粒子群-梯度算法在频率域地震波形反演中的应用
|
摘要
本文将优化领域应用较广的全局随机非线性粒子群算法与局部迭代梯度法相结合,构造了一种粒子群-梯度算法,并将其应用于频率域波形速度结构反演.数值实验结果表明,粒子群-梯度算法能继承梯度法快速收敛和粒子群法全局寻优的特点,适用于频率域波形反演问题,算法具有一定的抗噪能力,无论在计算精度还是在降低解的非唯一性方面,都有较明显的改善.
A PSO-gradient algorithm combined with the widely used global non-linear stochastic particle swarm optimization(PSO) algorithm and local iteration gradient method is proposed.It is applied to waveform velocity structure inversion in frequency domain.The results show that the PSO-gradient algorithm can inherit the rapid convergence characteristics of gradient method;it also has the same ability of searching global optimization as PSO method.As a suitable tool tackling waveform inversion problems,the PSO-gradient algorithm has the ability of anti-noise in a certain extent and significant improvements both in calculation accuracy and reducing the nonuniqueness of solution.
A PSO-gradient algorithm combined with the widely used global non-linear stochastic particle swarm optimization(PSO) algorithm and local iteration gradient method is proposed.It is applied to waveform velocity structure inversion in frequency domain.The results show that the PSO-gradient algorithm can inherit the rapid convergence characteristics of gradient method;it also has the same ability of searching global optimization as PSO method.As a suitable tool tackling waveform inversion problems,the PSO-gradient algorithm has the ability of anti-noise in a certain extent and significant improvements both in calculation accuracy and reducing the nonuniqueness of solution.
引文
[1]朱童.基于粒子群算法的地震波反演方法研究[D].北京:中国科学院地质与地球物理研究所,2011.Zhu T.Study of Seismic Inversion based on Particle SwarmOptimization[D](in Chinese).Beijing:Institute of Geologyand Geophysics,Chinese Academy of Sciences,2011.
[2]吴建平,明跃红,王椿镛.川滇地区速度结构的区域地震波形反演研究[J].地球物理学报,2006,49(5):1369-1376.Wu J P,Ming Y H,Wang C Y.Regional waveform inversionfor crustal and upper mantle velocity structure below Chuandi-an region[J].Chinese J.Geophys.(in Chinese),2006,49(5):1369-1376.
[3]何玉梅,郑天愉.利用地震波形反演研究震源破裂时空过程[J].地球物理学报,1998,41(2):281-289.He Y M,Zheng T Y.Investigation of earthquake rupture his-tories using waveform inversion method[J].Acta GeophysicaSinica(Chinese J.Geophys.)(in Chinese),1998,41(2):281-289.
[4]孟鸿鹰,刘贵忠.小波变换多尺度地震波形反演[J].地球物理学报,1999,42(2):241-248.Meng H Y,Liu G Z.Multiscale seismic waveform inversionby wavelet transform[J].Chinese J.Geophys.(in Chinese),1999,42(2):241-248.
[5]李少华,王彦宾,梁子斌,等.甘肃东南部地壳速度结构的区域地震波形反演[J].地球物理学报,2012,55(4):1186-1197.Li S H,Wang Y B,Liang Z B,et al.Crustal structure insoutheastern Gansu from regional seismic waveform inversion[J].Chinese J.Geophys.(in Chinese),2012,55(4):1186-1197.
[6]王守东,刘家琦,黄文虎.二维声波方程速度反演的一种方法[J].地球物理学报,1995,38(6):833-839.Wang S D,Liu J Q,Huang W H.A method of velocity inver-sion of two dimensional acoustic wave equation[J].Acta Geo-physica Sinica(Chinese J.Geophys.)(in Chinese),1995,38(6):833-839.
[7]朱童,李小凡,李一琼,等.基于改进粒子群算法的地震标量波方程反演[J].地球物理学报,2011,54(11):2951-2959.Zhu T,Li X F,Li Y Q,et al.Seismic scalar wave equationinversion based on an improved particle swarm optimization al-gorithm[J].Chinese J.Geophys.(in Chinese),2011,54(11):2951-2959.
[8]龙桂华,李小凡,张美根,等.频率域粘弹性声波透射波形速度反演[J].地震学报,2009,31(1):32-41.Long G H,Li X F,Zhang M G,et al.Visco-acoustic trans-mission waveform inversion for velocity structure in space-fre-quency domain[J].Acta Seismologica Sinica(in Chinese),2009,31(1):32-41.
