基于改进粒子群算法的地震标量波方程反演
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摘要
针对标准粒子群优化(PS())算法存在易出现早熟而陷入局部最优以及进化后期收敛速度慢等缺陷,通过考虑粒子所处位置间相互作用,提出了一种改进的并行粒子群优化算法.由于引入粒子位置间的相互影响,减少了粒子搜索过程盲目性,因此能有效提高算法的收敛速度.数值试验表明,这种改进的粒子群算法适用于二维标量波方程的速度反演,且算法具有对初始模型依赖性低、收敛速度快、反演结果稳定、抗噪能力强等特点,为进一步将该反演算法用于弹性波波动方程以及弹性参数反演提供了理论依据.
In the standard particle swarm optimization(PSO),the premature convergence of particles and slow convergence in the late process decrease the searching ability of the algorithm. In this paper,by taking the positions of the particles into consideration,we propose an improved parallel particle swarm optimization(IPPSO) algorithm,which can increase the efficiency,to reduce the blindness in the search process.The performance of this improved particle swarm optimization method in solving 2-D scalar wave equation inversion problems is investigated.Our numerical experiments indicate that this method is suitable for scalar velocity inversion problems since it has merits such as low dependence on initial model,high constringency speed,stable result and strong antinoise ability.The results hold promise for further elastic wave equation and elastic parameters inversion studies.
In the standard particle swarm optimization(PSO),the premature convergence of particles and slow convergence in the late process decrease the searching ability of the algorithm. In this paper,by taking the positions of the particles into consideration,we propose an improved parallel particle swarm optimization(IPPSO) algorithm,which can increase the efficiency,to reduce the blindness in the search process.The performance of this improved particle swarm optimization method in solving 2-D scalar wave equation inversion problems is investigated.Our numerical experiments indicate that this method is suitable for scalar velocity inversion problems since it has merits such as low dependence on initial model,high constringency speed,stable result and strong antinoise ability.The results hold promise for further elastic wave equation and elastic parameters inversion studies.
引文
[1]Tsien D S,Chen Y M.A numerical method for nonlinear inverse problems in fluid dynamics.Proc.Int.Conf. Comput.Meth.Nonlinear Mechs.Austin:Univ of Taxas Press,1974.935-943
[2]Chen Y M.Generalized pluse-spectrum technique.Geophysics, 1985,50(11):1664-1675
[3]Han B,Feng G F,Liu J Q.A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation.Applied Mathematics and Computation, 2006,172(1):406-420
[4]Cohen J K,Bleistein N.An inverse method for determining small variations in propagation speed.SIAM J.Appl.Math., 1977,32(4):784-799
[5]Tarantola A,Linearized inversion of seismic reflection data. Geophysical Prospecting,1984,32(6):998-1015
[6]Ikelle L T,Diet J P,Tarantola A.Linearized inversion of multi-offset seismic reflection data in the w-k domain. Geophysics,1986,51(6):1266-1276
[7]Zhang X K.Generalized inversion and its application in inverse scatting problems.J.Comput.Math.,1989,7(4): 374-382
[8]Clayton R W,Stolt R H.A Born-WKBJ inversion method for acoustic reflection data.Geophysics,1981,46(11):1559-1567
[9]Xie G Q.A new iterative method for solving the coefficient inverse problem of the wave equation.Comm.Pure and Appl.Math.,1986,39(3):307-322
[10]Mara P.Nonlinear two-dimensional elastic inversion of seismic reflection data.Geophysics,1987,52(9):1211- 1228
[11]Tarantola A.Theoretical background for the inversion of seismic waveforms,including elasticity and attenuation.Pure and Applied Geophysics,1988,128(1-2):365-399
[12]Bleistein N,Cohen J K,Hagin F G.Two and one-half dimensional born inversion with an arbitrary reference. Geophysics,1987,52(1):26-36
[13]Xie CQ,Li J H,Chen Y M.Gauss-Newton-Regulating method for solving coefficient inverse problem of partial differential equation and its convergence.J.Comput.Math., 1987,5(1):38-49
