基于改进遗传算法的瑞雷波频散曲线反演
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摘要
瑞雷波勘探具有快速、经济、轻便、无损、衰减小、抗干扰能力强且不受各地层速度关系的影响等优点,它已被广泛应用于地球物理勘探、人工地震勘探及超声无损检测等领域。通过反演瑞雷波频散曲线可以获取横波速度、地层厚度、变形模量、抗压抗折强度、地基承载力、泊松比、标准贯入击数等物理力学参数。
反演方面的研究是瑞雷波勘探的核心。遗传算法因其对初始模型要求较宽松,无需计算导数信息,易于实现等优点,比较适合于解决非线性、多参数的瑞雷波频散曲线反演问题,但其计算量大、效率低及早熟收敛等缺陷使得其在瑞雷波反演中的应用受到了阻碍。
本文针对以上问题,结合瑞雷波反演特点,对遗传算法进行了如下改进：
(1)动态选取线性定标的参数C；
(2)采用自适应交叉概率和自适应变异概率,加快种群往好的方向搜索速度；
(3)删除相同染色体(仅保留一个),并由部分适应度高的染色体变异以补充被删个体,以保持种群的多样性；
(4)分析了遗传算法中重复计算的可能性,在程序实现中避免了重复计算。
利用改进的遗传算法进行瑞雷波频散曲线反演,对层速度递增模型选取基阶频散曲线构造目标函数,而对含低速夹层的模型选用最大模频散曲线构造目标函数。结果表明,改进遗传算法有效地加快了最优解改善速度并提高了反演精度。最后利用实测频散曲线进行反演,也取得较好效果,验证了改进遗传算法的正确性和实用性。
Rayleigh surface wave exploration has many advantages, such as fast, economical, lightweight, non-destructive, low attenuation, strong anti-interference ability, and it is not affected by the velocity relations of layers. Therefore, it has been widely used in the areas of geophysical exploration, artificial seismic exploration and ultrasonic nondestructive testing, etc. By inversion of Rayleigh wave dispersion curves, we can obtain the following parameters of physical mechanics:shear wave velocity, formation thickness, modulus of deformation, compressive and flexural strength, bearing capacity of subsoil, Poisson's ratio and SPT blow count, etc.
Inversion research is the core of Rayleigh wave exploration. Genetic algorithm (GA) is suitable for solving nonlinear, multi-parameter inversion problems of Rayleigh wave dispersion curve because of its less stringent requirements on the initial model, without calculating the derivative and the easy implementation. However, some GA's defect, such as large calculation, inefficient work and premature convergence, make it impeded in the application of Rayleigh wave inversion.
In this paper, combined with characteristics of Rayleigh wave inversion, GA was improved as follows to overcome the above shortcomings.
(1) The parameter C of Linear calibration was selected dynamicly;
(2) Using self-adaptive crossover probability and mutation probability, it can make that the group search towards a good direction more quickly;
(3) Reserving one of the same chromosomes and removing others. Some chromosomes with high fitness was selected to mutate for generating new chromosomes which are used to substitute for the removed chromosomes;
(4) It can be indicated that there is possibility of reduplicate calculation of fitness by analysing the process of GA. The reduplicate calculation is avoided in programing of GA.
The improved genetic algorithm was applied in Rayleigh wave dispersion curves inversion. As for increasing velocity model, fundamental mode dispersion curve was selected to construct objective function. While the model with low-speed sandwich, maximum mode dispersion curve was selected to construct objective function. The results show that the improved genetic algorithm can accelerate the improvement of optimal solution and improve the inversion accuracy efficiently. Finally, using improved genetic algorithm to inverse the measured dispersion curve, we can obtain correct results. It verifies that the improved genetic algorithm is correct and practical.
