地震波交错网格高阶差分数值模拟研究
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摘要
研究目的:地震波数值模拟技术是勘探地球物理学中的重要组成部分,研究通过弹性波一阶速度-应力方程,采用交错网格高阶有限差分法实现了地震波在各向同性介质中的高精度的数值模拟,并采用完全匹配层(PML)吸收边界来消除边界反射,可取得较好的效果。研究结论:通过模型的正演计算和复杂模型的处理结果表明,交错网格高阶有限差分法数值模拟是一种快速有效的地震波数值模拟方法。可用于为地震勘探选择采集参数,优化观测系统提供依据,以提高采集数据的质量,有效地解决铁路勘察过程中的地质问题。
Research purposes: The technology of seismic wave numerical simulation is an important part in the geophysical prospecting.In this paper,based on the elastic-velocity-stress equation,the numerical simulation of seismic wave propagation in isotropic media is carried out with staggered-grid high-order finite-difference method,and the perfectly matched layer(PML) is used to absorpt boundary to eliminate the boundary reflection.The result of simulation is rather perfect. Research conclusions:The results of forward computation and the seismic process of a complex model show the staggered-grid high-order numerical simulation is a rapid and efficient simulation method for seismic wave propagation.This method can be used for the selection of acquisition parameters in seismic exploration and for the optimization of the observation system to improve the quality of the acquisition data and solve the geological problems in railway exploration.
Research purposes: The technology of seismic wave numerical simulation is an important part in the geophysical prospecting.In this paper,based on the elastic-velocity-stress equation,the numerical simulation of seismic wave propagation in isotropic media is carried out with staggered-grid high-order finite-difference method,and the perfectly matched layer(PML) is used to absorpt boundary to eliminate the boundary reflection.The result of simulation is rather perfect. Research conclusions:The results of forward computation and the seismic process of a complex model show the staggered-grid high-order numerical simulation is a rapid and efficient simulation method for seismic wave propagation.This method can be used for the selection of acquisition parameters in seismic exploration and for the optimization of the observation system to improve the quality of the acquisition data and solve the geological problems in railway exploration.
引文
[1]Virieux,J.SH-wave Propagation in HeterogenerousMedia:Velocity-stress Finite-difference Method[J].Geophysics,1984(11):1933-1957.
[2]Virieux,J.P-SV Wave Propagation in HeterogeneousMedia:Velocity-stress Finite-difference Method[J].Geophysic,1986(4):889-901.
[3]Lavender,A.R.Fourth-order Finite-difference P-SV Seismograms[J].Geophysics,1988(11):1425-1436.
[4]Dablain,M.A.The Application of High-orderDiffernceing to the Scalar Wave Equation[J].Geophysics,1986(1):54-66.
[5]Collino,F.,Tsogka,C.Application of the PerfectlyMatched Absorbing Layer Model to the LinearElastodynamic Problem in Anisotropic HeterogeneousMedia[J].Geophysics,2001(1):294-307.
[6]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(3):411-419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,etc.AStaggered-grid High-order Difference Method of One-order Elastic Wave Equation[J].Chinese Journal ofGeophysics(in Chinese),2000(3):411-419.
[7]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(6):856-864.Dong Liangguo,Ma Zaitian,Cao Jingzhong.A Studyon Stablity of the Staggered-grid High-orderDifference Method of First-order Elastic WaveEquation[J].Chinese Journal of Geophysics(inChinese),2000(6):856-864.
[8]周海滨,李志华.困难地形条件下地震反射在煤矿采空区的技术研究[J].铁道工程学报,2010(2):18-21.Zhou Haibin,Li Zhihua.Technical Research on theSeismic Reflection in Coal Seam Gob under DifficultTerrain Condition[J].Journal of Railway EngineeringSociety,2010(2):18-21.
[9]李志华,朱旭东.复杂地质隧道的综合物探技术[J].铁道工程学报,2008(8):58-61.Li Zhihua,Zhu Xudong.The Application of IntegratedGeophysical Exploration Technology in the TunnelUnder the Complicated Geological Conditions[J].Journal of Railway Engineering Society,2008(8):58-61.
[10]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(自然科学版),2003(6):17-21Pei Zhenglin,Mou Yongguang.Staggered-grid High-order Finit-dfference Modeling for SeismicPropagation in HeterogEneous Media[J].Journal ofthe Unversity of Petroleum,China,2003(6):17-21.
[11]王守东,声波方程完全匹层吸收边界[J].石油地球物理勘探,2003(1):31-34Wang Shoudong.Perfectly Matched Layer AbsorbingCondition for Acoustic Equation[J].Oil GeophysicalProspecting,2003(1):31-34
[2]Virieux,J.P-SV Wave Propagation in HeterogeneousMedia:Velocity-stress Finite-difference Method[J].Geophysic,1986(4):889-901.
[3]Lavender,A.R.Fourth-order Finite-difference P-SV Seismograms[J].Geophysics,1988(11):1425-1436.
[4]Dablain,M.A.The Application of High-orderDiffernceing to the Scalar Wave Equation[J].Geophysics,1986(1):54-66.
[5]Collino,F.,Tsogka,C.Application of the PerfectlyMatched Absorbing Layer Model to the LinearElastodynamic Problem in Anisotropic HeterogeneousMedia[J].Geophysics,2001(1):294-307.
[6]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(3):411-419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,etc.AStaggered-grid High-order Difference Method of One-order Elastic Wave Equation[J].Chinese Journal ofGeophysics(in Chinese),2000(3):411-419.
[7]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(6):856-864.Dong Liangguo,Ma Zaitian,Cao Jingzhong.A Studyon Stablity of the Staggered-grid High-orderDifference Method of First-order Elastic WaveEquation[J].Chinese Journal of Geophysics(inChinese),2000(6):856-864.
[8]周海滨,李志华.困难地形条件下地震反射在煤矿采空区的技术研究[J].铁道工程学报,2010(2):18-21.Zhou Haibin,Li Zhihua.Technical Research on theSeismic Reflection in Coal Seam Gob under DifficultTerrain Condition[J].Journal of Railway EngineeringSociety,2010(2):18-21.
[9]李志华,朱旭东.复杂地质隧道的综合物探技术[J].铁道工程学报,2008(8):58-61.Li Zhihua,Zhu Xudong.The Application of IntegratedGeophysical Exploration Technology in the TunnelUnder the Complicated Geological Conditions[J].Journal of Railway Engineering Society,2008(8):58-61.
[10]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(自然科学版),2003(6):17-21Pei Zhenglin,Mou Yongguang.Staggered-grid High-order Finit-dfference Modeling for SeismicPropagation in HeterogEneous Media[J].Journal ofthe Unversity of Petroleum,China,2003(6):17-21.
[11]王守东,声波方程完全匹层吸收边界[J].石油地球物理勘探,2003(1):31-34Wang Shoudong.Perfectly Matched Layer AbsorbingCondition for Acoustic Equation[J].Oil GeophysicalProspecting,2003(1):31-34
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