瑞雷波反演及转换波静校正中粒子群算法的研究及应用
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摘要
地震勘探中层析成像、剩余静校正、反褶积、AVO等问题都是反演问题。反演根据算法不同可分为线性（拟线性）反演和非线性反演。线性反演具有理论较为成熟、运算速度快等优点；但不足之处是容易受初始模型好坏的影响而陷入局部最优解。非线性反演的寻优效果不受初始模型的影响，理论上具有跳出局部最优解并寻找到全局最优解的能力，但是其缺陷是收敛速度慢、算法性能受参数选择影响较大。
本文首先介绍了粒子群算法。粒子群算法是一种非线性最优化算法，其基本思想是基于对自然界鸟群和鱼群的模拟。标准粒子群算法具有收敛速度快、易于实现、易于并行操作、调用参数少等优点。但其缺点是易发生“早熟”收敛。本文在标准粒子群算法的基础上，引入团体粒子形成了团体粒子群算法。团体粒子是一类特殊的粒子，所有团体粒子在算法进行过程中间始终保持一定的距离，这就从一定程度上减弱了标准粒子群算法由于粒子聚集导致的“早熟”收敛现象，使算法具有更强的全局寻优能力。
其次，本文研究了团体粒子群算法在瑞雷波频散曲线反演中的应用。瑞雷波是在自由表面处P波和SV波干涉产生的一种地震波。瑞雷波在分层介质中有频散现象，其相速度随频率变化的曲线称为频散曲线。瑞雷波的频散曲线与介质的纵、横波速度、密度及层厚有关，其中受横波速度和层厚的影响最大，因此可以利用瑞雷波的频散曲线反演近地表的横波速度结构。阻尼最小二乘法是瑞雷波反演的常用算法之一，它是一种线性算法，具有收敛速度快等优点，但其结果依赖初始值的好坏；而团体粒子群算法作为一种非线性算法，可以不依赖初始值的选取而搜索到全局最优解，但其收敛速度较慢。瑞雷波反演可仅反演基阶模式的频散曲线也可以联合反演多阶模式的频散曲线。研究表明，多阶模式联合反演可以提高结果的准确性和反演的稳定性。通过实验也证明了上述结论。
最后，本文研究转换波短波长大的静校正问题。随着社会的发展，人类对资源的需求不断增加，要求地质及地球物理学家对地下情况有更精细、更准确的认识。因此学者们一方面继续发展纵波反射波法勘探技术，另一方面研究并开展新的地震勘探理论与技术，如四维地震勘探、多波多分量地震勘探等。横波具有很多纵波不具有的性质，如其传播不受孔隙流体影响、穿过裂缝会发生横波分裂现象等。横波资料在判断岩性、裂缝和含油气性等方面有重要的作用。采用横波震源激发的横波勘探方式由于横波震源花费高且横波穿透深度较小而难以应用于实际生产中。利用转换波进行横波勘探相对于横波震源激发的横波勘探具有勘探深度大且成本小等优点。静校正是地震勘探数据处理中的一项重要环节，静校正的好坏会对后续处理产生很大的影响。对于转换波而言，由于其激发为纵波而接收为横波，因此其静校正量包括炮点的纵波静校正量和检波点的横波静校正量。一般在进行转换波处理前已完成了纵波处理，因此炮点的纵波静校正量可认为是已知的，因而转换波的静校正量就是检波点的横波静校正量。由于横波传播不受孔隙流体影响，其低速带底界面往往在潜水面之下，加之横波速度较低，其静校正量往往是同位置处纵波静校正量的2~10倍。由于转换波检波点横波的静校正量往往较大且变化剧烈，因此转换波的短波长静校正问题是一个典型的非线性、多极值的复杂问题，采用纵波勘探中常用的线性方法很难取得较好的效果。为了准确的估计转换波检波点的短波长较大的静校正量，本文研究了以叠加剖面的能量为目标函数，将团体粒子群算法与最大能量法进行了串行融合，并利用融合算法估算转换波检波点横波的短波长静校正量。模型试算证明本方法效果较好。
Seismic tomography, residual static correction, deconvolution, AVO and other issuesare the inverse problem of seismic exploration. Inversion can be divided into linear(quasi-linear) and nonlinear inversion according to different algorithms. Theadvantages of linear inversion are comparatively ripe theory, fast operation and so on.However, the disadvantage of it is falling into the local optimal solution since thealgorithm can be easily influenced by initial model. Optimization of nonlinearinversion doesn't depend on initial model and has the ability of jumping out of localoptimal solution and finding global optimization in theory, but the weaknesses areslow convergence speed and the algorithm performance are largely influenced byparameter selection.