反演方面的研究是瑞雷波勘探的核心。遗传算法因其对初始模型要求较宽松,无需计算导数信息,易于实现等优点,比较适合于解决非线性、多参数的瑞雷波频散曲线反演问题,但其计算量大、效率低及早熟收敛等缺陷使得其在瑞雷波反演中的应用受到了阻碍。
本文针对以上问题,结合瑞雷波反演特点,对遗传算法进行了如下改进：
(1)动态选取线性定标的参数C；
(2)采用自适应交叉概率和自适应变异概率,加快种群往好的方向搜索速度；
(3)删除相同染色体(仅保留一个),并由部分适应度高的染色体变异以补充被删个体,以保持种群的多样性；
(4)分析了遗传算法中重复计算的可能性,在程序实现中避免了重复计算。
利用改进的遗传算法进行瑞雷波频散曲线反演,对层速度递增模型选取基阶频散曲线构造目标函数,而对含低速夹层的模型选用最大模频散曲线构造目标函数。结果表明,改进遗传算法有效地加快了最优解改善速度并提高了反演精度。最后利用实测频散曲线进行反演,也取得较好效果,验证了改进遗传算法的正确性和实用性。
Rayleigh surface wave exploration has many advantages, such as fast, economical, lightweight, non-destructive, low attenuation, strong anti-interference ability, and it is not affected by the velocity relations of layers. Therefore, it has been widely used in the areas of geophysical exploration, artificial seismic exploration and ultrasonic nondestructive testing, etc. By inversion of Rayleigh wave dispersion curves, we can obtain the following parameters of physical mechanics:shear wave velocity, formation thickness, modulus of deformation, compressive and flexural strength, bearing capacity of subsoil, Poisson's ratio and SPT blow count, etc.
Inversion research is the core of Rayleigh wave exploration. Genetic algorithm (GA) is suitable for solving nonlinear, multi-parameter inversion problems of Rayleigh wave dispersion curve because of its less stringent requirements on the initial model, without calculating the derivative and the easy implementation. However, some GA's defect, such as large calculation, inefficient work and premature convergence, make it impeded in the application of Rayleigh wave inversion.
In this paper, combined with characteristics of Rayleigh wave inversion, GA was improved as follows to overcome the above shortcomings.
(1) The parameter C of Linear calibration was selected dynamicly;
(2) Using self-adaptive crossover probability and mutation probability, it can make that the group search towards a good direction more quickly;
(3) Reserving one of the same chromosomes and removing others. Some chromosomes with high fitness was selected to mutate for generating new chromosomes which are used to substitute for the removed chromosomes;
(4) It can be indicated that there is possibility of reduplicate calculation of fitness by analysing the process of GA. The reduplicate calculation is avoided in programing of GA.
The improved genetic algorithm was applied in Rayleigh wave dispersion curves inversion. As for increasing velocity model, fundamental mode dispersion curve was selected to construct objective function. While the model with low-speed sandwich, maximum mode dispersion curve was selected to construct objective function. The results show that the improved genetic algorithm can accelerate the improvement of optimal solution and improve the inversion accuracy efficiently. Finally, using improved genetic algorithm to inverse the measured dispersion curve, we can obtain correct results. It verifies that the improved genetic algorithm is correct and practical.
引文
[1]杨成林.瑞雷波勘探[M].北京：地质出版社,1993.
[2]J. Dorman and D. Prentiss. Study of shear velocity distribution by mantle Rayleigh waves[J]. Bull. Seism. Soc. Am.,1960,50:87-115.
[3]佐薇范.用GR-810激振系统进行勘探.日本VIC株式会社,1986.
[4]杨成林.瑞雷波勘探法原理及其应用[J].物探与化探,1989,13(6)：465-468.
[5]黄嘉正,周洪秋,关小平.工程地质中瑞利波法勘探的理论初探[J].物探与化探,1991,15(4)：268-277.
[6]朱裕林.瑞利波勘探在工程勘察中应用[J].工程勘探,1991,(1)：67-70.
[7]J. S. Heisey, K. H. Stoke and A. H. Meyer. Muduli of pavement systems from spectral analysis of surface waves. Transportation Research Record, No852, D.C. Washighton, 1982.
