三维多值走时地震波场重建及格林函数计算
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摘要
针对三维复杂介质地震波传播数值计算中出现的多值走时情况，阐述了地震波场重建及格林函数计算中的困难，提出一种在相空间拉格朗日流形上的波场重建及格林函数计算方法．本文算法应用于三维叠前深度偏移处理流程时，可高效地获得均匀网格点上地震波多值走时及振幅的数值计算结果．文中还阐明两类数值计算过程判据，以在多值走时区域及计算的全区域中，控制射线追踪过程中的射线密度及格林函数计算精度．算例验证了本文方法的有效性．
Based on wavefield construction, an efficient algorithm for multivalued traveltime wavefield is presented. This method overcomes the difflculties in ray series method in conventional configuration space due to complicated velocity structure by implementing the calculation in phase space instead. It solves out the required multi-valued traveltime and amplitude at the uniform dispersed grids efficiently when applied to 3-D prestack depth migration. Two criterions for controlling and balancing the global computational accuracy and efficiency are also discussed in this paper. The numerical examples show that our method is applicable to complicated geological models.
Based on wavefield construction, an efficient algorithm for multivalued traveltime wavefield is presented. This method overcomes the difflculties in ray series method in conventional configuration space due to complicated velocity structure by implementing the calculation in phase space instead. It solves out the required multi-valued traveltime and amplitude at the uniform dispersed grids efficiently when applied to 3-D prestack depth migration. Two criterions for controlling and balancing the global computational accuracy and efficiency are also discussed in this paper. The numerical examples show that our method is applicable to complicated geological models.
引文
[1] Operto S, Lambare G, Thierry P. CPU efficient ray + Born inversion for complex velocity field. In: EAGEConference Expanded Abstracts, 1997. 33.
[2] Vidale J. Finite-difference calculation of travel time. Bull. seism. Soc. am., 1988, 78:2062-2076.
[3] Van Trier J, Symes W W. Upwind finite difference calculation of traveltimes. Geophysics,1991, 56:812-821.
[4] Podvin P. Lecomte I.Finite difference computation of traveltimes in very contrasted velocity models: amassively parallel approach and its associated tools. Geophys. J. Int., 1991, 105:271-284.
[5]黄联捷,李幼铭,吴如山.用于图像重建的波前法射线追踪地球物理学报,1992,35(2):223-233.HUANG Lian-Jie, LI You-Ming, WU Ru-Shan. The wavefront ray tracing method for image reconstruction.Chinese J. Geophys. (in Chinese), 1992, 35(2): 223-233.
[6]刘洪,孟繁林,李幼铭.计算最小走时和射线路径的界面网全局方法地球物理学报,1995,38(1)823-831.LIU Hong, MENG Fan-Lin, LI You-Ming. The interface grid method for seeking global minimumtraveltime and the corresponding raypath.Chinese J Geophys. (in Chinese), 1995, 38(1): 823-831.
[7] Xiutian W, Waltham D. The stable beam seismic modeling method. Geophysics Pros., 1995, 43:939-961.
[8]高亮,李幼铭,陈旭荣等地震射线的辛几何算法尝试.见:国家自然科学基金“九五’重大项目“陆相油储地球物理理论及三维地质图像成图方法’年度研究课题进展及阶段成果摘要.1998,34GAO Liang, LI You-Ming, CHENG Xu-Rong, et al. Elementary study of symplectic geometrical algorithmfor ray tracing. In: Abstracts of annual progresses of National Natural Sciences Foundahon project "OilReservoir", 1998, 34.
[9] Chapman C H, A new method for computing synthetic seismograms. Geophys.J. R Astr. Soc., 1978, 54:481-518.
[10] Chapman C H. Drummond R Body wave seismograms in inhomogeneous media using Maslov asymptotictheory. Bull. Seism. Soc.Am.,1982, 72(6):277-317.
[11] Vinje V. Iversen E, Gjoystdal H. Traveltime and amplitude estimation using wavefront construction. In:EAEG Ann. Meetg, Abstract, 1992. 504-505.
[12] Sun Y. Computation of 2D multiple multiple arrival travel time fields by an interpolative shooting method. In: 62thSEG Ann. Meetg, Expanded Abstracts, 1992, 1320-1323.
[13] Langan R T, Lerche I, Cutler R T. Tracing of rays through heterogeneous media: an accurate and efficientprocedure. Geophysics, 1985, 50: 1456-1465.
[14] Lambare G, Lucio P S, Hanyga A. Two dimensional multivalued traveltime and amplitude maps byuniform sampling of a ray field. Geophys.J Int., 1996, 125.584-598.
