弹性介质中垂直地震剖面有限差分正演
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摘要
垂直地震剖面法可以通过认识反射和透射过程,深入了解地震波传播特性,又可以改善地表地震资料关于构造、地层和岩性的解释.本文是在基于垂直地震剖面的基本原理基础上,采用高阶交错网格有限差分数值求解二维弹性波方程,然后对常见的层状介质和岩溶介质模型分别进行模拟,根据模型合成了相关的垂直地震剖面记录,期间采用的是完全匹配层法吸收边界条件,从记录中可以看见该边界条件的简单而高效的优点,最后对模型的复杂程度的不足提出了进一步的要求以适应更复杂的地质条件.
Vertical seismic profiling can be used to get the reflections and refractions,deeply know the seismic propagation characteristics,and then explain the seismic data about -structures,layers,lithological character.Based on the theory of vertical seismic profile,this paper takes high order staggered-grid finite difference method to resolve the wave equation for the synthetic VSP in the layered media and the karst media.Meanwhile,it takes the perfectly matched layers method as the absorbing boundary condition,so it will deal with the boundary condition simply and efficiently.Finally it is more important that we get more complex models with more complex geological conditions.
Vertical seismic profiling can be used to get the reflections and refractions,deeply know the seismic propagation characteristics,and then explain the seismic data about -structures,layers,lithological character.Based on the theory of vertical seismic profile,this paper takes high order staggered-grid finite difference method to resolve the wave equation for the synthetic VSP in the layered media and the karst media.Meanwhile,it takes the perfectly matched layers method as the absorbing boundary condition,so it will deal with the boundary condition simply and efficiently.Finally it is more important that we get more complex models with more complex geological conditions.
引文
[1]Wyatt,K.D..Synthetic vertical seismic profiles:Geophysics, 1981,46(6):880-891.
[2]Ganley D C.A method for calculation synthetic seismograms which include the effect of absorption and dispersion. Geophysics,1981,46:1100.
[3](美)J.F.克莱鲍特著,许云泽.地震成像理论及方法.北京:石油工业出版社,199l. Clacrbout,J.F.,Xu Y.The theory and method of seismic tomography.Beijing:Petroleum Industry Press,1991.
[4]杨文采.非均匀层状介质中地震波速的成像.地球物理学报, 1990,33(2):265-282. Yang W C.Seismic velocity imaging of inhomogeneous layered medium.Chinese J.Geophys.(in Chinese),1990,33(2):265 -282.
[5]杨文采.地球物理反演的理论与方法.北京:地质出版社,1997. 124-354. Yang W C.The theory and method of geophysical inversion. Beijing.Geological Publishing House,1997.
[6]Haskell N A.The dispersion of surface waves on multilayered media:Bulletin of the seismological association of America, 1953,43:17-34.
[7]Wyatt K D,Wyatt S B.The determination of subsurface structural information using the vertical seismic profile: Geophysics,1982,47:465-466.
[8]Young T K.Computer modeling of vertical seismic profiling, Geophysical prospecting,1984,32:851-870.
[9]朱光明,胡建平,邱陶兴.零偏移距VSP射线追踪模型.石油物探,1985,24(4):32-40. Zhu G M,Hu J P,Qiu T X.Ray-tracing model of zero-offset VSP.Geophysical Prospecting for Petroleum,1985,24(4):32 -40.
[10]Michel Dietrich,Michel Bouchon.Synthetic vertical seismic pro files in elastic media:Geophysics,1985,50(2):224 - 234.
[11]王彦春,董毓明.粘弹介质零偏移距VSP计算.石油物探, 1990,29(2):45-52. Wang Y C,Dong Y M.Computing for the viscous elastic medium zero-offset VSP data.Geophysical Prospecting for Petroleum,1990,29(2):45-52.
[12]Dietrich M,Bouchon M.Synthetic vertical seismic pro-files in elastic media:Geophysics,1985,50:224-234.
[13]McMechan G A.Synthetic finite-offset vertical seismic profiles for laterally varying media:Geophysics,1985,50(4):627-636.
[14]朱光明,胡建平,邱陶兴.VSP非零偏移距任意界面渐进射线追踪模型.石油物探,1986,25(4):14-27. Zhu G M,Hu J P,Qiu T X.Asymptotic ray tracing modeling of VSP with arbitrary boundaries and offsets.Geophysical Prospecting for Petroleum,1986,25(4):14-27.
