地震波旅行时计算方法及其模型试验分析
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摘要
地震波旅行时的计算是地震波偏移成像技术和地震层析成像技术的核心内容,同时也是实现保幅叠前偏移成像的重要因素。推导了地震波波动方程高阶有限差分法计算格式,提出了最大绝对振幅能量节点初至旅行时拾取的方法。均匀介质模型试验表明,该方法与用解析解、程函方程法计算的旅行时等值线基本重合。基于层状介质模型、凹陷模型和Marmousi模型对方法的适用性进行了试验,将由该方法计算得到的初至旅行时作为叠前逆时成像条件,对凹陷模型和Marmousi模型的数值模拟记录进行了叠前逆时偏移成像,偏移叠加剖面很好地反映了模型的地质特征。
The computation of seismic wave travel-time is the core for seismic wave migration and seismic tomography,which is also an important factor for realizing amplitude-preservation pre-stack migration. We derived the high-order finite-difference computational format for seismic wave equation,and put forward to a method for picking up first arrival corresponding to maximal absolute amplitude energy while forward modeling.The experiment on the isotropic model shows that the contour maps of travel-time obtained by our method are almost overlapped with that of analytical method and eikonal equation method.The applicability of the method was tested on layered medium model,depression model and Marmousi model,what's more,the first-arrival travel-time calculated by our method was taken as the imaging condition to carry out pre-stack reverse-time migration on the numerical simulated records of depression model and Marmousi model.The migration and stack sections perfectly reflect the geologic characteristics of the models.
The computation of seismic wave travel-time is the core for seismic wave migration and seismic tomography,which is also an important factor for realizing amplitude-preservation pre-stack migration. We derived the high-order finite-difference computational format for seismic wave equation,and put forward to a method for picking up first arrival corresponding to maximal absolute amplitude energy while forward modeling.The experiment on the isotropic model shows that the contour maps of travel-time obtained by our method are almost overlapped with that of analytical method and eikonal equation method.The applicability of the method was tested on layered medium model,depression model and Marmousi model,what's more,the first-arrival travel-time calculated by our method was taken as the imaging condition to carry out pre-stack reverse-time migration on the numerical simulated records of depression model and Marmousi model.The migration and stack sections perfectly reflect the geologic characteristics of the models.
引文
[1]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟[J].中国海洋大学学报,2005,35(1):43-48
[2]Falk J,Tessmer E,Gajewski D.Efficient finite-difference modeling of seismic wave using locally adiustable time step[J].Geophysics Prospecting,1998,46(6): 603-616
[3]Lysmer J,Drake L A.A finite element method for seismology[J].Journal of Computational Physics, 1972,11(11):181-216
[4]Marfurt K J.Accuracy of finite-difference and finiteelement modeling of the scalar and elastic wave equations [J].Geophysics,1984,49(5):533-549
[5]杜启振,杨慧珠.方位各向异性粘弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2014
[6]Gaadag J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(6): 854-859
[7]Kosloff D D,Baysal E.Forward modeling by a Fourier method[J].Geophysics,1982,47(10): 1402-1421
[8]Tessmer E,Kosloff D.3-D elastic modeling with surface topography by a Chebychev spectral method [J].Geophysics,1994,59(3):464-473
[9]Bleistein N.On the imaging of reflectors in the earth [J].Geophysics,1987,52(3):931-942
[10]Hanitzsch C.Comparison of weights in prestack amplitude -preserving Kirchhoff depth migration[J]. Geophysics,1997,62(6):1812-1816
[11]Julian B R,Gubbins D.Three-dimensional seismic ray tracing[J].Geophysics,1977,42(1 ):95-114
[12]Lambare G,Lucio P S,Hanyga A.Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of a ray field[J].Geophysical Journal International,1996,125(2):584-598
[13]Schneider W A,Ranzinger K A,Balch A H,et al.A dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities[J].Geophysics,1992,57(1):39-50
[14]Moser T J.Shortest path calculation of travel time [J].Geophysics,1991,56(1):59-67
[15]Vidale J.Finite-difference calculation of traveltimes [J].Bulletin of the Seismiclogical Society of America, 1988,78(6):2062-2076
[16]Podvin P,LecomteⅠ.Finite-difference computation of traveltimes in very contrasted velocity models:a massively paralled approach and its associated tools[J].Geophysical Journal International,1991,105(1 ):271- 284
[17]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution of the eikonal equation along expanding wavefronts [J].Geophysics,1992,57(3):478-487
[18]Hole J A,Zelt B C.3-D finite-difference reflection traveltime[J].Geophysical Journal International, 1995,121(2):427-434
[19]Afnimar,Kazuki K.Finite difference traveltime calculation for head waves traveling along an irregular interface[J].Geophysical Journal International, 2000,143(3):729-734
[20]Sethian J A,Popovici A M.3-D traveltime computation using the fast marching method[J].Geophysics, 1999,64(3):516-523
