基于粒子群算法的瑞雷波频散曲线反演研究
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摘要
瑞雷波频散曲线反演的本质是对目标函数求极值的过程.传统的线性局部反演算法容易陷入局部极小值,增加了反演结果的不确定性.粒子群算法作为一种全局非线性优化手段,能够保证各搜索空间内局部寻优的同时,逼近全局最优,保证迭代反演的收敛性.建立含软夹层型地层模型,正演计算得到理论频散曲线,采用粒子群算法反演得到的横波速度与模型高度吻合.同时,在理论频散曲线中加入10%的高斯白噪声,粒子群算法的反演结果仍然具有很好的可靠程度.通过对实测频散曲线的反演表明:粒子群算法在含软夹层型地层的横波速度探测中相对于最小二乘法优势明显,具有很高的应用价值.
The inversion essence of Rayleigh wave dispersion curve is a process of seeking for minimum value of objective function.Conventional algorithms are more likely to get stuck in local optimum due to their linear characters,which results in uncertainty of the inverted velocity. As a global and non-linear method,particle swarm optimization has the ability to approach both local and global optimum at the same time, assuring the iterative convergence.Calculate theoretical dispersion curve by establishing geological model with soft interlayer. Then,invert this curve by particle swarm optimization to obtain shear wave velocity, which has a good accordance with the initial model. The inverted results still have high reliability when Gaussian white noise is involved at the ratio10%. The inversion of observed dispersion curve indicates that,PSO has more considerable value with higher precision than least square method during shear wave velocity detection with soft interlayer stratum.
The inversion essence of Rayleigh wave dispersion curve is a process of seeking for minimum value of objective function.Conventional algorithms are more likely to get stuck in local optimum due to their linear characters,which results in uncertainty of the inverted velocity. As a global and non-linear method,particle swarm optimization has the ability to approach both local and global optimum at the same time, assuring the iterative convergence.Calculate theoretical dispersion curve by establishing geological model with soft interlayer. Then,invert this curve by particle swarm optimization to obtain shear wave velocity, which has a good accordance with the initial model. The inverted results still have high reliability when Gaussian white noise is involved at the ratio10%. The inversion of observed dispersion curve indicates that,PSO has more considerable value with higher precision than least square method during shear wave velocity detection with soft interlayer stratum.
引文
Fan Y H,Liu J Q.2001.Research on the dispersion of Rayleigh waves in multilayered media[J].Journal of Harbin Institute of Technology(in Chinese),33(5):577-581.
Fu D G,Liu J P,Zhou L M,et al.2015.Inversion of multimode Rayleigh-wave dispersion curves of soft interlayer based on Bayesian theory[J].Chinese Journal of Geotechnical Engineering(in Chinese),37(2):321-329,doi:10.11779/CJGE201502016.
Li Q C,Yan X D,Sun Y C,et al.2016.Measurement of superstratum wave velocity with reflection wave on dip section[J].Progress in Geophysics(in Chinese),31(5):2124-2127,doi:10.6038/pg20160532.
Liu C,Qiao H Q,Guo Z Q,et al.2017.Shale pore structure inversion and shear wave velocity prediction based on particle swarm optimization(PSO)algorithm[J].Progress in Geophysics(in Chinese),32(2):689-695,doi:10.6038/pg20170232.
Luo Y H,Xia J H,Liu J P,et al.2008.Joint inversion of fundamental and higher mode Rayleigh waves[J].Chinese Journal of Geophysics(in Chinese),51(1):242-249,doi:10.3321/j.issn:0001-5733.2008.01.030.
Shao G Z,Li Q C.2011.Study on parameter simplifying in dispersion curves inversion of surface wave based on subdividing layer method[J].Journal of Earth Sciences and Environment(in Chinese),33(3):317-320.
Shao G Z,Li Q C,Wu H.2015.Dispersion curves and mode energy distribution of Rayleigh wave based on wavefield numerical simulation[J].Oil Geophysical Prospecting(in Chinese),50(2):306-315.
Song X H,Xiao B X,Huang R R,et al.2003.The inversion of dispersion curves using self-adaptively iterative damping least square method by combining equal thinner layers with weighting matrix[J].Geophysical&Geochemical Exploration(in Chinese),27(3):212-216.