[8]S. Nazarian & K. H. Stokoe. In situ determination of elastic moduli of pavement systems by spectral-of-surface-waves method. Research Report 437-2, Austin, Center for Transportation. Research, The University of Texas,1986.
[9]张忠苗,魏王伦,陈云敏,吴世明.瞬态面波测试技术在地基处理评价中应用[J].物探与化探,1992,16(1)：48-54.
[10]刘云桢,王振东.瞬态表面波法的数据采处理系统及其应用实例[J].物探与化探,1996,20(1)：28-33.
[11]肖柏勋,刘明贵,肖文治.一种新型的工程岩体探测震源——超磁致伸缩声波发射器[J].地学前缘,1996,3(1-2)：198-202.
[12]李绵飞.TRES-Ⅰ型多分量瑞利波勘探仪的研究及应用[J].物探与化探,1998,22(2)：129-133.
[13]肖柏勋.高模式瑞雷面波及其正反演研究：[博士学位论文].长沙：中南大学,2000.
[14]赵竹占,李华.表面波普分析法在评价地基处理效果中的应用[J].物探与化探,1994,18(5)：326-330.
[15]赵明.瑞利波法在工程勘察中的应用[J].勘察科学技术,1996,(5)：54-57.
[16]李哲生.瞬态多道瑞利波勘探技术在岩土工程勘察中的应用[J].工程勘察, 1996,(3)：66-68.
[17]宋先海.瑞雷波频散曲线的正反演研究：[硕士学位论文].武汉：中国地质大学,2001.
[18]Gabriels P, Snieder R, Nolet G. Insitu measurements of shear-wave velocity in sediments with higher-mode Rayleigh waves[J]. Geophysical Prospecting,1987,35: 187-196.
[19]刘云帧,王振东.瞬态面波法的数据采集处理系统及其应用实例[J].物探与化探,1996,20(1)：28-34.
[20]Ganji V, Gucunski N, Nazarian S. Automated inversion procedure for spectral analysis of surface waves[J]. Journal of Geotechnical and Geoenvironmental Engineering,1998, 124(8):757-770.
[21]杨成林,葛宝来,王炎.SM98瑞雷波仪测试原理及应用效果分析[J].物探与化探,2000,24(5)：332-339.
[22]Forbriger T. Inversion of shallow-seismic wavefields:Ⅱ. Inferring subsurface properites from wavefield transforms[J]. Geophysical Journal International,2003, 153:735-752
[23]Lai C G, Rix G J, Foti S, Roma V. Simultaneous measurement and inversion of surface wave dispersion and attenuation curves [J]. Soil Dynamics and Earthquake Engineering, 2002,22(9-12):923-930.
[24]Xia J, Miller R D, Park C B, Hunter J A, Harris J B, Ivanov J. Comparing shear-wave velocity profiles from multichannel analysis of surface wave with borehole measurements[J]. Soil Dynamics and Earthquake Engineering,2002,22(3):181-190.
[25]石耀霖,金文.面波频散反演地球内部构造的遗传算法[J].地球物理学报,1995,38(2)：189-198.
[26]Yamanaka H, Ishida H. Application of genetic algorithms to an inversion of surface wave dispersion data[J]. Bulletin of the seismological Society of America.,1996,86: 436-444.
[27]张碧星,肖柏勋,杨文杰等.瑞利波勘探中“之”字型频散曲线的形成机理及反演研究[J].地球物理学报,2000,43(4)：557-567.
[28]Dal Moro G and Pipan M. Joint inversion of surface wave dispersion curves and reflection travel times via multi-objective evolutionary algorithms[J]. Journal of Applied Geophysics.,2007,61(1):56-81.
[29]Martinez M D, Lana X, Olarte J, Badal J, Canas J A. Inversion of Rayleigh wave phase and group velocity by simulated annealing[J]. Physics of the Earth and Planetary Interiors,2000,122:3-17.
[30]Beaty K S, Schmitt D R. Repeatability of multimode Rayleigh-wave dispersion studies[J]. Geophysics,2003,68(3):782-790.