[9]Tarantola A.Linearized inversion of seismic reflection data[J].Geophysical Prospecting,1984,32(6):998-1015.
[10]Tarantola A.Theoretical background for the inversion of seismicwaveforms including elasticity and attenuation[J].Pure andApplied Geophysics,1988,128(1-2):365-399.
[11]Pratt R G.Frequency-domain elastic wave modeling by finitedifferences:A tool for crosshole seismic imaging[J].Geo-physics,1990,55(5):626-632.
[12]Pratt R G,Worthington M H.Inverse theory applied tomulti-source cross-hole tomography.Part 1:Acoustic wave-equation method[J].Geophysical Prospecting,1990,38(3):287-310.
[13]Pratt R G.Inverse theory applied to multi-source cross-holetomography.Part 2:Elastic wave-equation method[J].Geo-physical Prospecting,1990,38(3):311-329.
[14]Pratt R G,Shin C,Hicks G J.Gauss-Newton and full Newtonmethods in frequency-space seismic waveform inversion[J].Geophys.J.Int.,1998,133(2):341-362.
[15]Operto S,Virieux J,Amestoy P,et al.3Dfinite-differencefrequency-domain modeling of visco-acoustic wave propaga-tion using a massively parallel direct solver:a feasibility study[J].Geophysics,2007,72(5):195-211.
[16]Wang Y H,Rao Y.Reflection seismic waveform tomography[J].J.Geophys.Res.,2009,114(B3):B03304.
[17]Hu W Y,Abubakar A,Habashy T M.Simultaneousmultifrequency inversion of full-waveform seismic data[J].Geophysics,2009,74(2):R1-R14.
[18]许琨,王妙月.声波方程频率域有限元参数反演[J].地球物理学报,2001,44(6):852-864.Xu K,Wang M Y.Finite element inversion of the coefficientsof acoustic equation in frequency domain[J].Chinese J.Geo-phys.(in Chinese),2001,44(6):852-864.
[19]许琨,王妙月.利用地质规则块体建模方法的频率域有限元弹性波速度反演[J].地球物理学报,2004,47(4):708-717.Xu K,Wang M Y.Frequency-domain finite-element inver-sion of elastic-wave velocity using the geological regular-blocky-model method[J].Chinese J.Geophys.(in Chinese),2004,47(4):708-717.
[20]Xu K,Greenhalgh S A,Wang M Y.Comparison of source-independent methods of elastic waveform inversion[J].Geo-physics,2006,71(6):91-100.
[21]吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子[J].地球物理学进展,2007,22(3):896-904.Wu G C,Liang K.High precision finite difference operatorsfor qP wave equation in VTI media[J].Progress in Geophys.(in Chinese),2007,22(3):896-904.
[22]吴国忱,梁锴.VTI介质频率-空间域准P波正演模拟[J].石油地球物理勘探,2005,40(5):535-545.Wu G C,Liang K.Quasi P-wave forward modeling in fre-quency-space domain in VTI media[J].Oil Geophysical Pros-pecting(in Chinese),2005,40(5):535-545.
[23]吴国忱,梁锴.VTI介质准P波频率空间域组合边界条件研究[J].石油物探,2005,44(4):301-307.Wu G C,Liang K.Combined boundary conditions of quasi-Pwave within frequency-space domain in VTI media[J].Geo-physical Prospecting for Petroleum(in Chinese),2005,44(4):301-307.
[24]吴国忱,罗彩明,梁锴.TTI介质弹性波频率-空间域有限差分数值模拟[J].吉林大学学报(地球科学版),2007,37(5):1023-1033.Wu G C,Luo C M,Liang K.Frequency-space domain finitedifference numerical simulation of elastic wave in TTI media[J].Journal of Jilin University(Earth Science Edition)(inChinese),2007,37(5):1023-1033.
[25]梁锴,吴国忱,印兴耀.TTI介质qP波方程频率-空间域加权平均有限差分算子[J].石油地球物理勘探,2007,42(5):516-525.Liang K,Wu G C,Yin X Y.Weighted mean finite-differenceoperator of qP wave equation in frequency-space domain forTTI medium[J].Oil Geophysical Prospecting(in Chinese),2007,42(5):516-525.
[26]卞爱飞,於文辉,周华伟.频率域全波形反演方法研究进展[J].地球物理学进展,2010,25(3):982-993.Bian A F,Yu W H,Zhou H W.Progress in the frequency-domain full waveform inversion method[J].Progress in Geo-phys.(in Chinese),2010,25(3):982-993.
