wave and make the modeling result stable,accurate and reliable.
引文
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[3]邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限元解法[J].地球物理学报,2000,43(2):264-278Shao X M,Lan Z L.Finite element methods for theequations of waves in fluid-satureted porous media[J].Chinese Journal of Geophysics,2000,43(2):264-278
[4]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389Zhang M G,Wang M Y,Li X F,et al.Finite elementforward modeling of anisotropic elastic waves[J].Progress in Geophysics,2002,17(3):384-389
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[7]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):42-48Ma Y W,Zhan Z B,Gu H Y,et al.Numerical model-ing for seismic wave propagation via pseudospectralmethod[J].Geophysical Prospecting for Petroleum,2001,40(2):42-48
[8]符力耘,牟永光.弹性波边界元法正演模拟[J].地球物理学报,1994,37(4):521-529Fu L Y,Mou Y G.Boundary element method for e-lastic wave forward modeling[J].Chinese Journal ofGeophysics,1994,37(4):521-529
[9]胡善政,符力耘,裴正林.流体饱和多孔隙介质弹性波方程边界元解法研究[J].地球物理学报,2009,52(9):2364-2369Hu S Z,Fu L Y,Pei Z L.A boundary element meth-od for the 2-D wave equation in fluid-saturated por-ous media[J].Chinese Journal Geophysics,2009,52(9):2364-2369
[10]佘德平.波场数值模拟技术[J].勘探地球物理进展,2004,27(1):16-21She D P.On wave field numerical modeling tech-niques[J].Progress in Geophysics,2004,27(1):16-21
[11]张钋,刘洪,李幼铭.射线追踪方法的发展现状[J].地球物理学进展,2000,15(1):36-45Zhang P,Liu H,Li Y M.The situation and progressof ray tracing method research[J].Progress in Geo-physics,2000,15(1):36-45
[12]陈景波,秦孟兆.射线追踪、辛几何算法与波场的数值模拟[J].计算物理,2001,18(6):481-486Chen J B,Qin M Z.Ray tracing,symplectic algo-rithms and wave field simulation[J].Chinese Journalof Computational Physics,2001,18(6):481-486
[13]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143-148Zhang Y G.On numerical simulations of seismicwavefield[J].Geophysical Prospecting for Petrole-um,2003,42(2):143-148
[14]蔡其新,何佩军,秦广胜,等.有限差分数值模拟的最小频散算法及其应用[J].石油地球物理勘探,2003,38(3):247-251,262Cai Q X,He P J,Qin G S,et al.Minimum dispersionalgorithm by finite-difference numeric modeling andits applications[J].Oil Geophysical Prospecting,2003,38(3):247-251,262
[15]李景叶,陈小宏.横向各向同性介质地震波场数值模拟研究[J].地球物理学进展,2006,21(3):700-705Li J Y,Chen X H.Study on seismic wave field nu-merical simulation in transverse isotropic medium[J].Progress in Geophysics,2006,21(3):700-705
[16]Fornberg B.The pseudospectral method:compari-sons with finite differences for the elastic wave equa-tion[J].Geophysics,1987,52(4):438-501
[2]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419Dong L G,Ma Z T,Cao J Z,et al.A staggered-gridhigh-order difference method of one-order elasticwave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419
[3]邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限元解法[J].地球物理学报,2000,43(2):264-278Shao X M,Lan Z L.Finite element methods for theequations of waves in fluid-satureted porous media[J].Chinese Journal of Geophysics,2000,43(2):264-278
[4]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389Zhang M G,Wang M Y,Li X F,et al.Finite elementforward modeling of anisotropic elastic waves[J].Progress in Geophysics,2002,17(3):384-389
[5]薛东川,王尚旭,焦淑静.起伏地表复杂介质波动方程有限元数值模拟方法[J].地球物理学进展,2007,22(2):522-529Xue D C,Wang S X,Jiao S J.Wave equation finite-element modeling including rugged topography andcomplicated medium[J].Progress in Geophysics,2007,22(2):522-529
[6]张文生,何樵登.二维各向同性介质中的伪谱法模拟[J].石油地球物理勘探,1998,33(3):310-319Zhang W S,He Q D.Pseudospectral method simula-tion in two dimensional isotropic medium[J].Oil Ge-ophysical Prospecting,1998,33(3):310-319
[7]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):42-48Ma Y W,Zhan Z B,Gu H Y,et al.Numerical model-ing for seismic wave propagation via pseudospectralmethod[J].Geophysical Prospecting for Petroleum,2001,40(2):42-48
[8]符力耘,牟永光.弹性波边界元法正演模拟[J].地球物理学报,1994,37(4):521-529Fu L Y,Mou Y G.Boundary element method for e-lastic wave forward modeling[J].Chinese Journal ofGeophysics,1994,37(4):521-529
[9]胡善政,符力耘,裴正林.流体饱和多孔隙介质弹性波方程边界元解法研究[J].地球物理学报,2009,52(9):2364-2369Hu S Z,Fu L Y,Pei Z L.A boundary element meth-od for the 2-D wave equation in fluid-saturated por-ous media[J].Chinese Journal Geophysics,2009,52(9):2364-2369
[10]佘德平.波场数值模拟技术[J].勘探地球物理进展,2004,27(1):16-21She D P.On wave field numerical modeling tech-niques[J].Progress in Geophysics,2004,27(1):16-21
[11]张钋,刘洪,李幼铭.射线追踪方法的发展现状[J].地球物理学进展,2000,15(1):36-45Zhang P,Liu H,Li Y M.The situation and progressof ray tracing method research[J].Progress in Geo-physics,2000,15(1):36-45
[12]陈景波,秦孟兆.射线追踪、辛几何算法与波场的数值模拟[J].计算物理,2001,18(6):481-486Chen J B,Qin M Z.Ray tracing,symplectic algo-rithms and wave field simulation[J].Chinese Journalof Computational Physics,2001,18(6):481-486
[13]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143-148Zhang Y G.On numerical simulations of seismicwavefield[J].Geophysical Prospecting for Petrole-um,2003,42(2):143-148
[14]蔡其新,何佩军,秦广胜,等.有限差分数值模拟的最小频散算法及其应用[J].石油地球物理勘探,2003,38(3):247-251,262Cai Q X,He P J,Qin G S,et al.Minimum dispersionalgorithm by finite-difference numeric modeling andits applications[J].Oil Geophysical Prospecting,2003,38(3):247-251,262
[15]李景叶,陈小宏.横向各向同性介质地震波场数值模拟研究[J].地球物理学进展,2006,21(3):700-705Li J Y,Chen X H.Study on seismic wave field nu-merical simulation in transverse isotropic medium[J].Progress in Geophysics,2006,21(3):700-705
[16]Fornberg B.The pseudospectral method:compari-sons with finite differences for the elastic wave equa-tion[J].Geophysics,1987,52(4):438-501
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