Yang C L.1989.The principle and application of Rayleigh wave exploration method[J].Geophysical&Geochemical Exploration(in Chinese),13(6):465-468.
Zhang B X,Lu L Y,Bao G S.2002.A study on zigzag dispersion curves in Rayleigh wave exploration[J].Chinese Journal of Geophysics(in Chinese),5(2):263-274,doi:10.3321/j.issn:0001-5733.2002.02.013.
Zhang B X,Xiao B X,Yang W J,et al.2000.Mechanism of zigzag dispersion curves in Rayleigh exploration and its inversion study[J].Chinese Journal of Geophysics(in Chinese),43(4):557-567,doi:10.3321/j.issn:0001-5733.2000.04.017.
Zhang X Y,Du W F,Lu Y X.2016.The application of particle swarm optimization in the inversion of Rayleigh wave dispersion curve[J].Journal of Liaoning Technical University(Natural Science)(in Chinese),35(12):1527-1532,doi:10.11956/j.issn.1008-0562.2016.12.027.
凡友华,刘家琦.2001.层状介质中瑞雷面波的频散研究[J].哈尔滨工业大学学报,33(5):577-581.
付代光,刘江平,周黎明,等.2015.基于贝叶斯理论的软夹层多模式瑞雷波频散曲线反演研究[J].岩土工程学报,37(2):321-329,doi:10.11779/CJGE201502016.
李启成,闫晓丹,孙颖川,等.2016.利用瑞利面波进行岩性分层[J].地球物理学进展,31(5):2124-2127,doi:10.6038/pg20160532.
刘财,乔汉青,郭智奇,等.2017.基于粒子群算法的页岩孔隙结构反演及横波速度预测[J].地球物理学进展,32(2):689-695,doi:10.6038/pg20170232.
罗银河,夏江海,刘江平,等.2008.基阶与高阶瑞利波联合反演研究[J].地球物理学报,51(1):242-249,doi:10.3321/j.issn:0001-5733.2008.01.030.
邵广周,李庆春.2011.基于细化分层法探讨面波频散曲线反演参数的简化[J].地球科学与环境学报,33(3):317-320.
邵广周,李庆春,吴华.2015.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[J].石油地球物理勘探,50(2):306-315.
宋先海,肖柏勋,黄荣荣,等.2003.用等厚薄层权重自适应迭代阻尼最小二乘法反演瑞雷波频散曲线[J].物探与化探,27(3):212-216.
杨成林.1989.瑞雷波法勘探原理及其应用[J].物探与化探,13(6):465-468.
张碧星,鲁来玉,鲍光淑.2002.瑞利波勘探中“之”字形频散曲线研究[J].地球物理学报,45(2):263-274,doi:10.3321/j.issn:0001-5733.2002.02.013.
张碧星,肖柏勋,杨文杰,等.2000.瑞利波勘探中“之”形频散曲线的形成机理及反演研究[J].地球物理学报,43(4):557-567,doi:10.3321/j.issn:0001-5733.2000.04.017.
张晓阳,杜文凤,卢勇旭.2016.粒子群算法在面波频散曲线反演中的应用[J].辽宁工程技术大学学报(自然科学版),35(12):1527-1532,doi:10.11956/j.issn.1008-0562.2016.12.027.
Fu D G,Liu J P,Zhou L M,et al.2015.Inversion of multimode Rayleigh-wave dispersion curves of soft interlayer based on Bayesian theory[J].Chinese Journal of Geotechnical Engineering(in Chinese),37(2):321-329,doi:10.11779/CJGE201502016.
Li Q C,Yan X D,Sun Y C,et al.2016.Measurement of superstratum wave velocity with reflection wave on dip section[J].Progress in Geophysics(in Chinese),31(5):2124-2127,doi:10.6038/pg20160532.
Liu C,Qiao H Q,Guo Z Q,et al.2017.Shale pore structure inversion and shear wave velocity prediction based on particle swarm optimization(PSO)algorithm[J].Progress in Geophysics(in Chinese),32(2):689-695,doi:10.6038/pg20170232.
