利用粒子群优化算法快速、稳定反演瑞雷波频散曲线
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摘要
反演瑞雷波频散曲线能有效地获取横波速度和地层厚度,但基于局部线性化的瑞雷波频散曲线反演方法很难适应反演目标函数的非线性、多参数、多极值的特点。为此,提出并测试了一种新的基于全局优化策略的粒子群优化(PSO)算法的瑞雷波频散曲线反演方法。首先反演了三个理论模型的无噪声和含噪声数据,验证了PSO对瑞雷波数据反演的有效性与稳定性;然后将PSO与模拟退火法(SA)进行对比,说明PSO相对于SA具有全局收敛性强、收敛速度快、求解精度高的特点;最后,反演了来自美国怀俄明地区的实测数据,检验了PSO对瑞雷波数据反演的适用性。理论模型试算和实测资料分析表明,PSO可以用于瑞雷波频散曲线的定量解释。
Rayleigh-wave dispersion-curve inversion can effectively obtain shear wave velocity and formation thickness.However,Rayleigh-wave dispersioncurve inversion based on local linearization cannot adapt to inversion objective function characteristicssuch as non-linear,multi-parameters,and multi-extremums.To overcome this issue,we propose a new Rayleigh-wave dispersion-curve inversion based on a particle swarm optimization(PSO)algorithm for global optimization.We first invert synthetic data with noise and without noise of three theoretical models,and verify the effectiveness and stability of the PSO inversion of Rayleigh wave data.Then we compare PSO with simulated annealing(SA),and find that PSO has faster convergence and higher accuracy than SA.Finally,we apply this method into field seismic data from Wyoming in the United States to test its applicability.Theoretical and real data tests show that the proposed method can be used for the quantitative interpretation.
Rayleigh-wave dispersion-curve inversion can effectively obtain shear wave velocity and formation thickness.However,Rayleigh-wave dispersioncurve inversion based on local linearization cannot adapt to inversion objective function characteristicssuch as non-linear,multi-parameters,and multi-extremums.To overcome this issue,we propose a new Rayleigh-wave dispersion-curve inversion based on a particle swarm optimization(PSO)algorithm for global optimization.We first invert synthetic data with noise and without noise of three theoretical models,and verify the effectiveness and stability of the PSO inversion of Rayleigh wave data.Then we compare PSO with simulated annealing(SA),and find that PSO has faster convergence and higher accuracy than SA.Finally,we apply this method into field seismic data from Wyoming in the United States to test its applicability.Theoretical and real data tests show that the proposed method can be used for the quantitative interpretation.
引文
[1]李庆春,邵广周,刘金兰等.瑞雷面波勘探的过去、现在和未来.地球科学与环境学报,2006,28(3):74-77.Li Qingchun,Shao Guangzhou,Liu Jinlan et al.Past,present and future of Rayleigh surface wave exploration.Journal of Earth Sciences&Environment,2006,28(3):74-77.
[2]黄忠贤,李红谊,胥颐.中国西部及邻区岩石圈S波速度结构面波层析成像.地球物理学报,2014,57(12):3994-4004.Huang Zhongxian,Li Hongyi,Xu Yi.Lithospheric S-wave velocity structure of west China and neighboring areas from surface wave tomography.Chinese Journal of Geophysics,2014,57(12):3994-4004.
[3]潘佳铁,李永华,吴庆举等.中国东北地区地壳上地幔三维S波速度结构.地球物理学报,2014,57(7):2077-2087.Pan Jiatie,Li Yonghua,Wu Qingju et al.3-D S-wave velocity structure of crust and upper-mantle beneath the northeast China.Chinese Journal of Geophysics,2014,57(7):2077-2087.
[4]滕吉文,胡家富,张中杰等.喜马拉雅碰撞造山带和羌塘盆地的瑞雷波频散与三维速度结构.石油地球物理勘探,1998,33(5):632-648.Teng Jiwen,Hu Jiafu,Zhang Zhongjie et al.The frequency dispersions of Rayleigh waves and 3-D velocity structures in Himalayan collision orogenic zone and Qiangtang basin.OGP,1998,33(5):632-648.
[5]Xia J H.Estimation of near-surface shear-wave velocities and quality factors using multichannel analysis of surface-wave methods.Journal of Applied Geophysics,2014,103(2):140-151.
[6]刘江平,罗银河,何伟兵.相邻道瞬态瑞雷面波法与压实度检测.岩土工程学报,2009,31(11):1652-1659.Liu Jiangping,Luo Yinhe,He Weibing.Method of neighboring trace transient Rayleigh wave and its application in compactness inspection.Chinese Journal of Geotechnical Engineering,2009,31(11):1652-1659.
[7]Xia J H,Miller R D,Park C B.Estimation of nearsurface shear-wave velocity by inversion of Rayleigh waves.Geophysics,1999,64(3):691-700.