[27]Eberhart R,Kennedy J.A New Optimizer Using ParticleSwarm Theory[A]//IEEE.Proceedings of the Sixth Interna-tional Symposium on Micro Machine and Human Science[C].Piscataway:IEEE Service Center,1995:1942-1948.
[28]师学明,肖敏,范建柯,等.大地电磁阻尼粒子群优化反演法研究[J].地球物理学报,2009,52(4):1114-1120.Shi X M,Xiao M,Fan J K,et al.The damped PSO algo-rithm and its application for magnetotelluric sounding data in-version[J].Chinese J.Geophys.(in Chinese),2009,52(4):1114-1120.
[29]岳碧波,彭真明,洪余刚,等.基于粒子群优化算法的叠前角道集子波反演[J].地球物理学报,2009,52(12):3116-3123.Yue B B,Peng Z M,Hong Y G,et al.Wavelet inver-sion of pre-stack seismic angle-gather based on particle swarmoptimization algorithm[J].Chinese J.Geophys.(in Chi-nese),2009,52(12):3116-3123.
[30]聂茹,岳建华,邓帅奇.地震波阻抗反演的免疫粒子群算法[J].中国矿业大学学报,2010,39(5):733-739.Nie R,Yue J H,Deng S Q.Immune particle swarm optimi-zation for seismic wave impedance inversion[J].Journal ofChina University of Mining&Technology(in Chinese),2010,39(5):733-739.
[31]Shi Y,Eberhart R.Particle swarm optimization with fuzzy a-daptive inertia weight[A]//IEEE.Proceedings of Workshopon Particle Swarm Optimization[C].Indianapolis:PurdueSchool of Engineering and Technology,2001.
[32]朱童,李小凡,鲁明文.位置加权的改进粒子群算法[J].计算机工程与应用,2011,47(5):4-6.Zhu T,Li X F,Lu M W.Improved particle swarm optimiza-tion algorithm with position weighted[J].Computer Engi-neering and Applications(in Chinese),2011,47(5):4-6.
[33]Shin C,Yoon K,Marfurt K J,et al.Efficient calculation ofapartial-derivative wavefield using reciprocity for seismic im-aging and inversion[J].Geophysics,2001,66(6):1856-1863.
[34]Hustedt B,Operto S,Virieux J.Mixed-grid and staggered-grid finite-difference methods for frequency-domain acousticwave modelling[J].Geophys.J.Int.,2004,157(3):1269-1296.
[35]龙桂华.粘弹性介质中的地震波传播与波形反演研究[D].北京:中国科学院地质与地球物理研究所,2009.Long G H.The study of seismic wave propagation and wave-form inversion in viscoelastic media(in Chinese)[D].Bei-jing:Institute of Geology and Geophysics,Chinese Academyof Sciences,2009.
[36]Sirgue L,Pratt R G.Efficient waveform inversion and ima-ging:A strategy for selecting temporal frequencies[J].Geo-physics,2004,69(1):231-248.
[37]Ravaut C,Operto S,Improta L,et al.Multiscale imaging ofcomplex structures from multifold wide-aperture seismic databy frequency-domain full-waveform tomography:applicationto a thrust belt[J].Geophys.J.Int.,2004,159(3):1032-1056.
[2]吴建平,明跃红,王椿镛.川滇地区速度结构的区域地震波形反演研究[J].地球物理学报,2006,49(5):1369-1376.Wu J P,Ming Y H,Wang C Y.Regional waveform inversionfor crustal and upper mantle velocity structure below Chuandi-an region[J].Chinese J.Geophys.(in Chinese),2006,49(5):1369-1376.
[3]何玉梅,郑天愉.利用地震波形反演研究震源破裂时空过程[J].地球物理学报,1998,41(2):281-289.He Y M,Zheng T Y.Investigation of earthquake rupture his-tories using waveform inversion method[J].Acta GeophysicaSinica(Chinese J.Geophys.)(in Chinese),1998,41(2):281-289.
[4]孟鸿鹰,刘贵忠.小波变换多尺度地震波形反演[J].地球物理学报,1999,42(2):241-248.Meng H Y,Liu G Z.Multiscale seismic waveform inversionby wavelet transform[J].Chinese J.Geophys.(in Chinese),1999,42(2):241-248.
[5]李少华,王彦宾,梁子斌,等.甘肃东南部地壳速度结构的区域地震波形反演[J].地球物理学报,2012,55(4):1186-1197.Li S H,Wang Y B,Liang Z B,et al.Crustal structure insoutheastern Gansu from regional seismic waveform inversion[J].Chinese J.Geophys.(in Chinese),2012,55(4):1186-1197.