[15]徐升,杨长春,刘洪等.射线追踪的微变网格方法.地球物理学报,1996,39(3);23-34.XU Sheng, YANG Chang-Chun, LIU Hong, et al. Grid-changeable method for ray tracing. Chinese J.Geophys.(in Chinese), 1996, 39(3);23-34.
[16] Farra V, Madariaga K Seismic waveform modeling in heterogeneous media by ray perturbation theory. J.Geophys.Res., 1987, 92: 2697-2712.
[17]尹峰,李幼铭.反演二维非均匀介质背景中速度扰动的波动方程层析成像方法.见:杨文采,李幼铭等主编应用地震层析成像北京地质出版社, 1993:111-141.YIN Feng, LI You-Ming. Wave equation tomographic method for inversion of velocity distribution ininhomogeneous medium. In; Applied Seismic Tomography. edited by YANG Wen-Cai, LI You-Ming, et al.Beijing: Geological Press, 1993. 111-141.
[18]张钋,李幼铭,杨长春.波动方程Maslov射线解的有限差分计算.地球物理学报,1995, 38(增刊 1):74-80ZHANG Po, LI You-Ming, YANG Chang-Chun. Finite-difference calculation of Maslov asymptotic raysolution for wave equation. Chinese J. Geophys. (In Chinese), 1995, 38(supp. 1): 74-80.
[19]杨长春,张钋,张洪宙.利用合成地震记录的道集相关函数速度分析方法. CPS/SEG/EAGE国际地球物理研讨会论文详细摘要,1998,198-200.YANG Chang-Chun, ZHANG Po, ZHANG Hong-Zhou. Velocity analysis method with correlation functionof synthetic data on CMP gather. In: Expanded Abstracts (in Chinese), CPS / SEG / EAGE InternationalGeophysical Reference, 1998, 198-200.
[20]张永海,杨孔庆,李幼铭等.哈密顿体系的地震波传播模型.CPS/ SEG/ EAGE国际地球物理研讨会论文详细摘要.1998,639-640.ZHANG Yong-Hai, YANG Kong-Qing, LI You-Ming. Simulation of seismic waves by Hamilton system. In:Expanded Abstracts (in Chinese), CPS / SEG / EAGE International Geophysical Reference, 1998, 639-640.
[21] Chapman C H. The computation of body wave synthetic seismograms in laterally homogeneous media. Rev.Gophysics, 1985, 23: 105-163.
[22] Thomson C J, Chapman C H. An introduction to Maslov asymptohc method. J. R Astr.Soc.,1985, 83:143-168.
[23] Menahem B A, Beydoun W B. Range of validity of seismic ray and beam methods in generalinhomogeneous media. Geophys. J. R Astr. Soc., 1985, 82: 202-262.
[24]Gerveny V, Molotkov I A, Psencik I.地震学中的射线方法二刘福田等译北京地质出版社,1986Cerveny V, Molotkov I A, Psencik 1. Ray Series Method in Seismology (in Chinese). translated by LIUFu-Tian, et al. Beijing: Geological Press, 1987.
[25]杨国光,宋菲君.高等物理光学合肥中国科学技术人学出版社,1985.YANG Guo-Guang, SONG Fei-Jun. Advanced Physical Optics (in Chinese). Hefei: Publisher of Universityof Science and Technology of China. 1985.
[2] Vidale J. Finite-difference calculation of travel time. Bull. seism. Soc. am., 1988, 78:2062-2076.
[3] Van Trier J, Symes W W. Upwind finite difference calculation of traveltimes. Geophysics,1991, 56:812-821.
[4] Podvin P. Lecomte I.Finite difference computation of traveltimes in very contrasted velocity models: amassively parallel approach and its associated tools. Geophys. J. Int., 1991, 105:271-284.
[5]黄联捷,李幼铭,吴如山.用于图像重建的波前法射线追踪地球物理学报,1992,35(2):223-233.HUANG Lian-Jie, LI You-Ming, WU Ru-Shan. The wavefront ray tracing method for image reconstruction.Chinese J. Geophys. (in Chinese), 1992, 35(2): 223-233.
[6]刘洪,孟繁林,李幼铭.计算最小走时和射线路径的界面网全局方法地球物理学报,1995,38(1)823-831.LIU Hong, MENG Fan-Lin, LI You-Ming. The interface grid method for seeking global minimumtraveltime and the corresponding raypath.Chinese J Geophys. (in Chinese), 1995, 38(1): 823-831.
[7] Xiutian W, Waltham D. The stable beam seismic modeling method. Geophysics Pros., 1995, 43:939-961.
