二维电阻率层析成像的改进PSO非线性反演研究
发布时间：2018-10-14 16:15
【摘要】：电法勘探作为传统物探方法,在地质勘探、地下水勘察、油气开采以及金属探矿等领域都普遍应用。阻率层析成像(Electrical Resistance Tomography,简称ERT)是一种典型的电法勘探手段,以其场源实现简单、实施方便、分辨率高、经济实惠、穿透深度大等优点等成为物探技术的前沿课题之一,具有广泛的应用前景。由于电阻率剖面数据的计算精度和有效解释是其应用的重要指标,ERT电阻率数据反演解释是处理实际资料的主要手段,因此ERT数据的反演也一直是国内外专家学者广泛研究的焦点。本文在改进粒子群优化算法(Particle Swarm Optimization,简称PSO)对二维ERT模拟数据的非线性反演方面,开展了全面细致的研究工作,主要包括:(1)介绍ERT的发展以及反演现状,阐述了PSO算法的基本原理,总结相关改进方向。针对其全局搜索后期收敛慢,易陷入局部极值的缺点,提出本文改进PSO算法的方向——在各影响粒子群速度更新的参数中引入混沌搜索,并用典型多峰值函数测试标准粒子群算法、阻尼粒子群算法算法和本文的改进粒子群算法,实验结果表明,改进后的算法在搜索精度、收敛时间以及稳定性方面都优于标准PSO算法和阻尼PSO算法,在保证跳出局部极值的同时,提高了收敛速度。(2)详细推导了采用非结构三角形单元时,用有限元法离散微分方程,形成正演矩阵,求得波数域结果,经过傅里叶逆变换转换到空间域,完成正演研究。并在Matlab中编制正演FEM数值模拟程序,经过模型验证,对比解析解,证明FEM是一种较好的正演模拟方法。(3)阐述二维ERT反演理论,对比线性舍弃高次项的处理方法,推导出非线性反演的最小化目标函数,设计直流电阻率模型、时域激发极化模型和频域激发极化复电阻率正演模型,然后分别在加入一定程度噪声的三种正演模型数据上进行模拟反演,并将其性能与标准PSO算法和奥卡姆算法进行对比,模型实验表明,该方法不容易陷于局部最优,数值稳定性好,具有较快的收敛速度,具有较高的性能。
[Abstract]:As a traditional geophysical method, electrical exploration is widely used in geological exploration, groundwater exploration, oil and gas exploration and metal prospecting. Resistive rate tomography (Electrical Resistance Tomography,) is a typical method of electrical exploration. Because of its advantages of simple field source, convenient implementation, high resolution, economical benefit, high penetration depth and so on, it has become one of the frontier topics of geophysical exploration technology. It has wide application prospect. Because the calculation accuracy and effective interpretation of resistivity profile data are important indexes for its application, inversion interpretation of ERT resistivity data is the main means to process the actual data. Therefore, the inversion of ERT data has always been the focus of extensive research by experts and scholars at home and abroad. In this paper, a comprehensive and detailed study on nonlinear inversion of two-dimensional ERT simulation data based on improved particle swarm optimization (Particle Swarm Optimization,) algorithm called PSO is carried out, including: (1) introducing the development of ERT and the present situation of inversion. The basic principle of PSO algorithm is expounded, and the improvement direction is summarized. In view of the disadvantages of slow convergence and easy to fall into local extremum in the late stage of global search, this paper presents the direction of improved PSO algorithm, which is to introduce chaos search into the parameters that affect the velocity update of particle swarm. The standard particle swarm optimization algorithm, damping particle swarm optimization algorithm and the improved particle swarm optimization algorithm of this paper are tested with typical multi-peak function. The experimental results show that the improved algorithm is accurate in searching. The convergence time and stability are better than the standard PSO algorithm and the damped PSO algorithm. The convergence rate is improved while the local extremum is removed. (2) the finite element method is used to discretize the differential equations when the unstructured triangular element is used. The forward modeling matrix is formed, the wavenumber domain results are obtained, and the forward modeling is completed by the inverse Fourier transform to the spatial domain. The forward FEM numerical simulation program is compiled in Matlab. After model verification and analysis, it is proved that FEM is a good forward modeling method. (3) the theory of two-dimensional ERT inversion is expounded, and the processing method of linear renunciation of higher term is compared. The minimization objective function of nonlinear inversion is derived. The DC resistivity model, the time-domain induced polarization model and the frequency-domain induced polarization complex resistivity model are designed. Then the simulation inversion is carried out on the three kinds of forward modeling data with certain noise, and its performance is compared with the standard PSO algorithm and Occam algorithm. The model experiment shows that the method is not easy to be trapped in local optimum. It has good numerical stability, fast convergence speed and high performance.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.322
本文编号：2270972
[Abstract]:As a traditional geophysical method, electrical exploration is widely used in geological exploration, groundwater exploration, oil and gas exploration and metal prospecting. Resistive rate tomography (Electrical Resistance Tomography,) is a typical method of electrical exploration. Because of its advantages of simple field source, convenient implementation, high resolution, economical benefit, high penetration depth and so on, it has become one of the frontier topics of geophysical exploration technology. It has wide application prospect. Because the calculation accuracy and effective interpretation of resistivity profile data are important indexes for its application, inversion interpretation of ERT resistivity data is the main means to process the actual data. Therefore, the inversion of ERT data has always been the focus of extensive research by experts and scholars at home and abroad. In this paper, a comprehensive and detailed study on nonlinear inversion of two-dimensional ERT simulation data based on improved particle swarm optimization (Particle Swarm Optimization,) algorithm called PSO is carried out, including: (1) introducing the development of ERT and the present situation of inversion. The basic principle of PSO algorithm is expounded, and the improvement direction is summarized. In view of the disadvantages of slow convergence and easy to fall into local extremum in the late stage of global search, this paper presents the direction of improved PSO algorithm, which is to introduce chaos search into the parameters that affect the velocity update of particle swarm. The standard particle swarm optimization algorithm, damping particle swarm optimization algorithm and the improved particle swarm optimization algorithm of this paper are tested with typical multi-peak function. The experimental results show that the improved algorithm is accurate in searching. The convergence time and stability are better than the standard PSO algorithm and the damped PSO algorithm. The convergence rate is improved while the local extremum is removed. (2) the finite element method is used to discretize the differential equations when the unstructured triangular element is used. The forward modeling matrix is formed, the wavenumber domain results are obtained, and the forward modeling is completed by the inverse Fourier transform to the spatial domain. The forward FEM numerical simulation program is compiled in Matlab. After model verification and analysis, it is proved that FEM is a good forward modeling method. (3) the theory of two-dimensional ERT inversion is expounded, and the processing method of linear renunciation of higher term is compared. The minimization objective function of nonlinear inversion is derived. The DC resistivity model, the time-domain induced polarization model and the frequency-domain induced polarization complex resistivity model are designed. Then the simulation inversion is carried out on the three kinds of forward modeling data with certain noise, and its performance is compared with the standard PSO algorithm and Occam algorithm. The model experiment shows that the method is not easy to be trapped in local optimum. It has good numerical stability, fast convergence speed and high performance.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.322
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