Firstly, we introduce particle swarm optimization in this paper. Particle swarmoptimization is one of the nonlinear optimizations and its main thought is simulatingthe behavior of a flock of birds or a school of fish. Standard particle swarmoptimization own advantages such as, fast convergence speed, easy to implement,being prone to parallel operation and less call parameters. However, the disadvantageof it easily occurs “premature”. In this paper, we introduced group particles to formgroup particle swarm optimization based on standard particle swarm optimization.Group particles are one special class and all the group particles keep a certain distanceduring the algorithm execution process, thus it decreases “premature” of particleswarm optimization phenomenon caused by aggregation of particles in some degreeand the new algorithm has powerful ability of global searching.
Secondly, our study focuses on application of group particle swarm optimization applied on the inversion of Rayleigh wave dispersion curves. Rayleigh waves are atype of seismic wave caused by the interference of P and SV wave at free surface.Rayleigh waves have dispersion phenomenon in multilayer-medium and their phasevelocity changes along with frequency is defined as dispersion curves. Dispersioncurves relative to compressional and shear wave velocities, density and layerthickness, what's more, shear wave velocity and layer thickness among them areplaying more important roles. Thus we can use dispersion cures to inversenear-surface shear velocity structure. Levenberg–Marquardt algorithm is one ofcommon algorithms for Rayleigh waves inversion and a linear algorithm which hasthe merits, such as fast convergence speed. However, its results depend on the initialvalue. Group particle swarm optimization as a nonlinear algorithm can be independentof initial value and get global optimal solution, but it has lower convergence speed.Rayleigh waves inversion can only inverse fundamental mode of dispersion curve andalso can joint inverse multi-modes. Research results show that adding higher modes toinversion can increase accuracy of results and stability of inversion. The experimentsresults also prove the above conclusion.
Last but not least, we study the problem that large short wavelength shear wave staticscorrection. With the development of society, the demand for resources is increasingand which require geologists and geophysicists to get a more meticulous and accurateunderstanding of underground. On one hand scholars continue to developcompressional wave exploration technology. On the other hand they research anddevelop new theories and technologies of seismic exploration, such asFour-dimensional seismic exploration, multi-wave and multi-component seismicexploration. Shear wave has some properties which compressional wave does nothave, such as its propagation which is seldom sensitive to the porous fluid and shearwave splitting through fractures. Shear wave material plays an important role in determination of lithology, fracture and oil-gas possibility. Shear wave explorationwhich needs excitation of shear wave source is hard to be applied to practicalproduction, since shear wave source is expensive and the penetration depth of shearwave is small. Shear wave exploration using converted wave information hasadvantages of larger exploration depth and lower cost comparing with the one usingshear wave source. Static correction is an important step of seismic exploration and itwill largely influence the following steps. For converted wave, its excitation iscompressional wave and we can get shear wave information, so its static correctioncan be divided into static correction at source and static correction at receiver.Normally, compressional wave seismic data processing has been finished beforeconverted wave seismic data processing, so the static correction at source can beconsidered already being known which means converted wave static correction is thestatic correction at receiver. Since shear wave propagation is not influenced by theporous fluid, its low velocity zone is always below water table and shear wavevelocity is lower, its static correction is often2~10times as much as compressionalwave static correction at the same position. Converted wave static correction atreceiver is often large and changes dramatically and short wavelength converted wavestatics correction is typical nonlinear and multi-minimum problem, so it is hard to geta good result when using linear method. In order to estimate static correction of shortwavelength converted wave at receiver is large. In this paper the stack section energyis considered as objective function and group particle swarm optimization and themaximum energy method are serially fused, then we can estimate static correction ofshort wavelength converted wave at receiver by using serial algorithm. Model testproves that this method can get better results.
