用于速度自动拾取的路径积分优化法与光顺处理技术
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摘要
将用于图像处理的光顺技术引用到速度谱能量团曲面的处理环节,借以提高速度谱的分辨率,为最终获得高精确解提供一全新的途径.具体思路是基于路径积分优化法——Viterbi算法所具有的自动搜寻及获取最优解的功能,将其应用于地震资料处理中的速度自动拾取,使其向前做最大"能量团"的积分向后递归计算最优解——叠加速度,但这种解的准确性往往与所定义的目标函数——速度谱的分辨率有关.演算结果表明,Viterbi算法与关顺处理技术的有机结合,不仅提高了速度提取的精度,而且实现了速度的自动拾取,可提高常规地震资料处理的效率,从而可快捷地为叠前深度偏移提供所需初始速度模型.
In this paper,we introduce the Viterbi algorithm and apply it to auto pick the stack velocity.Here,the Viterbi algorithm makes the rule to integral the max velocity spectrum,"energy group",forward and to get the optimal solution in recursion backward.The veracity of the solution has relation to the objective function,namely,the resolution of velocity spectrum.Therefore,we introduce a method of fairing for image processing to smooth the surface of velocity spectrum,to improve the resolution of velocity spectrum,finally,to provide a new way to obtain a solution of high accuracy.The results showed that it is not only helpful to improve precision of velocity picked,but also to realize auto-picking velocity by the Viterbi algorithm combined with surface fairing.Therefore,it is not only helpful to improve the efficiency of the conventional seismic data processing,but also rapid to provide the initial velocity for pre-stack depth migration.
In this paper,we introduce the Viterbi algorithm and apply it to auto pick the stack velocity.Here,the Viterbi algorithm makes the rule to integral the max velocity spectrum,"energy group",forward and to get the optimal solution in recursion backward.The veracity of the solution has relation to the objective function,namely,the resolution of velocity spectrum.Therefore,we introduce a method of fairing for image processing to smooth the surface of velocity spectrum,to improve the resolution of velocity spectrum,finally,to provide a new way to obtain a solution of high accuracy.The results showed that it is not only helpful to improve precision of velocity picked,but also to realize auto-picking velocity by the Viterbi algorithm combined with surface fairing.Therefore,it is not only helpful to improve the efficiency of the conventional seismic data processing,but also rapid to provide the initial velocity for pre-stack depth migration.
引文
[1]Toldi J.Velocity analysis without picking[Ph.D.Thesis].Stanford:Stanford University,1985.
[2]Zhang L,Claerbout J.Automatic dip-picking by non-linearoptimization.SEP(67),1990:123-138.
[3]陈志德,刘振宽,李成斌.三维叠前深度偏移速度分析及蒙特卡洛自动层速度拾取.地球物理学报,2002,45(2):246-254.Chen Z D,Liu Z K,Li C B.3-D Pre-stack depth migrationvelocity analysis and automatic monte carlo velocity picking indepth.Chinese J.Geophys.(in Chinese),2002,45(2):246-254.
[4]McEliece R J.The Theory of Information and Coding.Massachusetts:Addison-Wesley Publishing Company,1977.
[5]Yoshua B.Markovian Models for Sequential Data[EB/OL].http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.5337.1996-10-22.
[6]Méndez L A T.Viterbi Algorithm in Text Recognition:Termproject for course:308-644B.Montreal:McGill University,1998.
[7]Zhang L.Automatic picking and its applications.SEP(70),1990:275-292.
[8]林年添,刘洪,李建勇.基于Viterbi算法的复杂地质体速度约束化自动拾取.地球物理学进展,2004,19(2):311-316.Lin N T,Liu H,Li J Y.Automatic picking velocity by theviterbi algorithm for the complex geological case.Progress inGeophysics(in Chinese),2004,19(2):311-316.
[9]Pérez-Arribas F,Suárez-Suárez J A,Fernández-Jambrina L.Automatic surface modelling of a ship hull.Computer AidedDesign,2006,38(6):584-594.
[10]李学艺,姜虹,陈松等.基于马尔可夫随机场的曲面光顺算法.西安交通大学学报,2003,37(3):241-244.Li X Y,Jiang H,Chen S,et al.Surface fairing algorithmbased on Markov random fields.Journal of Xi′an JiaotongUniversity(in Chinese),2003,37(3):241-244.
[11]Sariz E.An optimization approach for fairing of ship hullforms.Ocean Engineering,2006,33(16):2105-2118.
[12]林年添,柴慧婵,魏立杰等.速度谱曲面的光顺处理及其作用.地球物理学进展,2011,26(3):311-316.Lin N T,Chai H C,Wei L J,et al.Surface fairing with itsaction on the Velocity Spectrum.Progress in Geophysics(inChinese),2011,26(3):311-316.
[13]杨长春,倪彤光.一种高效的混合曲面光顺算法.计算机应用,2005,25(11):2609-2611.Yang C C,Ni T G.Efficient hybrid algorithm for meshsmoothing of surfaces.Journal of Computer Applications(in Chinese),2005,25(11):2609-2611.
[14]Luo X N,Liu N,Gao C Y.Fairing geometric modeling basedon 4-point interpolatory subdivision scheme.Journal ofComputational and Applied Mathematics,2004,163(1):189-197.
[15]Zhang C N,Zhang P F,Cheng F H.Fairing spline curvesand surfaces by minimizing energy.Computer-Aided Design,2001,33(13):913-923.
