基于压缩感知理论的地震数据重构方法研究

发布时间：2018-05-02 08:57

本文选题：压缩感知 + 稀疏　；参考：《吉林大学》2015年硕士论文

【摘要】：地震数据由于受到采集环境以及预处理等影响，往往会呈现不规则分布，这对地震数据的后期处理将产生不良影响。而基于压缩感知理论的重构方法能有效地恢复重构地震数据，提高分辨率。在传统的地震数据采集过程中，由于受到奈奎斯特采样定理的制约，地震数据的采集和存储需要更高的要求，这为地震勘探的发展带来了巨大的挑战。近些年发展起来的压缩感知（Compressive Sensing，CS）理论突破了奈奎斯特采样定理的限制。它表明，如果待处理的不完整数据本身是稀疏的，或者在某个变换域内是稀疏的，那么就有可能恢复重构出符合一定精度要求的完整数据。通常情况下，地震数据并不是稀疏的，但是可以找到一种稀疏变换域使其在该变换域内稀疏。傅里叶变换能将地震数据由时间-空间域转换到频率-波数域，它是一种比较有效的稀疏表示方法，为基于压缩感知理论的重构方法提供了理论前提条件。基于傅里叶变换的迭代阈值收缩算法是地震数据重构过程中比较常用的一种方法，但是传统的迭代阈值算法收敛速度较慢，降低了运算效率。本文基于压缩感知理论，引用了图像处理中的一种基于L1范数的迭代线性扩展阈值算法来解决地震数据重构问题。它不是直接通过最小化目标函数来估算重构数据，而是把这个过程参数化为一些基本阈值函数的线性组合，并通过最小化目标函数来求取线性加权系数，然后在迭代过程中更新该阈值函数。该算法的主要优势体现在每次只需要通过求解线性系数来解决这个优化问题。当基本的阈值函数满足一定的约束条件时，就能够保证这种算法的全局收敛性。同时，根据两步迭代阈值收缩算法能够加快收敛速度，本文也给出了基于两步迭代的线性阈值扩展算法的原理和流程，并将该算法与传统的迭代阈值算法进行了对比分析，，表明了该算法具有更快的收敛速度。理论模型和实际处理的结果表明，迭代线性扩展阈值算法不仅能有效地用于解决地震数据重构问题，并且拥有较好的抗噪能力，同时具备收敛速度较快的优点。
[Abstract]:Due to the influence of acquisition environment and preprocessing, seismic data often presents irregular distribution, which will have a negative impact on the post-processing of seismic data. The reconstruction method based on compression sensing theory can effectively restore reconstructed seismic data and improve resolution. In the process of traditional seismic data acquisition, because of the restriction of Nyquist sampling theorem, the acquisition and storage of seismic data need higher requirements, which brings great challenges to the development of seismic exploration. In recent years, compressed sensing theory has broken through the limitation of Nyquist sampling theorem. It shows that if the incomplete data to be processed is sparse itself or is sparse in a transform domain, it is possible to restore and reconstruct the complete data that meets the requirements of certain precision. In general, seismic data is not sparse, but a sparse transform domain can be found to make it sparse in that domain. Fourier transform can transform seismic data from time-space domain to frequency-wavenumber domain. It is an effective sparse representation method and provides a theoretical prerequisite for reconstruction method based on compression perception theory. Iterative threshold shrinkage algorithm based on Fourier transform is a commonly used method in seismic data reconstruction, but the traditional iterative threshold algorithm converges slowly and reduces the operation efficiency. Based on the theory of compression perception, an iterative linear extended threshold algorithm based on L1 norm in image processing is introduced to solve the problem of seismic data reconstruction. Instead of directly estimating the reconstructed data by minimizing the objective function, it converts the process parameter into a linear combination of some basic threshold functions, and obtains the linear weighting coefficient by minimizing the objective function. The threshold function is then updated during the iteration. The main advantage of the algorithm is that it only needs to solve the optimization problem by solving the linear coefficients at a time. The global convergence of the algorithm can be guaranteed when the basic threshold function satisfies certain constraints. At the same time, according to the two-step iterative threshold shrinkage algorithm can accelerate the convergence rate, this paper also gives the principle and flow of the linear threshold expansion algorithm based on two-step iteration, and compares the algorithm with the traditional iterative threshold algorithm. It shows that the algorithm has faster convergence speed. The theoretical model and practical processing results show that the iterative linear extended threshold algorithm can not only effectively solve the seismic data reconstruction problem, but also has a good anti-noise ability, and has the advantage of faster convergence speed.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.44

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