[6]王守东,刘家琦,黄文虎.二维声波方程速度反演的一种方法[J].地球物理学报,1995,38(6):833-839.Wang S D,Liu J Q,Huang W H.A method of velocity inver-sion of two dimensional acoustic wave equation[J].Acta Geo-physica Sinica(Chinese J.Geophys.)(in Chinese),1995,38(6):833-839.
[7]朱童,李小凡,李一琼,等.基于改进粒子群算法的地震标量波方程反演[J].地球物理学报,2011,54(11):2951-2959.Zhu T,Li X F,Li Y Q,et al.Seismic scalar wave equationinversion based on an improved particle swarm optimization al-gorithm[J].Chinese J.Geophys.(in Chinese),2011,54(11):2951-2959.
[8]龙桂华,李小凡,张美根,等.频率域粘弹性声波透射波形速度反演[J].地震学报,2009,31(1):32-41.Long G H,Li X F,Zhang M G,et al.Visco-acoustic trans-mission waveform inversion for velocity structure in space-fre-quency domain[J].Acta Seismologica Sinica(in Chinese),2009,31(1):32-41.
[9]Tarantola A.Linearized inversion of seismic reflection data[J].Geophysical Prospecting,1984,32(6):998-1015.
[10]Tarantola A.Theoretical background for the inversion of seismicwaveforms including elasticity and attenuation[J].Pure andApplied Geophysics,1988,128(1-2):365-399.
[11]Pratt R G.Frequency-domain elastic wave modeling by finitedifferences:A tool for crosshole seismic imaging[J].Geo-physics,1990,55(5):626-632.
[12]Pratt R G,Worthington M H.Inverse theory applied tomulti-source cross-hole tomography.Part 1:Acoustic wave-equation method[J].Geophysical Prospecting,1990,38(3):287-310.
[13]Pratt R G.Inverse theory applied to multi-source cross-holetomography.Part 2:Elastic wave-equation method[J].Geo-physical Prospecting,1990,38(3):311-329.
[14]Pratt R G,Shin C,Hicks G J.Gauss-Newton and full Newtonmethods in frequency-space seismic waveform inversion[J].Geophys.J.Int.,1998,133(2):341-362.
[15]Operto S,Virieux J,Amestoy P,et al.3Dfinite-differencefrequency-domain modeling of visco-acoustic wave propaga-tion using a massively parallel direct solver:a feasibility study[J].Geophysics,2007,72(5):195-211.
[16]Wang Y H,Rao Y.Reflection seismic waveform tomography[J].J.Geophys.Res.,2009,114(B3):B03304.
[17]Hu W Y,Abubakar A,Habashy T M.Simultaneousmultifrequency inversion of full-waveform seismic data[J].Geophysics,2009,74(2):R1-R14.
[18]许琨,王妙月.声波方程频率域有限元参数反演[J].地球物理学报,2001,44(6):852-864.Xu K,Wang M Y.Finite element inversion of the coefficientsof acoustic equation in frequency domain[J].Chinese J.Geo-phys.(in Chinese),2001,44(6):852-864.
[19]许琨,王妙月.利用地质规则块体建模方法的频率域有限元弹性波速度反演[J].地球物理学报,2004,47(4):708-717.Xu K,Wang M Y.Frequency-domain finite-element inver-sion of elastic-wave velocity using the geological regular-blocky-model method[J].Chinese J.Geophys.(in Chinese),2004,47(4):708-717.
[20]Xu K,Greenhalgh S A,Wang M Y.Comparison of source-independent methods of elastic waveform inversion[J].Geo-physics,2006,71(6):91-100.
[21]吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子[J].地球物理学进展,2007,22(3):896-904.Wu G C,Liang K.High precision finite difference operatorsfor qP wave equation in VTI media[J].Progress in Geophys.(in Chinese),2007,22(3):896-904.
[22]吴国忱,梁锴.VTI介质频率-空间域准P波正演模拟[J].石油地球物理勘探,2005,40(5):535-545.Wu G C,Liang K.Quasi P-wave forward modeling in fre-quency-space domain in VTI media[J].Oil Geophysical Pros-pecting(in Chinese),2005,40(5):535-545.
[23]吴国忱,梁锴.VTI介质准P波频率空间域组合边界条件研究[J].石油物探,2005,44(4):301-307.Wu G C,Liang K.Combined boundary conditions of quasi-Pwave within frequency-space domain in VTI media[J].Geo-physical Prospecting for Petroleum(in Chinese),2005,44(4):301-307.