[8]陈祥,孙进忠.改进的等效半空间法及瑞雷波频散曲线反演.地球物理学报,2006,49(2):569-576.Chen Xiang,Sun Jinzhong.An improved equivalent homogeneous half-space method and reverse fitting analysis of Rayleigh wave dispersion curve.Chinese Journal of Geophysics,2006,49(2):569-576.
[9]石耀霖,金文.面波频散反演地球内部构造的遗传算法.地球物理学报,1995,38(2):189-198.Shi Yaolin,Jin Wen.Genetic algorithms inversion of lithospheric structure from surface wave dispersion.Chinese Journal of Geophysics,1995,38(2):189-198.
[10]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567-573.Zhou Zhusheng,Liu Xiliang,Xiong Xiaoyu.Finitedifference modelling of Rayleigh surface wave in elastic media.Chinese Journal of Geophysics,2007,50(2):567-573.
[11]Xu Y X,Xia J H,Miller R D.Numerical investigation of implementation of air-earth boundary by acousticelastic boundary approach.Geophysics,2007,72(5):147-153.
[12]熊章强,张大洲,秦臻等.瑞雷波数值模拟中的边界条件及模拟实例分析.中南大学学报(自然科学版),2008,39(4):824-830.Xiong Zhangqiang,Zhang Dazhou,Qin Zhen et al.Boundary conditions and case analysis of numerical modeling of Rayleigh wave.Journal of Central South University(Science and Technology),2008,39(4):824-830.
[13]邵广周,李庆春,吴华.基于波场数值模拟的瑞利波频散曲线特征及各模式能量分布.石油地球物理勘探,2015,50(2):306-315.Shao Guangzhou,Li Qingchun,Wu Hua.Characteristics of Rayleigh wave dispersion curve based on wave field numerical simulation and energy distribution of each mode.OGP,2015,50(2):306-315.
[14]鲁来玉,何正勤,丁志峰等.基于背景噪声研究云南地区面波速度非均匀性和方位各向异性.地球物理学报,2014,57(3):822-836.Lu Laiyu,He Zhengqin,Ding Zhifeng et al.Azimuth anisotropy and velocity heterogeneity of Yunnan area based on seismic ambient noise.Chinese Journal of Geophysics,2014,57(3):822-836.
[15]余大新,李永华,吴庆举等.利用Rayleigh波相速度和群速度联合反演青藏高原东北缘S波速度结构.地球物理学报,2014,57(3):800-811.Yu Daxin,Li Yonghua,Wu Qingju et al.S-wave velocity structure of the northeastern Tibetan Plateau from joint inversion of Rayleigh wave phase and group velocities.Chinese Journal of Geophysics,2014,57(3):800-811.
[16]Zhang S X,Chan L S,Xia J H.The selection of field acquisition parameters for dispersion images from multichannel surface wave data.Pure and Applied Geophysics,2004,161(1):185-201.
[17]Luo Y H,Xia J H,Miller R D et al.Rayleigh wave dispersive energy imaging using a high resolution linear Radon transform.Pure and Applied Geophysics,2008,165(5):903-922.
[18]Lu L Y,Wang C H,Zhang B X.Inversion of multimode Rayleigh waves in the presence of a low-velocity layer:numerical and laboratory study.Geophysical Journal International,2007,168(3):1235-1246.
[19]张碧星,肖柏勋,杨文杰等.瑞利波勘探中"之"形频散曲线的形成机理及反演研究.地球物理学报,2000,43(4):557-567.Zhang Bixing,Xiao Baixun,Yang Wenjie et al.Mechanism of zigzag dispersion curves in Rayleigh exploration and its inversion study.Chinese Journal of Geophysics,2000,43(4):557-567.
[20]Zhang S X,Chan L S.Possible effects of misidentified mode number on Rayleigh wave inversion.Journal of Applied Geophysics,2003,53(1):17-29.
[21]崔建文.一种改进的全局优化算法及其在面波频散曲线反演中的应用.地球物理学报,2004,47(3):521-527.Cui Jianwen.An improved global optimization method and its application to the inversion of surface wave dispersion curves.Chinese Journal of Geophysics,2004,47(3):521-527.
[22]Kennedy J,Eberhart R C.Particle swarm optimization.IEEE International Conference on Neural Networks,Piscataway,NJ:IEEE Service Center,1995,4:1942-1948.
[23]Shi Y,Eberhart R C.A modified particle swarm optimizer.IEEE International Conference on Evolutionary Computation,Anchorage,Alaska,1998.
[24]Clerc M.The swarm and the queen:towards a deterministic and adaptive particle swarm optimization.Proceedings of the IEEE Congress of Evolutionary Computation.Piscataway,NJ:IEEE Service Center,1999,1951-1957.
