多维地震信号正则化处理方法研究

发布时间：2018-04-15 23:38

本文选题：地震信号恢复 + 张量奇异值分解　；参考：《电子科技大学》2017年硕士论文

【摘要】：随着煤层气、页岩气等非常规能源勘探开发的不断深入,地震勘探对数据的规则性和完整性提出了更高要求。然而由于障碍物、禁采区、采集成本等因素的影响,导致地震数据不完整、不规则;常规的处理方法往往过于粗糙,难以满足实际生产需要。根据地震数据的固有特性(如稀疏性、低秩性),采取更加有效的算法进行地震数据重建,已经成为当前研究的热点。多维地震信号恢复就是根据地震数据的特点加入正则化约束,从而实现地震数据的重构。目前地震信号处理中加入的约束主要有核范数正则化和字典学习正则化稀疏表示,其中大多数求解都是针对于二维地震数据,并未有效利用多维地震信号间的信息,结果恢复的精度不高,重构不出大量缺失的数据;同样常用的张量分解方法没有很好利用多维地震数据间的冗余性。本文针对地震数据恢复中存在的问题进行研究,采用新的张量分解方法进行处理,具体工作概括如下:1.针对矩阵奇异值分解中恢复不出规则缺失、压制噪声不理想的情况,本文提出了一种Hankel张量核范数正则化的地震信号恢复方法。该方法通过一种新的张量分解方法将Hankel矩阵和张量核范数有效的结合起来,构建新的目标函数;通过交替方向乘子法求解各个变量,同时引入随机张量奇异值分解方法缓解了Hankel矩阵带来的时间复杂度过高的问题,采用阻尼截断的方法来降低了秩选取所引起的误差。该方法能够有效重构缺失地震数据并压制随机噪声。2.针对矩阵字典学习中不容易恢复整道地震数据缺失的情况,本文提出一种张量字典学习正则化稀疏表示处理方法。该方法将一种新的张量乘积方法应用于张量字典学习过程中,构建新的目标函数;通过交替迭代算法求解稀疏系数,分别在时域和频域求解各自的变量;通过拉格朗日对偶的方法训练张量字典,提高了计算速度;最后迭代更新张量字典和张量稀疏系数,实现缺失地震信号的重构。
[Abstract]:With the further exploration and development of unconventional energy sources such as coalbed methane, shale gas, seismic exploration has put forward higher requirements for the regularity and integrity of data.However, due to the influence of obstacles, no mining areas, acquisition cost and other factors, seismic data are incomplete and irregular, and the conventional processing methods are often too rough to meet the actual production needs.According to the inherent characteristics of seismic data, such as sparsity and low rank, a more effective algorithm for seismic data reconstruction has become the focus of current research.Multi-dimensional seismic signal restoration is to add regularization constraints according to the characteristics of seismic data, so as to achieve seismic data reconstruction.At present, the constraints in seismic signal processing are mainly kernel norm regularization and dictionary learning regularization sparse representation. Most of the solutions are aimed at two-dimensional seismic data, and the information between multidimensional seismic signals is not used effectively.The result is that the precision of restoration is not high, and the missing data can not be reconstructed, and Zhang Liang's decomposition method, which is also commonly used, does not make good use of the redundancy between multidimensional seismic data.In this paper, the problems existing in seismic data recovery are studied, and the new Zhang Liang decomposition method is used to deal with them. The concrete work is summarized as follows: 1.In this paper, a method of seismic signal recovery based on the regularization of Hankel Zhang Liang kernel norm is proposed to solve the problem that the rule of restoration is not missing and the suppression noise is not ideal in the singular value decomposition of matrix.In this method, a new objective function is constructed by combining the Hankel matrix with Zhang Liang kernel norm effectively by a new Zhang Liang decomposition method, and each variable is solved by alternating direction multiplier method.At the same time, the stochastic Zhang Liang singular value decomposition method is introduced to alleviate the high time complexity caused by the Hankel matrix, and the damping truncation method is used to reduce the error caused by rank selection.This method can effectively reconstruct missing seismic data and suppress random noise.In view of the fact that it is not easy to recover the missing seismic data in matrix dictionary learning, this paper presents a new method of learning regular sparse representation by Zhang Liang dictionary.In this method, a new Zhang Liang product method is applied to the learning process of Zhang Liang dictionary, a new objective function is constructed, the sparse coefficients are solved by alternating iteration algorithm, and their variables are solved in time domain and frequency domain, respectively.Zhang Liang dictionary is trained by Lagrangian duality method, and the calculation speed is improved. At last, we iteratively update Zhang Liang dictionary and Zhang Liang sparse coefficient to realize the reconstruction of missing seismic signal.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.4

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