[15]Aminzadeh F,Mendel J M.Synthetic vertical seismic profiles for non-normal incidence plane waves:Geophysics,1985, 50:178-188.
[16]肖春燕,庄东海,金耀祖.垂直地震剖面的有限元正演模拟.江汉石油学院学报,1944,16(supp):80-86. Xiao C Y,Zhuang D H,Jin Y Z.Forword modeling VSP by finite element method.Journal of Jianghan Petroleum Institute,1994,16(supp):80-86.
[17]王成礼,李秉富等.一种斜井VSP的正演模型.青岛海洋大学学报,1995,25(3):382-390. Wang C L,Li B F.A forward model of deviate well VSP. Journal of Ocean University of Qingdao,1995,25(3):382- 390.
[18]李锐坚.VPS高阶有限差分正演模型.西安石油学院学报, 1996,11(2):38-42. Li R J.High order finite difference modeling for VSP of acoustic wave equation.Journal of Xi'an Petroleum Institute, 1996,11(2):38-42.
[19]胡建平.变偏移距VSP射线追踪模型.西安工程学院学报, 1998,20(supp):7-10. Hu J P.Walkway VSP ray tracing model.Journal of Xi'an Engineering University,1998,20(supp):7 - 10.
[20]王成礼,韩文功,王延光,董良国.VSP弹性波方程正演模拟与波场分析.油气地球物理,2006,4(4):7-15. Wang C L,Han W G.The equation forward modeling and wave field analysis of VSP elastic wave.Petroleum Geophysics,2006,4(4 ):7 - 15.
[21]董良国,马在田,曹景忠等.一阶弹性波动方程交错网格高阶差分解法.地球物理学报,2000,43(3):411-419. Dong L G,Ma Z T,Cao J Z.A staggered-grid high-order difference method of one-order elastic wave equation.Chinese J.Geophys.(in Chinese),2000,43(3):411-419.
[22]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移.地球物理学报,2009,52(3):801-807. Du Q Z,Qin T.Multicomponent prestack reverse-time migration of elastic waves in transverse isotropic medium, Chinese J.Geophys.(in Chinese),2009,52(3):801-807.
[23]王润秋,李兰兰,李会俭.塔里木地区勘探地震正演模拟研究.地球物理学报,2010,53(8):1875-1882. Wang R Q,Li L L,Li H J.Forward modeling research for seismic exploration of Tarim area.Chinese J.Geophys.(in Chinese),2010,53(8):1875- 1882.
[24]张文波.井间地震交错网格高阶差分数值模拟及逆时偏移成像研究:[博士论文].长安大学,2005. Zhang W B.Research on cross-hole seismic simulation with staggered grid high order difference method and reverse-time migration imaging:[Ph.D.thesis](in Chinese).Changan University,2005.
[25]杨志峰,王煊.高精度有限差分方法研究进展.自然科学进展,1999,9(9):769-779. Yang Z F,Wang X.Advances in finite difference method with high accuracy,Progress in natural science,1999,9(9):769- 779.
[26]Aki,K.and P.G.Richards.Quantitative Seismology,W. H.Freeman and Co.,San Francisco,1980.
[27]Xu Y X.Finite-difference modeling of high-frequency rayleigh-wave propagation for near-surface applications.Expanded Abstract,75th SEG Meeting,Houston,2005.
[28]Xu Y X,Xia J H,R.Miller.Numerical investigation of implementation of air/earth boundary by acoustic/elastic boundary approach:Geophysics,2007,in Press.
[29]王永刚.完全匹配层吸收边界条件的研究.中国石油大学学报,2007,31:20-26. Wang Y G.Study of absorbing boundary condition by perfectly matched layer.Journal of china university of petroleum,2007,31:20-26.
[30]陈浩,王秀明,赵海波.旋转交错网格有限差分及其完全匹配层吸收边界条件.科学通报,2006,51(17):1985-1995. Chen H,Wang X M,Zhao H B.A rotated staggered grid finite difference with the absorbing boundary condition of a perfectly matched layer.Chinese science bulletin,2006,51 (17):1985-1995.
[31]Francis Collino and Chrysoula Tsoka.Application of the perfectly matched absorbing layer model to the liner electrodynamics problem in anisotropic heterogeneous media. Geophysics 2001,166:294-307.
[32]孙建国.复杂地表条件下地球物理数值模拟方法评述.世界地质,2007,26(3):345-357. Sun J G.Methods for numerical modeling of geophysical fields under complex topographical conditions:a critical review. Global Geology(in Chinese),2007,26(3):345-357.