[31]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[J].地球物理学报,2004,47(3)：521-527.
[32]Calderon-Macias C, Luke B. Improved parameterization to invert Rayleigh-wave data for shallow profiles containing stiff inclusions [J]. Geophysics,2007,72(1):1-10.
[33]Van der Baan M, Jutten C. Neural networks in geophysics applications [J]. Geophysics, 2000,65(4):1032-1047.
[34]Wu H. Feasibility of artificial neural network approach to inversion of spectral analysis of surface waves data for pavement structures. PhD Disssertation. University of Texas, 2001.
[35]宋先海.基于模式识别法的高频瑞雷波频散曲线非线性反演研究：[博士学位论文].武汉：中国地质大学,2008.
[36]雷英杰,张善文,李续武,周创明.遗传算法工具箱及应用[M],西安：西安电子科技大学出版社,2005.
[37]杜月云,周子平.针对传统遗传算法中存在的不足的改进[J].广西轻工业,2007,104(7)：58-63.
[38]姚志红.多元共生遗传算法研究及其在藻类智能模式识别中的应用：[博士学位论文].上海：上海大学,2007.
[39]兰海,汪宇涵,张利军.基于改进自适应遗传算法的船舶电力系统滤波装置优化配置[J].船电技术,2009,29(6)：1-5.
[40]N. A. Haskell. The dispersion of surface waves on multilayered media[J]. Bull. siesm. Soc.Am.,1953,43:17-34.
[41]F. Schwab. Surface-wave dispersion computations:Knopoff s method[J]. Bull. Seism. Soc.Am.,1970,60:1491-1520.
[42]J. W. Dunkin. Computation of modal solutions in layered elastic media at high frequencies[J]. Bull.Seism. Soc.Am.,1965,55:335-358.
[43]H.T. Waston. A note on fast computation of Rayleigh wave dispersion in multisayered half-space[J]. Bull. Seism. Soc. Am.,1970,60:161-166.
[44]P. W. Buchen & R. Ben-Hador. Free-mode surface-wave computations[J]. Geophys. J. Int.,1996,124:869-887.
[45]Kennett B L N, Kerry N J. Seismic waves in a stratified halfspace[J]. Geophys. J. R. astr. Soc,1979,57:557-583.
[46]A. Abo-Zena. Dispersion function computations for unlimited frequency values[J]. Geophys. J. R. astr. Soc.,1979,58:91-105.
[47]凡友华,刘家琦.层状介质中瑞雷面波的频散研究[J].哈尔滨工业大学学报,2001,33(5)：577-581.
[48]Willialm Menke. Comment on' Dispersion function computations for unlimited frequency values' by Anas Abo-Zena[J]. Geophys. J. R. astr. Soc,1979,59:315-323.
[49]鲁来玉.分层介质半空间瑞利波模式分析和介质参数反演：[博士论文].北京：中国科学院声学研究所,2004.
[50]丁彦礼,单娜琳.瑞利面波最大模频散曲线的反演解释方法[J].桂林工学院学报,2007,27(3)：322-328.
[51]杨天春.瑞利波“之”字形频散与道路结构频散曲线的正演研究：[博士论文].长沙：中南大学,2004.
[52]熊章强.复杂介质中瑞雷面波的正演模拟及传播特征研究：[博士论文].武汉：中国地质大学,2006.
[53]罗银河,夏江海,刘江平,刘庆生.基阶与高阶瑞利波联合反演研究[J].地球物理学报,2008,51(1)：242-249.
[2]J. Dorman and D. Prentiss. Study of shear velocity distribution by mantle Rayleigh waves[J]. Bull. Seism. Soc. Am.,1960,50:87-115.
[3]佐薇范.用GR-810激振系统进行勘探.日本VIC株式会社,1986.
[4]杨成林.瑞雷波勘探法原理及其应用[J].物探与化探,1989,13(6)：465-468.