[14]孙豪志,范祯祥.弹性波介质中纵、横波速度反演.石油地球物理勘探,1994,29(6):678-684 Sun H Z.Fan Z X.P and S-wave velocity inversions in elastic medium.Oil Geophysical Prospecting(in Chinese),1994, 29(6):678-684
[15]Sen M K,Stoffa P L.Nonlinear one-dimensional seismic waveform inversion using simulated annealing.Geophysics, 1991,56(10):1624-1638
[16]Stoffa P L,Sen M K.Nonlinear multi-parameter optimization using genetic algorithms:Inversion of plane-wave seismograms. Geophysics,1991,56(11).1794-1810
[17]冯国锋.波动方程反问题的多尺度—信赖域反演方法.哈尔滨:哈尔滨工业大学,2006 Feng G F.Multi-Scale Trust Region Inversion Methods for Inverse Problem of Wave Equations(in Chinese).Harbin: Harbin Institute of Technology,2006
[18]Eberhart R,Kennedy J.A new optimizer using particle swarm theory.In:IEEE.Proceedings of the Sixth International Symposium on Micro Machine and Human Science.Piscataway: IEEE Service Center,1995.39-43
[19]王福昌,王永革,胡顺田.粒子群算法在主震断层面参数估??计中的应用.地震研究,2008,31(2):149-153 Wang F C.Wang Y G,Hu S T.Application of particle swarm optimization to the estimation of mainshock fault plane parameters.Journal of Seismological Research(in Chinese), 2008,31(2):149-153
[20]李刚毅,蔡涵鹏.基于粒子群优化算法的波阻抗反演研究.勘探地球物理进展,2008,31(3):187-191 Li G Y,Cai H P.Wave impedance inversion based on particle swarm optimization.Progress in Exploration Geophysics(in Chinese),2008,31(3):187-191
[21]Shi Y,Eberhart R.A modified particle swarm optimizer.In: Proceeding of the IEEE Conference on Evolutionary Computation.Piscataway,NJ:IEEE Press,1998.69-73
[22]Shi Y,Eberhart R.Fuzzy adaptive particle swarm optimization.In:Proceeding of the IEEE Conference on Evolutionary Computation.Seoul,Korea,2001,101-106
[23]Natsuki Higashi,Hitoshi Iba.Particle swarm optimization with Gaussian mutation.In:Proceedings of the Swarm Intelligence Symposium,SIS2003 and IEEE,2003.72-79
[24]L(?)vbjerg M,Rasmussen T K,Krink T.Hybrid particle swarm optimiser with breeding and subpopulations.In: Proceedings of the Genetic and Evolutionary Computation Conference,2001
[25]朱童,李小凡,鲁明文.位置加权的改进粒子群算法.计算机工程与应用,2011,47(5):4-6 Zhu T,Li X F,Lu M W.Improved particle swarm optimization algorithm with position weighted.Computer Engineering and Applications(in Chinese),2011,47(5):4-6
[26]张建科.几类改进的粒子群算法.西安:西安电子科技大学, 2006 Zhang J K.Several Classes of Improved Particle Swarm Optimization(in Chinese).Xi'an:Xidian University,2006
[27]王守东,刘家琦,黄文虎.二维声波方程速度反演的一种方法.地球物理学报,1995,38(6):833-839 Wang S D,Liu J Q,Huang W H.A method of velocity inversion of two dimensional acoustic wave equation.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),1995, 38(6):833-839
[28]赵勇,岳继光,李炳宇等.一种新的求解复杂函数优化问题的并行粒子群算法.计算机工程与应用,2005,41(16): 58-60 Zhao Y,Yue J G,Li B Y,et al.A parallel particle swarm optimization algorithm based on multigroup for solving complex functions optimization.Computer Engineering and Applications(in Chinese),2005,41(16):58-60
[29]李一琼,李小凡,朱童.基于辛格式奇异核褶积微分算子的地震标量波场模拟.地球物理学报,2011,54(7):1827- 1834 Li Y Q,Li X F,Zhu T.The seismic scalar wave field modeling by symplectic scheme and singular kernel convolutional differentiator.Chinese J.Geophys.(in Chinese),2011,54(7): 1827-1834
[2]Chen Y M.Generalized pluse-spectrum technique.Geophysics, 1985,50(11):1664-1675
[3]Han B,Feng G F,Liu J Q.A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation.Applied Mathematics and Computation, 2006,172(1):406-420
[4]Cohen J K,Bleistein N.An inverse method for determining small variations in propagation speed.SIAM J.Appl.Math., 1977,32(4):784-799
[5]Tarantola A,Linearized inversion of seismic reflection data. Geophysical Prospecting,1984,32(6):998-1015
[6]Ikelle L T,Diet J P,Tarantola A.Linearized inversion of multi-offset seismic reflection data in the w-k domain. Geophysics,1986,51(6):1266-1276
[7]Zhang X K.Generalized inversion and its application in inverse scatting problems.J.Comput.Math.,1989,7(4): 374-382
[8]Clayton R W,Stolt R H.A Born-WKBJ inversion method for acoustic reflection data.Geophysics,1981,46(11):1559-1567