[33]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005. Mou Y G,Pei Z L.Seismic numerical modeling for 3-D complex media(in Chinese).Beijing:Petroleum Industry Press,2005.
[34]高静怀,杨森林,王大兴.利用VSP资料直达波的包络峰值处瞬时频率提取介质品质因子.地球物理学报,2008,5l(3): 853-861. Gao J H,Yang S I,Wang D X.Quality factor extraction using instanteous frequency at envelope peak of direct waves of VSP data.Chinese J.Geophys.(in Chinese),2008,51(3): 853-861.
[35]Ge J D,Puiol J,Pezshk S,et al.Determination of shallow shear-wave velocity at Mississippi Embayment sites using vertical seismic profiling data.Bulletin of the seismological society of America,2007,97(2):614-623.
[2]Ganley D C.A method for calculation synthetic seismograms which include the effect of absorption and dispersion. Geophysics,1981,46:1100.
[3](美)J.F.克莱鲍特著,许云泽.地震成像理论及方法.北京:石油工业出版社,199l. Clacrbout,J.F.,Xu Y.The theory and method of seismic tomography.Beijing:Petroleum Industry Press,1991.
[4]杨文采.非均匀层状介质中地震波速的成像.地球物理学报, 1990,33(2):265-282. Yang W C.Seismic velocity imaging of inhomogeneous layered medium.Chinese J.Geophys.(in Chinese),1990,33(2):265 -282.
[5]杨文采.地球物理反演的理论与方法.北京:地质出版社,1997. 124-354. Yang W C.The theory and method of geophysical inversion. Beijing.Geological Publishing House,1997.
[6]Haskell N A.The dispersion of surface waves on multilayered media:Bulletin of the seismological association of America, 1953,43:17-34.
[7]Wyatt K D,Wyatt S B.The determination of subsurface structural information using the vertical seismic profile: Geophysics,1982,47:465-466.
[8]Young T K.Computer modeling of vertical seismic profiling, Geophysical prospecting,1984,32:851-870.
[9]朱光明,胡建平,邱陶兴.零偏移距VSP射线追踪模型.石油物探,1985,24(4):32-40. Zhu G M,Hu J P,Qiu T X.Ray-tracing model of zero-offset VSP.Geophysical Prospecting for Petroleum,1985,24(4):32 -40.
[10]Michel Dietrich,Michel Bouchon.Synthetic vertical seismic pro files in elastic media:Geophysics,1985,50(2):224 - 234.
[11]王彦春,董毓明.粘弹介质零偏移距VSP计算.石油物探, 1990,29(2):45-52. Wang Y C,Dong Y M.Computing for the viscous elastic medium zero-offset VSP data.Geophysical Prospecting for Petroleum,1990,29(2):45-52.
[12]Dietrich M,Bouchon M.Synthetic vertical seismic pro-files in elastic media:Geophysics,1985,50:224-234.
[13]McMechan G A.Synthetic finite-offset vertical seismic profiles for laterally varying media:Geophysics,1985,50(4):627-636.
[14]朱光明,胡建平,邱陶兴.VSP非零偏移距任意界面渐进射线追踪模型.石油物探,1986,25(4):14-27. Zhu G M,Hu J P,Qiu T X.Asymptotic ray tracing modeling of VSP with arbitrary boundaries and offsets.Geophysical Prospecting for Petroleum,1986,25(4):14-27.
[15]Aminzadeh F,Mendel J M.Synthetic vertical seismic profiles for non-normal incidence plane waves:Geophysics,1985, 50:178-188.
[16]肖春燕,庄东海,金耀祖.垂直地震剖面的有限元正演模拟.江汉石油学院学报,1944,16(supp):80-86. Xiao C Y,Zhuang D H,Jin Y Z.Forword modeling VSP by finite element method.Journal of Jianghan Petroleum Institute,1994,16(supp):80-86.
[17]王成礼,李秉富等.一种斜井VSP的正演模型.青岛海洋大学学报,1995,25(3):382-390. Wang C L,Li B F.A forward model of deviate well VSP. Journal of Ocean University of Qingdao,1995,25(3):382- 390.
[18]李锐坚.VPS高阶有限差分正演模型.西安石油学院学报, 1996,11(2):38-42. Li R J.High order finite difference modeling for VSP of acoustic wave equation.Journal of Xi'an Petroleum Institute, 1996,11(2):38-42.