[8]高亮,李幼铭,陈旭荣等地震射线的辛几何算法尝试.见:国家自然科学基金“九五’重大项目“陆相油储地球物理理论及三维地质图像成图方法’年度研究课题进展及阶段成果摘要.1998,34GAO Liang, LI You-Ming, CHENG Xu-Rong, et al. Elementary study of symplectic geometrical algorithmfor ray tracing. In: Abstracts of annual progresses of National Natural Sciences Foundahon project "OilReservoir", 1998, 34.
[9] Chapman C H, A new method for computing synthetic seismograms. Geophys.J. R Astr. Soc., 1978, 54:481-518.
[10] Chapman C H. Drummond R Body wave seismograms in inhomogeneous media using Maslov asymptotictheory. Bull. Seism. Soc.Am.,1982, 72(6):277-317.
[11] Vinje V. Iversen E, Gjoystdal H. Traveltime and amplitude estimation using wavefront construction. In:EAEG Ann. Meetg, Abstract, 1992. 504-505.
[12] Sun Y. Computation of 2D multiple multiple arrival travel time fields by an interpolative shooting method. In: 62thSEG Ann. Meetg, Expanded Abstracts, 1992, 1320-1323.
[13] Langan R T, Lerche I, Cutler R T. Tracing of rays through heterogeneous media: an accurate and efficientprocedure. Geophysics, 1985, 50: 1456-1465.
[14] Lambare G, Lucio P S, Hanyga A. Two dimensional multivalued traveltime and amplitude maps byuniform sampling of a ray field. Geophys.J Int., 1996, 125.584-598.
[15]徐升,杨长春,刘洪等.射线追踪的微变网格方法.地球物理学报,1996,39(3);23-34.XU Sheng, YANG Chang-Chun, LIU Hong, et al. Grid-changeable method for ray tracing. Chinese J.Geophys.(in Chinese), 1996, 39(3);23-34.
[16] Farra V, Madariaga K Seismic waveform modeling in heterogeneous media by ray perturbation theory. J.Geophys.Res., 1987, 92: 2697-2712.
[17]尹峰,李幼铭.反演二维非均匀介质背景中速度扰动的波动方程层析成像方法.见:杨文采,李幼铭等主编应用地震层析成像北京地质出版社, 1993:111-141.YIN Feng, LI You-Ming. Wave equation tomographic method for inversion of velocity distribution ininhomogeneous medium. In; Applied Seismic Tomography. edited by YANG Wen-Cai, LI You-Ming, et al.Beijing: Geological Press, 1993. 111-141.
[18]张钋,李幼铭,杨长春.波动方程Maslov射线解的有限差分计算.地球物理学报,1995, 38(增刊 1):74-80ZHANG Po, LI You-Ming, YANG Chang-Chun. Finite-difference calculation of Maslov asymptotic raysolution for wave equation. Chinese J. Geophys. (In Chinese), 1995, 38(supp. 1): 74-80.
[19]杨长春,张钋,张洪宙.利用合成地震记录的道集相关函数速度分析方法. CPS/SEG/EAGE国际地球物理研讨会论文详细摘要,1998,198-200.YANG Chang-Chun, ZHANG Po, ZHANG Hong-Zhou. Velocity analysis method with correlation functionof synthetic data on CMP gather. In: Expanded Abstracts (in Chinese), CPS / SEG / EAGE InternationalGeophysical Reference, 1998, 198-200.
[20]张永海,杨孔庆,李幼铭等.哈密顿体系的地震波传播模型.CPS/ SEG/ EAGE国际地球物理研讨会论文详细摘要.1998,639-640.ZHANG Yong-Hai, YANG Kong-Qing, LI You-Ming. Simulation of seismic waves by Hamilton system. In:Expanded Abstracts (in Chinese), CPS / SEG / EAGE International Geophysical Reference, 1998, 639-640.
[21] Chapman C H. The computation of body wave synthetic seismograms in laterally homogeneous media. Rev.Gophysics, 1985, 23: 105-163.
[22] Thomson C J, Chapman C H. An introduction to Maslov asymptohc method. J. R Astr.Soc.,1985, 83:143-168.
[23] Menahem B A, Beydoun W B. Range of validity of seismic ray and beam methods in generalinhomogeneous media. Geophys. J. R Astr. Soc., 1985, 82: 202-262.
[24]Gerveny V, Molotkov I A, Psencik I.地震学中的射线方法二刘福田等译北京地质出版社,1986Cerveny V, Molotkov I A, Psencik 1. Ray Series Method in Seismology (in Chinese). translated by LIUFu-Tian, et al. Beijing: Geological Press, 1987.
[25]杨国光,宋菲君.高等物理光学合肥中国科学技术人学出版社,1985.YANG Guo-Guang, SONG Fei-Jun. Advanced Physical Optics (in Chinese). Hefei: Publisher of Universityof Science and Technology of China. 1985.
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