Luo Y H,Xia J H,Liu J P,et al.2008.Joint inversion of fundamental and higher mode Rayleigh waves[J].Chinese Journal of Geophysics(in Chinese),51(1):242-249,doi:10.3321/j.issn:0001-5733.2008.01.030.
Shao G Z,Li Q C.2011.Study on parameter simplifying in dispersion curves inversion of surface wave based on subdividing layer method[J].Journal of Earth Sciences and Environment(in Chinese),33(3):317-320.
Shao G Z,Li Q C,Wu H.2015.Dispersion curves and mode energy distribution of Rayleigh wave based on wavefield numerical simulation[J].Oil Geophysical Prospecting(in Chinese),50(2):306-315.
Song X H,Xiao B X,Huang R R,et al.2003.The inversion of dispersion curves using self-adaptively iterative damping least square method by combining equal thinner layers with weighting matrix[J].Geophysical&Geochemical Exploration(in Chinese),27(3):212-216.
Yang C L.1989.The principle and application of Rayleigh wave exploration method[J].Geophysical&Geochemical Exploration(in Chinese),13(6):465-468.
Zhang B X,Lu L Y,Bao G S.2002.A study on zigzag dispersion curves in Rayleigh wave exploration[J].Chinese Journal of Geophysics(in Chinese),5(2):263-274,doi:10.3321/j.issn:0001-5733.2002.02.013.
Zhang B X,Xiao B X,Yang W J,et al.2000.Mechanism of zigzag dispersion curves in Rayleigh exploration and its inversion study[J].Chinese Journal of Geophysics(in Chinese),43(4):557-567,doi:10.3321/j.issn:0001-5733.2000.04.017.
Zhang X Y,Du W F,Lu Y X.2016.The application of particle swarm optimization in the inversion of Rayleigh wave dispersion curve[J].Journal of Liaoning Technical University(Natural Science)(in Chinese),35(12):1527-1532,doi:10.11956/j.issn.1008-0562.2016.12.027.
凡友华,刘家琦.2001.层状介质中瑞雷面波的频散研究[J].哈尔滨工业大学学报,33(5):577-581.
付代光,刘江平,周黎明,等.2015.基于贝叶斯理论的软夹层多模式瑞雷波频散曲线反演研究[J].岩土工程学报,37(2):321-329,doi:10.11779/CJGE201502016.
李启成,闫晓丹,孙颖川,等.2016.利用瑞利面波进行岩性分层[J].地球物理学进展,31(5):2124-2127,doi:10.6038/pg20160532.
刘财,乔汉青,郭智奇,等.2017.基于粒子群算法的页岩孔隙结构反演及横波速度预测[J].地球物理学进展,32(2):689-695,doi:10.6038/pg20170232.
罗银河,夏江海,刘江平,等.2008.基阶与高阶瑞利波联合反演研究[J].地球物理学报,51(1):242-249,doi:10.3321/j.issn:0001-5733.2008.01.030.
邵广周,李庆春.2011.基于细化分层法探讨面波频散曲线反演参数的简化[J].地球科学与环境学报,33(3):317-320.
邵广周,李庆春,吴华.2015.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[J].石油地球物理勘探,50(2):306-315.
宋先海,肖柏勋,黄荣荣,等.2003.用等厚薄层权重自适应迭代阻尼最小二乘法反演瑞雷波频散曲线[J].物探与化探,27(3):212-216.
杨成林.1989.瑞雷波法勘探原理及其应用[J].物探与化探,13(6):465-468.
张碧星,鲁来玉,鲍光淑.2002.瑞利波勘探中“之”字形频散曲线研究[J].地球物理学报,45(2):263-274,doi:10.3321/j.issn:0001-5733.2002.02.013.
张碧星,肖柏勋,杨文杰,等.2000.瑞利波勘探中“之”形频散曲线的形成机理及反演研究[J].地球物理学报,43(4):557-567,doi:10.3321/j.issn:0001-5733.2000.04.017.
张晓阳,杜文凤,卢勇旭.2016.粒子群算法在面波频散曲线反演中的应用[J].辽宁工程技术大学学报(自然科学版),35(12):1527-1532,doi:10.11956/j.issn.1008-0562.2016.12.027.