基于差分进化算法的叠前AVO反演
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摘要
针对传统的线性化迭代反演算法对初始模型依赖程度较高、反演过程容易陷入局部最优的问题,本文研究了一种基于差分进化算法的叠前反演方法。该方法利用差分的简单变异操作和一对一的竞争生存策略,对初始模型的依赖程度较低,全局收敛能力较强,且具有操作简单、运算速度快的特点,是解决复杂优化问题的一种有效方法。针对叠前地震反演问题,本文以贝叶斯理论为基础,结合似然函数与先验约束信息,建立反演目标函数,然后利用差分进化算法对初始模型进行优化,直至目标函数取得全局最优值。模型试算验证了该方法是可行的,且对初始模型的依赖程度较弱,具有较好的全局收敛能力;将该方法应用于实际叠前道集数据,得到了分辨率较高的反演结果。
As the conventional linear iteration inversion algorithm highly depends on the initial model and may easily lead the solution to be trapped into local optimal solution,this paper studies a pre-stack inversion method on the basis of the differential evolution algorithm.The differential evolution algorithm makes use of simple mutation operations based on difference and one-to-one competitive survival strategies.The algorithm is not strongly dependent on the initial models and has strong global convergence ability,simple operations and fast calculation speed.All these advantages make it an effective technical means to solve complex optimization problems.In view of pre-stacked seismic inversion problems,an objective function is established based on Bayesian theory with the combination of the likelihood function and prior constraint information.Then the initial model is optimized constantly by the differential evolution algorithm until the objective function reaches the global optimum.Model trial indicates that the method is reliable,and also displays weak dependency on the initial model and good global converge ability.Inversion results with high resolution are obtained by applying it to real pre-stacked gathers.
As the conventional linear iteration inversion algorithm highly depends on the initial model and may easily lead the solution to be trapped into local optimal solution,this paper studies a pre-stack inversion method on the basis of the differential evolution algorithm.The differential evolution algorithm makes use of simple mutation operations based on difference and one-to-one competitive survival strategies.The algorithm is not strongly dependent on the initial models and has strong global convergence ability,simple operations and fast calculation speed.All these advantages make it an effective technical means to solve complex optimization problems.In view of pre-stacked seismic inversion problems,an objective function is established based on Bayesian theory with the combination of the likelihood function and prior constraint information.Then the initial model is optimized constantly by the differential evolution algorithm until the objective function reaches the global optimum.Model trial indicates that the method is reliable,and also displays weak dependency on the initial model and good global converge ability.Inversion results with high resolution are obtained by applying it to real pre-stacked gathers.
引文
[1]师学明,王家映.地球物理资料非线性反演方法讲座(三)——模拟退火法.工程地球物理学报,2007,4(3):165～174Shi Xueming,Wang Jiaying.Lecture on non-linearmethods in geophysics(3):Simulated annealingmethod.China Journal of Engineering Geophysics,2007,4(3):165～174