本文首先介绍了粒子群算法。粒子群算法是一种非线性最优化算法，其基本思想是基于对自然界鸟群和鱼群的模拟。标准粒子群算法具有收敛速度快、易于实现、易于并行操作、调用参数少等优点。但其缺点是易发生“早熟”收敛。本文在标准粒子群算法的基础上，引入团体粒子形成了团体粒子群算法。团体粒子是一类特殊的粒子，所有团体粒子在算法进行过程中间始终保持一定的距离，这就从一定程度上减弱了标准粒子群算法由于粒子聚集导致的“早熟”收敛现象，使算法具有更强的全局寻优能力。
其次，本文研究了团体粒子群算法在瑞雷波频散曲线反演中的应用。瑞雷波是在自由表面处P波和SV波干涉产生的一种地震波。瑞雷波在分层介质中有频散现象，其相速度随频率变化的曲线称为频散曲线。瑞雷波的频散曲线与介质的纵、横波速度、密度及层厚有关，其中受横波速度和层厚的影响最大，因此可以利用瑞雷波的频散曲线反演近地表的横波速度结构。阻尼最小二乘法是瑞雷波反演的常用算法之一，它是一种线性算法，具有收敛速度快等优点，但其结果依赖初始值的好坏；而团体粒子群算法作为一种非线性算法，可以不依赖初始值的选取而搜索到全局最优解，但其收敛速度较慢。瑞雷波反演可仅反演基阶模式的频散曲线也可以联合反演多阶模式的频散曲线。研究表明，多阶模式联合反演可以提高结果的准确性和反演的稳定性。通过实验也证明了上述结论。
最后，本文研究转换波短波长大的静校正问题。随着社会的发展，人类对资源的需求不断增加，要求地质及地球物理学家对地下情况有更精细、更准确的认识。因此学者们一方面继续发展纵波反射波法勘探技术，另一方面研究并开展新的地震勘探理论与技术，如四维地震勘探、多波多分量地震勘探等。横波具有很多纵波不具有的性质，如其传播不受孔隙流体影响、穿过裂缝会发生横波分裂现象等。横波资料在判断岩性、裂缝和含油气性等方面有重要的作用。采用横波震源激发的横波勘探方式由于横波震源花费高且横波穿透深度较小而难以应用于实际生产中。利用转换波进行横波勘探相对于横波震源激发的横波勘探具有勘探深度大且成本小等优点。静校正是地震勘探数据处理中的一项重要环节，静校正的好坏会对后续处理产生很大的影响。对于转换波而言，由于其激发为纵波而接收为横波，因此其静校正量包括炮点的纵波静校正量和检波点的横波静校正量。一般在进行转换波处理前已完成了纵波处理，因此炮点的纵波静校正量可认为是已知的，因而转换波的静校正量就是检波点的横波静校正量。由于横波传播不受孔隙流体影响，其低速带底界面往往在潜水面之下，加之横波速度较低，其静校正量往往是同位置处纵波静校正量的2~10倍。由于转换波检波点横波的静校正量往往较大且变化剧烈，因此转换波的短波长静校正问题是一个典型的非线性、多极值的复杂问题，采用纵波勘探中常用的线性方法很难取得较好的效果。为了准确的估计转换波检波点的短波长较大的静校正量，本文研究了以叠加剖面的能量为目标函数，将团体粒子群算法与最大能量法进行了串行融合，并利用融合算法估算转换波检波点横波的短波长静校正量。模型试算证明本方法效果较好。
Seismic tomography, residual static correction, deconvolution, AVO and other issuesare the inverse problem of seismic exploration. Inversion can be divided into linear(quasi-linear) and nonlinear inversion according to different algorithms. Theadvantages of linear inversion are comparatively ripe theory, fast operation and so on.However, the disadvantage of it is falling into the local optimal solution since thealgorithm can be easily influenced by initial model. Optimization of nonlinearinversion doesn't depend on initial model and has the ability of jumping out of localoptimal solution and finding global optimization in theory, but the weaknesses areslow convergence speed and the algorithm performance are largely influenced byparameter selection.