[9]Xie G Q.A new iterative method for solving the coefficient inverse problem of the wave equation.Comm.Pure and Appl.Math.,1986,39(3):307-322
[10]Mara P.Nonlinear two-dimensional elastic inversion of seismic reflection data.Geophysics,1987,52(9):1211- 1228
[11]Tarantola A.Theoretical background for the inversion of seismic waveforms,including elasticity and attenuation.Pure and Applied Geophysics,1988,128(1-2):365-399
[12]Bleistein N,Cohen J K,Hagin F G.Two and one-half dimensional born inversion with an arbitrary reference. Geophysics,1987,52(1):26-36
[13]Xie CQ,Li J H,Chen Y M.Gauss-Newton-Regulating method for solving coefficient inverse problem of partial differential equation and its convergence.J.Comput.Math., 1987,5(1):38-49
[14]孙豪志,范祯祥.弹性波介质中纵、横波速度反演.石油地球物理勘探,1994,29(6):678-684 Sun H Z.Fan Z X.P and S-wave velocity inversions in elastic medium.Oil Geophysical Prospecting(in Chinese),1994, 29(6):678-684
[15]Sen M K,Stoffa P L.Nonlinear one-dimensional seismic waveform inversion using simulated annealing.Geophysics, 1991,56(10):1624-1638
[16]Stoffa P L,Sen M K.Nonlinear multi-parameter optimization using genetic algorithms:Inversion of plane-wave seismograms. Geophysics,1991,56(11).1794-1810
[17]冯国锋.波动方程反问题的多尺度—信赖域反演方法.哈尔滨:哈尔滨工业大学,2006 Feng G F.Multi-Scale Trust Region Inversion Methods for Inverse Problem of Wave Equations(in Chinese).Harbin: Harbin Institute of Technology,2006
[18]Eberhart R,Kennedy J.A new optimizer using particle swarm theory.In:IEEE.Proceedings of the Sixth International Symposium on Micro Machine and Human Science.Piscataway: IEEE Service Center,1995.39-43
[19]王福昌,王永革,胡顺田.粒子群算法在主震断层面参数估??计中的应用.地震研究,2008,31(2):149-153 Wang F C.Wang Y G,Hu S T.Application of particle swarm optimization to the estimation of mainshock fault plane parameters.Journal of Seismological Research(in Chinese), 2008,31(2):149-153
[20]李刚毅,蔡涵鹏.基于粒子群优化算法的波阻抗反演研究.勘探地球物理进展,2008,31(3):187-191 Li G Y,Cai H P.Wave impedance inversion based on particle swarm optimization.Progress in Exploration Geophysics(in Chinese),2008,31(3):187-191
[21]Shi Y,Eberhart R.A modified particle swarm optimizer.In: Proceeding of the IEEE Conference on Evolutionary Computation.Piscataway,NJ:IEEE Press,1998.69-73
[22]Shi Y,Eberhart R.Fuzzy adaptive particle swarm optimization.In:Proceeding of the IEEE Conference on Evolutionary Computation.Seoul,Korea,2001,101-106
[23]Natsuki Higashi,Hitoshi Iba.Particle swarm optimization with Gaussian mutation.In:Proceedings of the Swarm Intelligence Symposium,SIS2003 and IEEE,2003.72-79
[24]L(?)vbjerg M,Rasmussen T K,Krink T.Hybrid particle swarm optimiser with breeding and subpopulations.In: Proceedings of the Genetic and Evolutionary Computation Conference,2001
[25]朱童,李小凡,鲁明文.位置加权的改进粒子群算法.计算机工程与应用,2011,47(5):4-6 Zhu T,Li X F,Lu M W.Improved particle swarm optimization algorithm with position weighted.Computer Engineering and Applications(in Chinese),2011,47(5):4-6
[26]张建科.几类改进的粒子群算法.西安:西安电子科技大学, 2006 Zhang J K.Several Classes of Improved Particle Swarm Optimization(in Chinese).Xi'an:Xidian University,2006
[27]王守东,刘家琦,黄文虎.二维声波方程速度反演的一种方法.地球物理学报,1995,38(6):833-839 Wang S D,Liu J Q,Huang W H.A method of velocity inversion of two dimensional acoustic wave equation.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),1995, 38(6):833-839
[28]赵勇,岳继光,李炳宇等.一种新的求解复杂函数优化问题的并行粒子群算法.计算机工程与应用,2005,41(16): 58-60 Zhao Y,Yue J G,Li B Y,et al.A parallel particle swarm optimization algorithm based on multigroup for solving complex functions optimization.Computer Engineering and Applications(in Chinese),2005,41(16):58-60
[29]李一琼,李小凡,朱童.基于辛格式奇异核褶积微分算子的地震标量波场模拟.地球物理学报,2011,54(7):1827- 1834 Li Y Q,Li X F,Zhu T.The seismic scalar wave field modeling by symplectic scheme and singular kernel convolutional differentiator.Chinese J.Geophys.(in Chinese),2011,54(7): 1827-1834
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