[24]吴国忱,罗彩明,梁锴.TTI介质弹性波频率-空间域有限差分数值模拟[J].吉林大学学报(地球科学版),2007,37(5):1023-1033.Wu G C,Luo C M,Liang K.Frequency-space domain finitedifference numerical simulation of elastic wave in TTI media[J].Journal of Jilin University(Earth Science Edition)(inChinese),2007,37(5):1023-1033.
[25]梁锴,吴国忱,印兴耀.TTI介质qP波方程频率-空间域加权平均有限差分算子[J].石油地球物理勘探,2007,42(5):516-525.Liang K,Wu G C,Yin X Y.Weighted mean finite-differenceoperator of qP wave equation in frequency-space domain forTTI medium[J].Oil Geophysical Prospecting(in Chinese),2007,42(5):516-525.
[26]卞爱飞,於文辉,周华伟.频率域全波形反演方法研究进展[J].地球物理学进展,2010,25(3):982-993.Bian A F,Yu W H,Zhou H W.Progress in the frequency-domain full waveform inversion method[J].Progress in Geo-phys.(in Chinese),2010,25(3):982-993.
[27]Eberhart R,Kennedy J.A New Optimizer Using ParticleSwarm Theory[A]//IEEE.Proceedings of the Sixth Interna-tional Symposium on Micro Machine and Human Science[C].Piscataway:IEEE Service Center,1995:1942-1948.
[28]师学明,肖敏,范建柯,等.大地电磁阻尼粒子群优化反演法研究[J].地球物理学报,2009,52(4):1114-1120.Shi X M,Xiao M,Fan J K,et al.The damped PSO algo-rithm and its application for magnetotelluric sounding data in-version[J].Chinese J.Geophys.(in Chinese),2009,52(4):1114-1120.
[29]岳碧波,彭真明,洪余刚,等.基于粒子群优化算法的叠前角道集子波反演[J].地球物理学报,2009,52(12):3116-3123.Yue B B,Peng Z M,Hong Y G,et al.Wavelet inver-sion of pre-stack seismic angle-gather based on particle swarmoptimization algorithm[J].Chinese J.Geophys.(in Chi-nese),2009,52(12):3116-3123.
[30]聂茹,岳建华,邓帅奇.地震波阻抗反演的免疫粒子群算法[J].中国矿业大学学报,2010,39(5):733-739.Nie R,Yue J H,Deng S Q.Immune particle swarm optimi-zation for seismic wave impedance inversion[J].Journal ofChina University of Mining&Technology(in Chinese),2010,39(5):733-739.
[31]Shi Y,Eberhart R.Particle swarm optimization with fuzzy a-daptive inertia weight[A]//IEEE.Proceedings of Workshopon Particle Swarm Optimization[C].Indianapolis:PurdueSchool of Engineering and Technology,2001.
[32]朱童,李小凡,鲁明文.位置加权的改进粒子群算法[J].计算机工程与应用,2011,47(5):4-6.Zhu T,Li X F,Lu M W.Improved particle swarm optimiza-tion algorithm with position weighted[J].Computer Engi-neering and Applications(in Chinese),2011,47(5):4-6.
[33]Shin C,Yoon K,Marfurt K J,et al.Efficient calculation ofapartial-derivative wavefield using reciprocity for seismic im-aging and inversion[J].Geophysics,2001,66(6):1856-1863.
[34]Hustedt B,Operto S,Virieux J.Mixed-grid and staggered-grid finite-difference methods for frequency-domain acousticwave modelling[J].Geophys.J.Int.,2004,157(3):1269-1296.
[35]龙桂华.粘弹性介质中的地震波传播与波形反演研究[D].北京:中国科学院地质与地球物理研究所,2009.Long G H.The study of seismic wave propagation and wave-form inversion in viscoelastic media(in Chinese)[D].Bei-jing:Institute of Geology and Geophysics,Chinese Academyof Sciences,2009.
[36]Sirgue L,Pratt R G.Efficient waveform inversion and ima-ging:A strategy for selecting temporal frequencies[J].Geo-physics,2004,69(1):231-248.
[37]Ravaut C,Operto S,Improta L,et al.Multiscale imaging ofcomplex structures from multifold wide-aperture seismic databy frequency-domain full-waveform tomography:applicationto a thrust belt[J].Geophys.J.Int.,2004,159(3):1032-1056.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心