[19]胡建平.变偏移距VSP射线追踪模型.西安工程学院学报, 1998,20(supp):7-10. Hu J P.Walkway VSP ray tracing model.Journal of Xi'an Engineering University,1998,20(supp):7 - 10.
[20]王成礼,韩文功,王延光,董良国.VSP弹性波方程正演模拟与波场分析.油气地球物理,2006,4(4):7-15. Wang C L,Han W G.The equation forward modeling and wave field analysis of VSP elastic wave.Petroleum Geophysics,2006,4(4 ):7 - 15.
[21]董良国,马在田,曹景忠等.一阶弹性波动方程交错网格高阶差分解法.地球物理学报,2000,43(3):411-419. Dong L G,Ma Z T,Cao J Z.A staggered-grid high-order difference method of one-order elastic wave equation.Chinese J.Geophys.(in Chinese),2000,43(3):411-419.
[22]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移.地球物理学报,2009,52(3):801-807. Du Q Z,Qin T.Multicomponent prestack reverse-time migration of elastic waves in transverse isotropic medium, Chinese J.Geophys.(in Chinese),2009,52(3):801-807.
[23]王润秋,李兰兰,李会俭.塔里木地区勘探地震正演模拟研究.地球物理学报,2010,53(8):1875-1882. Wang R Q,Li L L,Li H J.Forward modeling research for seismic exploration of Tarim area.Chinese J.Geophys.(in Chinese),2010,53(8):1875- 1882.
[24]张文波.井间地震交错网格高阶差分数值模拟及逆时偏移成像研究:[博士论文].长安大学,2005. Zhang W B.Research on cross-hole seismic simulation with staggered grid high order difference method and reverse-time migration imaging:[Ph.D.thesis](in Chinese).Changan University,2005.
[25]杨志峰,王煊.高精度有限差分方法研究进展.自然科学进展,1999,9(9):769-779. Yang Z F,Wang X.Advances in finite difference method with high accuracy,Progress in natural science,1999,9(9):769- 779.
[26]Aki,K.and P.G.Richards.Quantitative Seismology,W. H.Freeman and Co.,San Francisco,1980.
[27]Xu Y X.Finite-difference modeling of high-frequency rayleigh-wave propagation for near-surface applications.Expanded Abstract,75th SEG Meeting,Houston,2005.
[28]Xu Y X,Xia J H,R.Miller.Numerical investigation of implementation of air/earth boundary by acoustic/elastic boundary approach:Geophysics,2007,in Press.
[29]王永刚.完全匹配层吸收边界条件的研究.中国石油大学学报,2007,31:20-26. Wang Y G.Study of absorbing boundary condition by perfectly matched layer.Journal of china university of petroleum,2007,31:20-26.
[30]陈浩,王秀明,赵海波.旋转交错网格有限差分及其完全匹配层吸收边界条件.科学通报,2006,51(17):1985-1995. Chen H,Wang X M,Zhao H B.A rotated staggered grid finite difference with the absorbing boundary condition of a perfectly matched layer.Chinese science bulletin,2006,51 (17):1985-1995.
[31]Francis Collino and Chrysoula Tsoka.Application of the perfectly matched absorbing layer model to the liner electrodynamics problem in anisotropic heterogeneous media. Geophysics 2001,166:294-307.
[32]孙建国.复杂地表条件下地球物理数值模拟方法评述.世界地质,2007,26(3):345-357. Sun J G.Methods for numerical modeling of geophysical fields under complex topographical conditions:a critical review. Global Geology(in Chinese),2007,26(3):345-357.
[33]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005. Mou Y G,Pei Z L.Seismic numerical modeling for 3-D complex media(in Chinese).Beijing:Petroleum Industry Press,2005.
[34]高静怀,杨森林,王大兴.利用VSP资料直达波的包络峰值处瞬时频率提取介质品质因子.地球物理学报,2008,5l(3): 853-861. Gao J H,Yang S I,Wang D X.Quality factor extraction using instanteous frequency at envelope peak of direct waves of VSP data.Chinese J.Geophys.(in Chinese),2008,51(3): 853-861.
[35]Ge J D,Puiol J,Pezshk S,et al.Determination of shallow shear-wave velocity at Mississippi Embayment sites using vertical seismic profiling data.Bulletin of the seismological society of America,2007,97(2):614-623.
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