[5]黄嘉正,周洪秋,关小平.工程地质中瑞利波法勘探的理论初探[J].物探与化探,1991,15(4)：268-277.
[6]朱裕林.瑞利波勘探在工程勘察中应用[J].工程勘探,1991,(1)：67-70.
[7]J. S. Heisey, K. H. Stoke and A. H. Meyer. Muduli of pavement systems from spectral analysis of surface waves. Transportation Research Record, No852, D.C. Washighton, 1982.
[8]S. Nazarian & K. H. Stokoe. In situ determination of elastic moduli of pavement systems by spectral-of-surface-waves method. Research Report 437-2, Austin, Center for Transportation. Research, The University of Texas,1986.
[9]张忠苗,魏王伦,陈云敏,吴世明.瞬态面波测试技术在地基处理评价中应用[J].物探与化探,1992,16(1)：48-54.
[10]刘云桢,王振东.瞬态表面波法的数据采处理系统及其应用实例[J].物探与化探,1996,20(1)：28-33.
[11]肖柏勋,刘明贵,肖文治.一种新型的工程岩体探测震源——超磁致伸缩声波发射器[J].地学前缘,1996,3(1-2)：198-202.
[12]李绵飞.TRES-Ⅰ型多分量瑞利波勘探仪的研究及应用[J].物探与化探,1998,22(2)：129-133.
[13]肖柏勋.高模式瑞雷面波及其正反演研究：[博士学位论文].长沙：中南大学,2000.
[14]赵竹占,李华.表面波普分析法在评价地基处理效果中的应用[J].物探与化探,1994,18(5)：326-330.
[15]赵明.瑞利波法在工程勘察中的应用[J].勘察科学技术,1996,(5)：54-57.
[16]李哲生.瞬态多道瑞利波勘探技术在岩土工程勘察中的应用[J].工程勘察, 1996,(3)：66-68.
[17]宋先海.瑞雷波频散曲线的正反演研究：[硕士学位论文].武汉：中国地质大学,2001.
[18]Gabriels P, Snieder R, Nolet G. Insitu measurements of shear-wave velocity in sediments with higher-mode Rayleigh waves[J]. Geophysical Prospecting,1987,35: 187-196.
[19]刘云帧,王振东.瞬态面波法的数据采集处理系统及其应用实例[J].物探与化探,1996,20(1)：28-34.
[20]Ganji V, Gucunski N, Nazarian S. Automated inversion procedure for spectral analysis of surface waves[J]. Journal of Geotechnical and Geoenvironmental Engineering,1998, 124(8):757-770.
[21]杨成林,葛宝来,王炎.SM98瑞雷波仪测试原理及应用效果分析[J].物探与化探,2000,24(5)：332-339.
[22]Forbriger T. Inversion of shallow-seismic wavefields:Ⅱ. Inferring subsurface properites from wavefield transforms[J]. Geophysical Journal International,2003, 153:735-752
[23]Lai C G, Rix G J, Foti S, Roma V. Simultaneous measurement and inversion of surface wave dispersion and attenuation curves [J]. Soil Dynamics and Earthquake Engineering, 2002,22(9-12):923-930.
[24]Xia J, Miller R D, Park C B, Hunter J A, Harris J B, Ivanov J. Comparing shear-wave velocity profiles from multichannel analysis of surface wave with borehole measurements[J]. Soil Dynamics and Earthquake Engineering,2002,22(3):181-190.
[25]石耀霖,金文.面波频散反演地球内部构造的遗传算法[J].地球物理学报,1995,38(2)：189-198.
[26]Yamanaka H, Ishida H. Application of genetic algorithms to an inversion of surface wave dispersion data[J]. Bulletin of the seismological Society of America.,1996,86: 436-444.
[27]张碧星,肖柏勋,杨文杰等.瑞利波勘探中“之”字型频散曲线的形成机理及反演研究[J].地球物理学报,2000,43(4)：557-567.
[28]Dal Moro G and Pipan M. Joint inversion of surface wave dispersion curves and reflection travel times via multi-objective evolutionary algorithms[J]. Journal of Applied Geophysics.,2007,61(1):56-81.
