大地电磁数据非线性反演方法研究
发布时间：2018-11-20 21:16
【摘要】：大地电磁法作为一种重要的地球物理勘探手段,现已被广泛应用于研究地壳和上地幔地质构造以及深部矿产勘探。作为连接地球物理观测与解释的桥梁,反演方法研究一直都是学者关注的热点。本文首先将智能优化算法——果蝇优化算法引入到大地电磁数据反演,避免线性化迭代方法需要计算偏导数矩阵、对初始模型依赖等缺点。果蝇优化算法具有原理简单、控制参数少,容易程序实现等优点,通过对标准果蝇优化算法的分析,发现其在处理高维、多峰的目标函数时存在收敛缓慢、易陷入局部极值的情况,为此对其进行了改进,加入了差分进化算法的交叉操作和变异操作,增加了果蝇的种群多样性,提高全局优化能力,同时利用变异尺度因子,将果蝇的固定搜索步长方式改为逐步递减的搜索步长,以达到平衡算法全局优化和局部优化的目的。利用多个测试函数对改进的果蝇优化算法进行测试,并与标准果蝇算法以及差分进化算法结果进行了比较,结果表明改进的果蝇优化算法具有寻优快,优化精度高,不易早熟收敛的优点。在此基础上,结合大地电磁反演理论,利用改进果蝇优化算法对大地电磁一维模型进行反演,并利用不同噪声水平的模型对算法进行了测试,结果表明改进的果蝇优化算法能有效的处理大地电磁数据,反演结果精度高,算法鲁棒性好。本文还对基于贝叶斯理论的统计反演方法进行了研究,对非线性贝叶斯反演的基本原理、目前常见的非线性数值采样方法进行了归纳和总结。贝叶斯反演理论将反演模型参数看成是随机变量,反演的结果是统计意义上的后验概率分布,能直观的对结果进行评价。基于变维反演的思想,利用可逆跳跃马尔科夫链蒙特卡洛方法对一维大地电磁数据进行反演。贝叶斯反演结果基于大量样本,因此采样速度的快慢对算法具有重要影响,为了加快算法收敛速度,利用改进的并行回火技术,将副本之间的相邻交换方式替换为随机交换方式,使得算法能够快速对整个空间进行采样,获得解的大量样本。结果表明变维反演能够有效的对层状介质进行自动分层,有效减少人为因素的干扰,并行回火技术能够加速采样过程收敛。
[Abstract]:As an important geophysical exploration method, magnetotelluric method has been widely used to study the geological structure of crust and upper mantle, as well as deep mineral exploration. As a bridge between geophysical observation and interpretation, the research of inversion method has always been a hot topic. In this paper, an intelligent optimization algorithm, Drosophila optimization algorithm, is introduced to magnetotelluric data inversion, which avoids the disadvantages of computing partial derivative matrix and dependence on initial model in order to avoid linearization iteration. Drosophila optimization algorithm has the advantages of simple principle, few control parameters and easy programming. Through the analysis of the standard Drosophila optimization algorithm, it is found that the algorithm has slow convergence in dealing with high-dimensional and multi-peak objective functions. It is easy to fall into local extremum, so it is improved by adding the crossover operation and mutation operation of differential evolution algorithm to increase the diversity of Drosophila population and improve the ability of global optimization. At the same time, the variation scale factor is used. In order to achieve the goal of global and local optimization, the fixed search step of Drosophila was changed to a progressively decreasing search step. The improved Drosophila optimization algorithm is tested by several test functions and compared with the results of the standard Drosophila algorithm and the differential evolutionary algorithm. The results show that the improved algorithm has the advantages of fast searching and high precision. The advantage of not being easy to converge prematurely. On this basis, combined with the magnetotelluric inversion theory, the improved Drosophila optimization algorithm is used to inverse the magnetotelluric one-dimensional model, and the algorithm is tested by the model with different noise levels. The results show that the improved algorithm can deal with magnetotelluric data effectively, and the inversion results are accurate and robust. The statistical inversion method based on Bayesian theory is also studied in this paper. The basic principle of nonlinear Bayesian inversion and the common nonlinear numerical sampling methods are summarized and summarized. Bayesian inversion theory regards the parameters of the inversion model as random variables, and the result of inversion is a statistical posteriori probability distribution, which can directly evaluate the results. Based on the idea of variable dimensional inversion, the reversible jump Markov chain Monte Carlo method is used to inverse the one-dimensional magnetotelluric data. The result of Bayesian inversion is based on a large number of samples, so the speed of sampling has an important effect on the algorithm. In order to speed up the convergence of the algorithm, an improved parallel tempering technique is used. By replacing the adjacent exchange between replicas with random switching, the algorithm can quickly sample the whole space and obtain a large number of samples of the solution. The results show that the variable dimension inversion can effectively delaminate the layered media automatically and reduce the interference of human factors effectively. The parallel tempering technique can accelerate the convergence of the sampling process.
【学位授予单位】：中国地质大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：P631.325
[Abstract]:As an important geophysical exploration method, magnetotelluric method has been widely used to study the geological structure of crust and upper mantle, as well as deep mineral exploration. As a bridge between geophysical observation and interpretation, the research of inversion method has always been a hot topic. In this paper, an intelligent optimization algorithm, Drosophila optimization algorithm, is introduced to magnetotelluric data inversion, which avoids the disadvantages of computing partial derivative matrix and dependence on initial model in order to avoid linearization iteration. Drosophila optimization algorithm has the advantages of simple principle, few control parameters and easy programming. Through the analysis of the standard Drosophila optimization algorithm, it is found that the algorithm has slow convergence in dealing with high-dimensional and multi-peak objective functions. It is easy to fall into local extremum, so it is improved by adding the crossover operation and mutation operation of differential evolution algorithm to increase the diversity of Drosophila population and improve the ability of global optimization. At the same time, the variation scale factor is used. In order to achieve the goal of global and local optimization, the fixed search step of Drosophila was changed to a progressively decreasing search step. The improved Drosophila optimization algorithm is tested by several test functions and compared with the results of the standard Drosophila algorithm and the differential evolutionary algorithm. The results show that the improved algorithm has the advantages of fast searching and high precision. The advantage of not being easy to converge prematurely. On this basis, combined with the magnetotelluric inversion theory, the improved Drosophila optimization algorithm is used to inverse the magnetotelluric one-dimensional model, and the algorithm is tested by the model with different noise levels. The results show that the improved algorithm can deal with magnetotelluric data effectively, and the inversion results are accurate and robust. The statistical inversion method based on Bayesian theory is also studied in this paper. The basic principle of nonlinear Bayesian inversion and the common nonlinear numerical sampling methods are summarized and summarized. Bayesian inversion theory regards the parameters of the inversion model as random variables, and the result of inversion is a statistical posteriori probability distribution, which can directly evaluate the results. Based on the idea of variable dimensional inversion, the reversible jump Markov chain Monte Carlo method is used to inverse the one-dimensional magnetotelluric data. The result of Bayesian inversion is based on a large number of samples, so the speed of sampling has an important effect on the algorithm. In order to speed up the convergence of the algorithm, an improved parallel tempering technique is used. By replacing the adjacent exchange between replicas with random switching, the algorithm can quickly sample the whole space and obtain a large number of samples of the solution. The results show that the variable dimension inversion can effectively delaminate the layered media automatically and reduce the interference of human factors effectively. The parallel tempering technique can accelerate the convergence of the sampling process.
【学位授予单位】：中国地质大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：P631.325
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