[21]Nichols D E.Maximum energy traveltimes calculated in the seismic frequency band[J].Geophysics, 1996,61(1):253-263
[22]Shin S,Shin C,Kim W.Traveltime calculation using monochromatic one-way wave equation[J].Expanded Abstracts of 70~(th) Annual Internat SEG Mtg, 2000,2313-2316
[23]Shin C,Ko S,Kim W,et al.Traveltime calculations from frequency-domain downward-continuation algorithms [J].Geophysics,2003,68(4):1380-1388
[24]Shin C S,Ko S W,Marfurt K,et al.Wave equation calculation of most energetic traveltimes and amplitudes for Kirchhoff prestack migration[J].Geophysics, 2003,68(6):2040-2042
[25]秦义龙,张中杰,Shin Changsoo,等.利用单频双程波动方程计算初至走时及其振幅[J].地球物理学报,2005,48(2):423-428
[26]薛东川,王尚旭.波动方程有限元叠前逆时偏移[J].石油地球物理勘探,2008,43(1):17-21
[27]杨微,陈可洋.加权吸收边界条件的优化设计[J].石油物探,2009,48(3):244-246,251
[28]陈可洋,杨微.优化的三维地震波双重吸收边界条件[J].勘探地球物理进展,2009,32(3):179-181,206
[29]陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79
[30]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34
[31]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
[32]陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236
[33]陈可洋,杨微,吴清岭,等.几种地震波叠后深度偏移方法的比较[J].勘探地球物理进展,2009,32(4):257- 260
[34]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478
[2]Falk J,Tessmer E,Gajewski D.Efficient finite-difference modeling of seismic wave using locally adiustable time step[J].Geophysics Prospecting,1998,46(6): 603-616
[3]Lysmer J,Drake L A.A finite element method for seismology[J].Journal of Computational Physics, 1972,11(11):181-216
[4]Marfurt K J.Accuracy of finite-difference and finiteelement modeling of the scalar and elastic wave equations [J].Geophysics,1984,49(5):533-549
[5]杜启振,杨慧珠.方位各向异性粘弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2014
[6]Gaadag J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(6): 854-859
[7]Kosloff D D,Baysal E.Forward modeling by a Fourier method[J].Geophysics,1982,47(10): 1402-1421
[8]Tessmer E,Kosloff D.3-D elastic modeling with surface topography by a Chebychev spectral method [J].Geophysics,1994,59(3):464-473
[9]Bleistein N.On the imaging of reflectors in the earth [J].Geophysics,1987,52(3):931-942
[10]Hanitzsch C.Comparison of weights in prestack amplitude -preserving Kirchhoff depth migration[J]. Geophysics,1997,62(6):1812-1816
[11]Julian B R,Gubbins D.Three-dimensional seismic ray tracing[J].Geophysics,1977,42(1 ):95-114
[12]Lambare G,Lucio P S,Hanyga A.Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of a ray field[J].Geophysical Journal International,1996,125(2):584-598
[13]Schneider W A,Ranzinger K A,Balch A H,et al.A dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities[J].Geophysics,1992,57(1):39-50
[14]Moser T J.Shortest path calculation of travel time [J].Geophysics,1991,56(1):59-67
[15]Vidale J.Finite-difference calculation of traveltimes [J].Bulletin of the Seismiclogical Society of America, 1988,78(6):2062-2076
[16]Podvin P,LecomteⅠ.Finite-difference computation of traveltimes in very contrasted velocity models:a massively paralled approach and its associated tools[J].Geophysical Journal International,1991,105(1 ):271- 284
[17]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution of the eikonal equation along expanding wavefronts [J].Geophysics,1992,57(3):478-487
[18]Hole J A,Zelt B C.3-D finite-difference reflection traveltime[J].Geophysical Journal International, 1995,121(2):427-434
[19]Afnimar,Kazuki K.Finite difference traveltime calculation for head waves traveling along an irregular interface[J].Geophysical Journal International, 2000,143(3):729-734
[20]Sethian J A,Popovici A M.3-D traveltime computation using the fast marching method[J].Geophysics, 1999,64(3):516-523
[21]Nichols D E.Maximum energy traveltimes calculated in the seismic frequency band[J].Geophysics, 1996,61(1):253-263
[22]Shin S,Shin C,Kim W.Traveltime calculation using monochromatic one-way wave equation[J].Expanded Abstracts of 70~(th) Annual Internat SEG Mtg, 2000,2313-2316
[23]Shin C,Ko S,Kim W,et al.Traveltime calculations from frequency-domain downward-continuation algorithms [J].Geophysics,2003,68(4):1380-1388
[24]Shin C S,Ko S W,Marfurt K,et al.Wave equation calculation of most energetic traveltimes and amplitudes for Kirchhoff prestack migration[J].Geophysics, 2003,68(6):2040-2042
[25]秦义龙,张中杰,Shin Changsoo,等.利用单频双程波动方程计算初至走时及其振幅[J].地球物理学报,2005,48(2):423-428
[26]薛东川,王尚旭.波动方程有限元叠前逆时偏移[J].石油地球物理勘探,2008,43(1):17-21
[27]杨微,陈可洋.加权吸收边界条件的优化设计[J].石油物探,2009,48(3):244-246,251
[28]陈可洋,杨微.优化的三维地震波双重吸收边界条件[J].勘探地球物理进展,2009,32(3):179-181,206
[29]陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79
[30]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34
[31]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
[32]陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236
[33]陈可洋,杨微,吴清岭,等.几种地震波叠后深度偏移方法的比较[J].勘探地球物理进展,2009,32(4):257- 260
[34]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478
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