高密度电阻率正则化反演及应用研究
发布时间：2018-07-29 21:06
【摘要】：高密度电阻率法是一种重要的浅层地球物理方法,其应用十分广泛,特别是在水文、工程、环境地质调查等方面的应用越来越深入。为了提高精度和效率,并使其取得更好的应用效果,高效的电阻率反演技术是必不可少的。因此,有必要对电阻率反演技术进行更多的研究和讨论。本文采用有限单元法实现了2.5D高密度电阻率正演研究,并基于Tikhonov正则化反演思想构建反演目标函数,实现了不同反演最优化方法和不同稳定因子的2.5D高密度电阻率反演研究。首先,从2.5D高密度电阻率满足的微分方程及边界条件出发,推导了关于电位的变分问题,采用三角单元网格剖分技术,推导了线性插值单元刚度矩阵的表达式,同时对刚度矩阵采用高效的变宽带存储方式及结合线性方程组的直接求解技术,最终实现了2.5D高密度电阻率的正演计算。通过设置水平层状介质及垂直接触带的模型验证了算法的正确性。其次,针对高密度电阻率反演问题,本文构建了高密度电阻率反演正则化目标函数,采用了电极互换原理实现了偏导数矩阵的快速计算,对不同反演最优化方法的收敛性进行研究,详细分析了反演结果。研究了不同的稳定因子并进行了大量试算,详细分析了稳定因子对反演结果的影响及采用改进的L-curve正则化因子自动选择算法等技术提高了反演解的稳定性。通过研究最优化算法发现,共轭梯度法反演效果稳定,收敛速度适中,高斯牛顿法反演效果理想,收敛速度快,拟牛顿法与高斯牛顿法收敛速度相当,最速下降法效果最差。稳定因子的主要功能是对模型解的空间进行限制,以减少多解性,求得稳定解。通过对稳定因子的研究可知,在高斯牛顿法的反演中,最小范数稳定因子和最大平滑稳定因子反演得到的异常模型边界是光滑渐变的;而最小梯度支持稳定因子具有更好的识别陡变异常体边界的能力,有利于实现陡变边界反演。
[Abstract]:High density resistivity method is an important shallow geophysical method, and its application is very extensive, especially in hydrology, engineering, environmental geological survey and so on. In order to improve the accuracy and efficiency, and achieve better application effect, high efficiency resistivity inversion technology is essential. Therefore, it is necessary to do more research and discussion on resistivity inversion technology. In this paper, the forward modeling of 2.5D high density resistivity is realized by finite element method, and the inversion objective function is constructed based on the idea of Tikhonov regularization inversion, and the 2.5D inversion of high density resistivity with different inversion optimization methods and different stability factors is realized. Firstly, based on the differential equation and boundary condition of 2.5D high density resistivity, the variational problem of potential is derived. The expression of linear interpolation element stiffness matrix is derived by using triangular element mesh generation technique. At the same time, the forward calculation of 2.5D high density resistivity is realized by using the efficient variable wideband storage method and the direct solution technique of linear equations for stiffness matrix. The correctness of the algorithm is verified by setting the model of horizontal layered medium and vertical contact band. Secondly, in order to solve the problem of high density resistivity inversion, the regularization objective function of high density resistivity inversion is constructed, and the fast calculation of partial derivative matrix is realized by using the principle of electrode exchange. The convergence of different inversion optimization methods is studied and the inversion results are analyzed in detail. The different stability factors are studied and a large number of experiments are carried out. The influence of the stability factors on the inversion results is analyzed in detail, and the stability of the inversion solution is improved by using the improved L-curve regularization factor automatic selection algorithm. By studying the optimization algorithm, it is found that the inversion effect of conjugate gradient method is stable, the convergence rate is moderate, the inversion effect of Gao Si Newton method is ideal and the convergence rate is fast, the convergence speed of quasi-Newton method is comparable to that of Gao Si Newton method, and the effect of steepest descent method is the worst. The main function of the stability factor is to limit the space of the model solution in order to reduce the multiplicity and obtain the stable solution. Through the study of the stability factor, we can know that in the inversion of Gao Si Newton method, the boundary of the abnormal model obtained by the inversion of the minimum norm stability factor and the maximum smooth stability factor is smooth and gradual. The minimum gradient support stability factor has a better ability to identify the boundary of the steeply variable anomaly, which is helpful for the inversion of the steeply variable boundary.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.322
本文编号：2154020
[Abstract]:High density resistivity method is an important shallow geophysical method, and its application is very extensive, especially in hydrology, engineering, environmental geological survey and so on. In order to improve the accuracy and efficiency, and achieve better application effect, high efficiency resistivity inversion technology is essential. Therefore, it is necessary to do more research and discussion on resistivity inversion technology. In this paper, the forward modeling of 2.5D high density resistivity is realized by finite element method, and the inversion objective function is constructed based on the idea of Tikhonov regularization inversion, and the 2.5D inversion of high density resistivity with different inversion optimization methods and different stability factors is realized. Firstly, based on the differential equation and boundary condition of 2.5D high density resistivity, the variational problem of potential is derived. The expression of linear interpolation element stiffness matrix is derived by using triangular element mesh generation technique. At the same time, the forward calculation of 2.5D high density resistivity is realized by using the efficient variable wideband storage method and the direct solution technique of linear equations for stiffness matrix. The correctness of the algorithm is verified by setting the model of horizontal layered medium and vertical contact band. Secondly, in order to solve the problem of high density resistivity inversion, the regularization objective function of high density resistivity inversion is constructed, and the fast calculation of partial derivative matrix is realized by using the principle of electrode exchange. The convergence of different inversion optimization methods is studied and the inversion results are analyzed in detail. The different stability factors are studied and a large number of experiments are carried out. The influence of the stability factors on the inversion results is analyzed in detail, and the stability of the inversion solution is improved by using the improved L-curve regularization factor automatic selection algorithm. By studying the optimization algorithm, it is found that the inversion effect of conjugate gradient method is stable, the convergence rate is moderate, the inversion effect of Gao Si Newton method is ideal and the convergence rate is fast, the convergence speed of quasi-Newton method is comparable to that of Gao Si Newton method, and the effect of steepest descent method is the worst. The main function of the stability factor is to limit the space of the model solution in order to reduce the multiplicity and obtain the stable solution. Through the study of the stability factor, we can know that in the inversion of Gao Si Newton method, the boundary of the abnormal model obtained by the inversion of the minimum norm stability factor and the maximum smooth stability factor is smooth and gradual. The minimum gradient support stability factor has a better ability to identify the boundary of the steeply variable anomaly, which is helpful for the inversion of the steeply variable boundary.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.322
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