[2]师学明,王家映.地球物理资料非线性反演方法讲座(四)——遗传算法.工程地球物理学报,2008,5(2):129～140Shi Xueming,Wang Jiaying.Lecture on non-linearmethods in geophysics(4):Genetic algorithm.ChinaJournal of Engineering Geophysics,2008,5(2):129～140
[3]Wang Danyang,Zhang Guangzhi.AVO simultaneousinversion using Markov Chain Monte Carlo.SEGTechnical Program Expanded Abstracts,2010,29:444～448
[4]杨培杰.地震子波盲提取与非线性反演[博士学位论文].山东青岛:中国石油大学(华东)地质资源与地质工程系,2008
[5]Storn Rainer,Price Kenneth.Differential evolution:Asimple and efficient herristic for globle optimization o-ver continuous spaces.Journal of Globle Optimiza-tion,1997,11:341～359
[6]吴亮红.差分进化算法及应用研究[硕士学位论文].湖南长沙:湖南大学电气与信息工程系,2007
[7]吴亮红,王耀南,周少武等.采用非固定多段映射罚函数的非线性约束优化差分进化算法.系统工程理论与实践,2007,3(3):128～133Wu Lianghong,Wang Yaonan,Zhou Shaowu et al.Differential evolution for nonlinear constrained opti-mization using non-stationary multistage assignmentpenalty function.Systems Engineering Theory&Practice,2007,3(3):128～133
[8]刘波,王凌,金以慧.差分进化算法研究进展.控制与决策,2007,22(7):721～729Liu Bo,Wang Ling,Jin Yihui.Advances in differen-tial evolution.Control and Decision,2007,22(7):721～729
[9]陈华,范宜仁,邓少贵等.双侧向测井反演的差分进化算法.物探化探技术,2009,31(4):377～380Chen Hua,Fan Yiren,Deng Shaogui et al.The dif-ferential evolutional method of dual-lateral log inver-sion.Computing Techniques for Geophysical andGeochemical Exploration,2009,31(4):377～380
[10]潘克家,王文娟,谭永基等.基于混合差分进化算法的地球物理线性反演.地球物理学报,2009,52(12):3083～3090Pan Kejia,Wang Wenjuan,Tan Yongji et al.Geo-physical linear inversion based on hybrid differentialevolution algorithm.Chinese Journal of Geophys,2009,52(12):3083～3090
[11]Li Zhiwei,Hao Tianyao.A global optimizing ap-proach for waveform inversion of receiver functions.Computers&Geosciences,2010,36:871～880
[12]汪超,赵伟,高静怀.一种用于波形反演的改进差分进化算法.石油地球物理勘探,2012,47(2):225～230Wang Chao,Zhao Wei and Gao Jinghuai.Waveforminversion with an improved differential evolution algo-rithm.OGP,2012,47(2):225～230
[13]Saraswat Puneet,Sen Mrinal K.Simultaneous sto-chastic inversion of prestack seismic data using hy-brid evolutionary algorithm.SEG Technical ProgramExpanded Abstracts,2010,29:2850～2854
[14]杨培杰,印兴耀.非线性二次规划贝叶斯叠前反演.地球物理学报,2008,51(6):1876～1882Yang Peijie,Yin Xingyao.Non-linear quadratic pro-gramming Bayesian prestack inversion.Chinese Jour-nal of Geophys,2008,51(6):1876～1882
[15]栾丽君,谭力静,牛奔.一种基于粒子群优化算法和差分进化算法的新型混合全局优化算法.信息与控制,2007,36(6):708～714Luan Lijun,Tan Lijing,Niu Ben.A novel hybridglobal optimization algorithm based on particle swarmoptimization and differential evolution.Informationand Control,2007,36(3):708～714
[16]刘真.差分进化算法在多目标优化中的应用研究[硕士学位论文].山东青岛:中国石油大学(华东)计算机科学与技术系,2010
[17]李少鹏.AVO地震参数反演方法研究及其应用[硕士学位论文].山东青岛:中国石油大学(华东)地球物理系,2009
[18]张繁昌,刘杰,印兴耀等.修正柯西约束地震盲反褶积方法.石油地球物理勘探,2008,43(4):391～396Zhang Fanchang,Liu Jie,Yin Xingyao et al.Modi-fied Cauchy constrained seismic blind deconvolution.OGP,2008,43(4):391～396
[19]张广智,王丹阳,印兴耀.利用MCMC方法估算地震参数.石油地球物理勘探,2011,46(4):605～609Zhang Guangzhi,Wang Danyang and Yin Xingyao.Seismic parameters estimation using Markov ChainMonte Carlo method.OGP,2011,46(4):605～609