[29]Martinez M D, Lana X, Olarte J, Badal J, Canas J A. Inversion of Rayleigh wave phase and group velocity by simulated annealing[J]. Physics of the Earth and Planetary Interiors,2000,122:3-17.
[30]Beaty K S, Schmitt D R. Repeatability of multimode Rayleigh-wave dispersion studies[J]. Geophysics,2003,68(3):782-790.
[31]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[J].地球物理学报,2004,47(3)：521-527.
[32]Calderon-Macias C, Luke B. Improved parameterization to invert Rayleigh-wave data for shallow profiles containing stiff inclusions [J]. Geophysics,2007,72(1):1-10.
[33]Van der Baan M, Jutten C. Neural networks in geophysics applications [J]. Geophysics, 2000,65(4):1032-1047.
[34]Wu H. Feasibility of artificial neural network approach to inversion of spectral analysis of surface waves data for pavement structures. PhD Disssertation. University of Texas, 2001.
[35]宋先海.基于模式识别法的高频瑞雷波频散曲线非线性反演研究：[博士学位论文].武汉：中国地质大学,2008.
[36]雷英杰,张善文,李续武,周创明.遗传算法工具箱及应用[M],西安：西安电子科技大学出版社,2005.
[37]杜月云,周子平.针对传统遗传算法中存在的不足的改进[J].广西轻工业,2007,104(7)：58-63.
[38]姚志红.多元共生遗传算法研究及其在藻类智能模式识别中的应用：[博士学位论文].上海：上海大学,2007.
[39]兰海,汪宇涵,张利军.基于改进自适应遗传算法的船舶电力系统滤波装置优化配置[J].船电技术,2009,29(6)：1-5.
[40]N. A. Haskell. The dispersion of surface waves on multilayered media[J]. Bull. siesm. Soc.Am.,1953,43:17-34.
[41]F. Schwab. Surface-wave dispersion computations:Knopoff s method[J]. Bull. Seism. Soc.Am.,1970,60:1491-1520.
[42]J. W. Dunkin. Computation of modal solutions in layered elastic media at high frequencies[J]. Bull.Seism. Soc.Am.,1965,55:335-358.
[43]H.T. Waston. A note on fast computation of Rayleigh wave dispersion in multisayered half-space[J]. Bull. Seism. Soc. Am.,1970,60:161-166.
[44]P. W. Buchen & R. Ben-Hador. Free-mode surface-wave computations[J]. Geophys. J. Int.,1996,124:869-887.
[45]Kennett B L N, Kerry N J. Seismic waves in a stratified halfspace[J]. Geophys. J. R. astr. Soc,1979,57:557-583.
[46]A. Abo-Zena. Dispersion function computations for unlimited frequency values[J]. Geophys. J. R. astr. Soc.,1979,58:91-105.
[47]凡友华,刘家琦.层状介质中瑞雷面波的频散研究[J].哈尔滨工业大学学报,2001,33(5)：577-581.
[48]Willialm Menke. Comment on' Dispersion function computations for unlimited frequency values' by Anas Abo-Zena[J]. Geophys. J. R. astr. Soc,1979,59:315-323.
[49]鲁来玉.分层介质半空间瑞利波模式分析和介质参数反演：[博士论文].北京：中国科学院声学研究所,2004.
[50]丁彦礼,单娜琳.瑞利面波最大模频散曲线的反演解释方法[J].桂林工学院学报,2007,27(3)：322-328.
[51]杨天春.瑞利波“之”字形频散与道路结构频散曲线的正演研究：[博士论文].长沙：中南大学,2004.
[52]熊章强.复杂介质中瑞雷面波的正演模拟及传播特征研究：[博士论文].武汉：中国地质大学,2006.
[53]罗银河,夏江海,刘江平,刘庆生.基阶与高阶瑞利波联合反演研究[J].地球物理学报,2008,51(1)：242-249.