[25]蔡涵鹏,贺振华,黄德济.基于粒子群优化算法波阻抗反演的研究与应用.石油地球物理勘探,2008,43(5):535-539.Cai Hanpeng,He Zhenhua,Huang Deji.Research and application of wave impedance inversion based on particle swarm optimization algorithm.OGP,2008,43(5):535-539.
[26]谢玮,王彦春,刘建军等.基于粒子群优化最小二乘支持向量机的非线性AVO反演.石油地球物理勘探,2016,51(6):1187-1194.Xie Wei,Wang Yanchun,Liu Jianjun et al.Nonlinear AVO inversion based on particle swarm optimization least squares support vector machines.OGP,2016,51(6):1187-1194.
[27]方中于,王丽萍,杜家元等.基于混合智能优化算法的非线性AVO反演.石油地球物理勘探,2017,52(4):797-804.Fang Zhongyu,Wang Liping,Du Jiayuan et al.Nonlinear AVO inversion based on hybrid intelligent optimization algorithm.OGP,2017,52(4):797-804.
[28]凡友华,刘家琦,肖柏勋.计算瑞利波频散曲线的快速矢量传递算法.湖南大学学报(自然科学版),2002,29(5):25-30.Fan Youhua,Liu Jiaqi,Xiao Baixun.Fast vector-transfer algorithm for computation of Rayleigh wave dispersion curves.Journal of Hunan University(Natural Sciences Edition),2002,29(5):25-30.
[2]黄忠贤,李红谊,胥颐.中国西部及邻区岩石圈S波速度结构面波层析成像.地球物理学报,2014,57(12):3994-4004.Huang Zhongxian,Li Hongyi,Xu Yi.Lithospheric S-wave velocity structure of west China and neighboring areas from surface wave tomography.Chinese Journal of Geophysics,2014,57(12):3994-4004.
[3]潘佳铁,李永华,吴庆举等.中国东北地区地壳上地幔三维S波速度结构.地球物理学报,2014,57(7):2077-2087.Pan Jiatie,Li Yonghua,Wu Qingju et al.3-D S-wave velocity structure of crust and upper-mantle beneath the northeast China.Chinese Journal of Geophysics,2014,57(7):2077-2087.
[4]滕吉文,胡家富,张中杰等.喜马拉雅碰撞造山带和羌塘盆地的瑞雷波频散与三维速度结构.石油地球物理勘探,1998,33(5):632-648.Teng Jiwen,Hu Jiafu,Zhang Zhongjie et al.The frequency dispersions of Rayleigh waves and 3-D velocity structures in Himalayan collision orogenic zone and Qiangtang basin.OGP,1998,33(5):632-648.
[5]Xia J H.Estimation of near-surface shear-wave velocities and quality factors using multichannel analysis of surface-wave methods.Journal of Applied Geophysics,2014,103(2):140-151.
[6]刘江平,罗银河,何伟兵.相邻道瞬态瑞雷面波法与压实度检测.岩土工程学报,2009,31(11):1652-1659.Liu Jiangping,Luo Yinhe,He Weibing.Method of neighboring trace transient Rayleigh wave and its application in compactness inspection.Chinese Journal of Geotechnical Engineering,2009,31(11):1652-1659.
[7]Xia J H,Miller R D,Park C B.Estimation of nearsurface shear-wave velocity by inversion of Rayleigh waves.Geophysics,1999,64(3):691-700.
[8]陈祥,孙进忠.改进的等效半空间法及瑞雷波频散曲线反演.地球物理学报,2006,49(2):569-576.Chen Xiang,Sun Jinzhong.An improved equivalent homogeneous half-space method and reverse fitting analysis of Rayleigh wave dispersion curve.Chinese Journal of Geophysics,2006,49(2):569-576.
[9]石耀霖,金文.面波频散反演地球内部构造的遗传算法.地球物理学报,1995,38(2):189-198.Shi Yaolin,Jin Wen.Genetic algorithms inversion of lithospheric structure from surface wave dispersion.Chinese Journal of Geophysics,1995,38(2):189-198.
[10]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟.地球物理学报,2007,50(2):567-573.Zhou Zhusheng,Liu Xiliang,Xiong Xiaoyu.Finitedifference modelling of Rayleigh surface wave in elastic media.Chinese Journal of Geophysics,2007,50(2):567-573.
[11]Xu Y X,Xia J H,Miller R D.Numerical investigation of implementation of air-earth boundary by acousticelastic boundary approach.Geophysics,2007,72(5):147-153.
[12]熊章强,张大洲,秦臻等.瑞雷波数值模拟中的边界条件及模拟实例分析.中南大学学报(自然科学版),2008,39(4):824-830.Xiong Zhangqiang,Zhang Dazhou,Qin Zhen et al.Boundary conditions and case analysis of numerical modeling of Rayleigh wave.Journal of Central South University(Science and Technology),2008,39(4):824-830.