[2]师学明,王家映.地球物理资料非线性反演方法讲座(四)——遗传算法.工程地球物理学报,2008,5(2):129～140Shi Xueming,Wang Jiaying.Lecture on non-linearmethods in geophysics(4):Genetic algorithm.ChinaJournal of Engineering Geophysics,2008,5(2):129～140
[3]Wang Danyang,Zhang Guangzhi.AVO simultaneousinversion using Markov Chain Monte Carlo.SEGTechnical Program Expanded Abstracts,2010,29:444～448
[4]杨培杰.地震子波盲提取与非线性反演[博士学位论文].山东青岛:中国石油大学(华东)地质资源与地质工程系,2008
[5]Storn Rainer,Price Kenneth.Differential evolution:Asimple and efficient herristic for globle optimization o-ver continuous spaces.Journal of Globle Optimiza-tion,1997,11:341～359
[6]吴亮红.差分进化算法及应用研究[硕士学位论文].湖南长沙:湖南大学电气与信息工程系,2007
[7]吴亮红,王耀南,周少武等.采用非固定多段映射罚函数的非线性约束优化差分进化算法.系统工程理论与实践,2007,3(3):128～133Wu Lianghong,Wang Yaonan,Zhou Shaowu et al.Differential evolution for nonlinear constrained opti-mization using non-stationary multistage assignmentpenalty function.Systems Engineering Theory&Practice,2007,3(3):128～133
[8]刘波,王凌,金以慧.差分进化算法研究进展.控制与决策,2007,22(7):721～729Liu Bo,Wang Ling,Jin Yihui.Advances in differen-tial evolution.Control and Decision,2007,22(7):721～729
[9]陈华,范宜仁,邓少贵等.双侧向测井反演的差分进化算法.物探化探技术,2009,31(4):377～380Chen Hua,Fan Yiren,Deng Shaogui et al.The dif-ferential evolutional method of dual-lateral log inver-sion.Computing Techniques for Geophysical andGeochemical Exploration,2009,31(4):377～380
[10]潘克家,王文娟,谭永基等.基于混合差分进化算法的地球物理线性反演.地球物理学报,2009,52(12):3083～3090Pan Kejia,Wang Wenjuan,Tan Yongji et al.Geo-physical linear inversion based on hybrid differentialevolution algorithm.Chinese Journal of Geophys,2009,52(12):3083～3090
[11]Li Zhiwei,Hao Tianyao.A global optimizing ap-proach for waveform inversion of receiver functions.Computers&Geosciences,2010,36:871～880
[12]汪超,赵伟,高静怀.一种用于波形反演的改进差分进化算法.石油地球物理勘探,2012,47(2):225～230Wang Chao,Zhao Wei and Gao Jinghuai.Waveforminversion with an improved differential evolution algo-rithm.OGP,2012,47(2):225～230
[13]Saraswat Puneet,Sen Mrinal K.Simultaneous sto-chastic inversion of prestack seismic data using hy-brid evolutionary algorithm.SEG Technical ProgramExpanded Abstracts,2010,29:2850～2854
[14]杨培杰,印兴耀.非线性二次规划贝叶斯叠前反演.地球物理学报,2008,51(6):1876～1882Yang Peijie,Yin Xingyao.Non-linear quadratic pro-gramming Bayesian prestack inversion.Chinese Jour-nal of Geophys,2008,51(6):1876～1882
[15]栾丽君,谭力静,牛奔.一种基于粒子群优化算法和差分进化算法的新型混合全局优化算法.信息与控制,2007,36(6):708～714Luan Lijun,Tan Lijing,Niu Ben.A novel hybridglobal optimization algorithm based on particle swarmoptimization and differential evolution.Informationand Control,2007,36(3):708～714
[16]刘真.差分进化算法在多目标优化中的应用研究[硕士学位论文].山东青岛:中国石油大学(华东)计算机科学与技术系,2010
[17]李少鹏.AVO地震参数反演方法研究及其应用[硕士学位论文].山东青岛:中国石油大学(华东)地球物理系,2009
[18]张繁昌,刘杰,印兴耀等.修正柯西约束地震盲反褶积方法.石油地球物理勘探,2008,43(4):391～396Zhang Fanchang,Liu Jie,Yin Xingyao et al.Modi-fied Cauchy constrained seismic blind deconvolution.OGP,2008,43(4):391～396
[19]张广智,王丹阳,印兴耀.利用MCMC方法估算地震参数.石油地球物理勘探,2011,46(4):605～609Zhang Guangzhi,Wang Danyang and Yin Xingyao.Seismic parameters estimation using Markov ChainMonte Carlo method.OGP,2011,46(4):605～609
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