Firstly, we introduce particle swarm optimization in this paper. Particle swarmoptimization is one of the nonlinear optimizations and its main thought is simulatingthe behavior of a flock of birds or a school of fish. Standard particle swarmoptimization own advantages such as, fast convergence speed, easy to implement,being prone to parallel operation and less call parameters. However, the disadvantageof it easily occurs “premature”. In this paper, we introduced group particles to formgroup particle swarm optimization based on standard particle swarm optimization.Group particles are one special class and all the group particles keep a certain distanceduring the algorithm execution process, thus it decreases “premature” of particleswarm optimization phenomenon caused by aggregation of particles in some degreeand the new algorithm has powerful ability of global searching.
Secondly, our study focuses on application of group particle swarm optimization applied on the inversion of Rayleigh wave dispersion curves. Rayleigh waves are atype of seismic wave caused by the interference of P and SV wave at free surface.Rayleigh waves have dispersion phenomenon in multilayer-medium and their phasevelocity changes along with frequency is defined as dispersion curves. Dispersioncurves relative to compressional and shear wave velocities, density and layerthickness, what's more, shear wave velocity and layer thickness among them areplaying more important roles. Thus we can use dispersion cures to inversenear-surface shear velocity structure. Levenberg–Marquardt algorithm is one ofcommon algorithms for Rayleigh waves inversion and a linear algorithm which hasthe merits, such as fast convergence speed. However, its results depend on the initialvalue. Group particle swarm optimization as a nonlinear algorithm can be independentof initial value and get global optimal solution, but it has lower convergence speed.Rayleigh waves inversion can only inverse fundamental mode of dispersion curve andalso can joint inverse multi-modes. Research results show that adding higher modes toinversion can increase accuracy of results and stability of inversion. The experimentsresults also prove the above conclusion.
Last but not least, we study the problem that large short wavelength shear wave staticscorrection. With the development of society, the demand for resources is increasingand which require geologists and geophysicists to get a more meticulous and accurateunderstanding of underground. On one hand scholars continue to developcompressional wave exploration technology. On the other hand they research anddevelop new theories and technologies of seismic exploration, such asFour-dimensional seismic exploration, multi-wave and multi-component seismicexploration. Shear wave has some properties which compressional wave does nothave, such as its propagation which is seldom sensitive to the porous fluid and shearwave splitting through fractures. Shear wave material plays an important role in determination of lithology, fracture and oil-gas possibility. Shear wave explorationwhich needs excitation of shear wave source is hard to be applied to practicalproduction, since shear wave source is expensive and the penetration depth of shearwave is small. Shear wave exploration using converted wave information hasadvantages of larger exploration depth and lower cost comparing with the one usingshear wave source. Static correction is an important step of seismic exploration and itwill largely influence the following steps. For converted wave, its excitation iscompressional wave and we can get shear wave information, so its static correctioncan be divided into static correction at source and static correction at receiver.Normally, compressional wave seismic data processing has been finished beforeconverted wave seismic data processing, so the static correction at source can beconsidered already being known which means converted wave static correction is thestatic correction at receiver. Since shear wave propagation is not influenced by theporous fluid, its low velocity zone is always below water table and shear wavevelocity is lower, its static correction is often2~10times as much as compressionalwave static correction at the same position. Converted wave static correction atreceiver is often large and changes dramatically and short wavelength converted wavestatics correction is typical nonlinear and multi-minimum problem, so it is hard to geta good result when using linear method. In order to estimate static correction of shortwavelength converted wave at receiver is large. In this paper the stack section energyis considered as objective function and group particle swarm optimization and themaximum energy method are serially fused, then we can estimate static correction ofshort wavelength converted wave at receiver by using serial algorithm. Model testproves that this method can get better results.
引文
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