[13]邵广周,李庆春,吴华.基于波场数值模拟的瑞利波频散曲线特征及各模式能量分布.石油地球物理勘探,2015,50(2):306-315.Shao Guangzhou,Li Qingchun,Wu Hua.Characteristics of Rayleigh wave dispersion curve based on wave field numerical simulation and energy distribution of each mode.OGP,2015,50(2):306-315.
[14]鲁来玉,何正勤,丁志峰等.基于背景噪声研究云南地区面波速度非均匀性和方位各向异性.地球物理学报,2014,57(3):822-836.Lu Laiyu,He Zhengqin,Ding Zhifeng et al.Azimuth anisotropy and velocity heterogeneity of Yunnan area based on seismic ambient noise.Chinese Journal of Geophysics,2014,57(3):822-836.
[15]余大新,李永华,吴庆举等.利用Rayleigh波相速度和群速度联合反演青藏高原东北缘S波速度结构.地球物理学报,2014,57(3):800-811.Yu Daxin,Li Yonghua,Wu Qingju et al.S-wave velocity structure of the northeastern Tibetan Plateau from joint inversion of Rayleigh wave phase and group velocities.Chinese Journal of Geophysics,2014,57(3):800-811.
[16]Zhang S X,Chan L S,Xia J H.The selection of field acquisition parameters for dispersion images from multichannel surface wave data.Pure and Applied Geophysics,2004,161(1):185-201.
[17]Luo Y H,Xia J H,Miller R D et al.Rayleigh wave dispersive energy imaging using a high resolution linear Radon transform.Pure and Applied Geophysics,2008,165(5):903-922.
[18]Lu L Y,Wang C H,Zhang B X.Inversion of multimode Rayleigh waves in the presence of a low-velocity layer:numerical and laboratory study.Geophysical Journal International,2007,168(3):1235-1246.
[19]张碧星,肖柏勋,杨文杰等.瑞利波勘探中"之"形频散曲线的形成机理及反演研究.地球物理学报,2000,43(4):557-567.Zhang Bixing,Xiao Baixun,Yang Wenjie et al.Mechanism of zigzag dispersion curves in Rayleigh exploration and its inversion study.Chinese Journal of Geophysics,2000,43(4):557-567.
[20]Zhang S X,Chan L S.Possible effects of misidentified mode number on Rayleigh wave inversion.Journal of Applied Geophysics,2003,53(1):17-29.
[21]崔建文.一种改进的全局优化算法及其在面波频散曲线反演中的应用.地球物理学报,2004,47(3):521-527.Cui Jianwen.An improved global optimization method and its application to the inversion of surface wave dispersion curves.Chinese Journal of Geophysics,2004,47(3):521-527.
[22]Kennedy J,Eberhart R C.Particle swarm optimization.IEEE International Conference on Neural Networks,Piscataway,NJ:IEEE Service Center,1995,4:1942-1948.
[23]Shi Y,Eberhart R C.A modified particle swarm optimizer.IEEE International Conference on Evolutionary Computation,Anchorage,Alaska,1998.
[24]Clerc M.The swarm and the queen:towards a deterministic and adaptive particle swarm optimization.Proceedings of the IEEE Congress of Evolutionary Computation.Piscataway,NJ:IEEE Service Center,1999,1951-1957.
[25]蔡涵鹏,贺振华,黄德济.基于粒子群优化算法波阻抗反演的研究与应用.石油地球物理勘探,2008,43(5):535-539.Cai Hanpeng,He Zhenhua,Huang Deji.Research and application of wave impedance inversion based on particle swarm optimization algorithm.OGP,2008,43(5):535-539.
[26]谢玮,王彦春,刘建军等.基于粒子群优化最小二乘支持向量机的非线性AVO反演.石油地球物理勘探,2016,51(6):1187-1194.Xie Wei,Wang Yanchun,Liu Jianjun et al.Nonlinear AVO inversion based on particle swarm optimization least squares support vector machines.OGP,2016,51(6):1187-1194.
[27]方中于,王丽萍,杜家元等.基于混合智能优化算法的非线性AVO反演.石油地球物理勘探,2017,52(4):797-804.Fang Zhongyu,Wang Liping,Du Jiayuan et al.Nonlinear AVO inversion based on hybrid intelligent optimization algorithm.OGP,2017,52(4):797-804.
[28]凡友华,刘家琦,肖柏勋.计算瑞利波频散曲线的快速矢量传递算法.湖南大学学报(自然科学版),2002,29(5):25-30.Fan Youhua,Liu Jiaqi,Xiao Baixun.Fast vector-transfer algorithm for computation of Rayleigh wave dispersion curves.Journal of Hunan University(Natural Sciences Edition),2002,29(5):25-30.