[16]甘屹,齐从谦,陈亚洲.基于遗传算法的曲线曲面光顺.同济大学学报(自然科学版),2002,30(3):322-325,334.Gan Y,Qi C Q,Chen Y Z.Smoothing of curves and surfacesbased on genetic algorithm.Journal of Tongji University(Natural Science)(in Chinese),2002,30(3):322-325,334.
[17]Renka J R.Constructing fair curves and surfaces with aSobolev gradient method.Computer Aided Geometric Design,2004,21(2):137-149.
[18]Xu G L.Surface fairing and featuring by mean curvaturemotions.Journal of Computational and Applied Mathematics,2004,163(1):295-309.
[19]林年添.保重心脉冲压缩滤波及其在速度自动拾取中的应用[博士学位论文].北京:中国科学院研究生院,2004.Lin N T.Automatic Picking Velocity by Gravity CenterPreserved Pulse Compressed Filter and the Viterbi Algorithm[Ph.D.Thesis](in Chinese).Beijing:Chinese Academy ofSciences,2004.
[20]Taner M T,Koehler F,Sheriff R E.Complex seismic traceanalysis.Geophysics,1979,44(6):1041-1063.
[2]Zhang L,Claerbout J.Automatic dip-picking by non-linearoptimization.SEP(67),1990:123-138.
[3]陈志德,刘振宽,李成斌.三维叠前深度偏移速度分析及蒙特卡洛自动层速度拾取.地球物理学报,2002,45(2):246-254.Chen Z D,Liu Z K,Li C B.3-D Pre-stack depth migrationvelocity analysis and automatic monte carlo velocity picking indepth.Chinese J.Geophys.(in Chinese),2002,45(2):246-254.
[4]McEliece R J.The Theory of Information and Coding.Massachusetts:Addison-Wesley Publishing Company,1977.
[5]Yoshua B.Markovian Models for Sequential Data[EB/OL].http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.5337.1996-10-22.
[6]Méndez L A T.Viterbi Algorithm in Text Recognition:Termproject for course:308-644B.Montreal:McGill University,1998.
[7]Zhang L.Automatic picking and its applications.SEP(70),1990:275-292.
[8]林年添,刘洪,李建勇.基于Viterbi算法的复杂地质体速度约束化自动拾取.地球物理学进展,2004,19(2):311-316.Lin N T,Liu H,Li J Y.Automatic picking velocity by theviterbi algorithm for the complex geological case.Progress inGeophysics(in Chinese),2004,19(2):311-316.
[9]Pérez-Arribas F,Suárez-Suárez J A,Fernández-Jambrina L.Automatic surface modelling of a ship hull.Computer AidedDesign,2006,38(6):584-594.
[10]李学艺,姜虹,陈松等.基于马尔可夫随机场的曲面光顺算法.西安交通大学学报,2003,37(3):241-244.Li X Y,Jiang H,Chen S,et al.Surface fairing algorithmbased on Markov random fields.Journal of Xi′an JiaotongUniversity(in Chinese),2003,37(3):241-244.
[11]Sariz E.An optimization approach for fairing of ship hullforms.Ocean Engineering,2006,33(16):2105-2118.
[12]林年添,柴慧婵,魏立杰等.速度谱曲面的光顺处理及其作用.地球物理学进展,2011,26(3):311-316.Lin N T,Chai H C,Wei L J,et al.Surface fairing with itsaction on the Velocity Spectrum.Progress in Geophysics(inChinese),2011,26(3):311-316.
[13]杨长春,倪彤光.一种高效的混合曲面光顺算法.计算机应用,2005,25(11):2609-2611.Yang C C,Ni T G.Efficient hybrid algorithm for meshsmoothing of surfaces.Journal of Computer Applications(in Chinese),2005,25(11):2609-2611.
[14]Luo X N,Liu N,Gao C Y.Fairing geometric modeling basedon 4-point interpolatory subdivision scheme.Journal ofComputational and Applied Mathematics,2004,163(1):189-197.
[15]Zhang C N,Zhang P F,Cheng F H.Fairing spline curvesand surfaces by minimizing energy.Computer-Aided Design,2001,33(13):913-923.
[16]甘屹,齐从谦,陈亚洲.基于遗传算法的曲线曲面光顺.同济大学学报(自然科学版),2002,30(3):322-325,334.Gan Y,Qi C Q,Chen Y Z.Smoothing of curves and surfacesbased on genetic algorithm.Journal of Tongji University(Natural Science)(in Chinese),2002,30(3):322-325,334.
[17]Renka J R.Constructing fair curves and surfaces with aSobolev gradient method.Computer Aided Geometric Design,2004,21(2):137-149.
[18]Xu G L.Surface fairing and featuring by mean curvaturemotions.Journal of Computational and Applied Mathematics,2004,163(1):295-309.
[19]林年添.保重心脉冲压缩滤波及其在速度自动拾取中的应用[博士学位论文].北京:中国科学院研究生院,2004.Lin N T.Automatic Picking Velocity by Gravity CenterPreserved Pulse Compressed Filter and the Viterbi Algorithm[Ph.D.Thesis](in Chinese).Beijing:Chinese Academy ofSciences,2004.
[20]Taner M T,Koehler F,Sheriff R E.Complex seismic traceanalysis.Geophysics,1979,44(6):1041-1063.
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