基于贪婪—快速迭代收缩阈值的Radon变换及其在多次波压制中的应用

多次波的存在严重影响了地震资料的解释精度，有效压制多次波是地震资料处理过程中的重要环节。目前，抛物线Radon变换是压制多次波的常用方法。针对抛物线Radon变换这一逆问题的求解，目前行业内应用最多的是迭代收缩阈值算法(Iterative Shrinkage Thresholding Algorithm，ISTA)。该方法在计算精度和计算效率方面优势明显，但对庞大的地震数据而言，处理效率仍需进一步提高。为提高抛物线Radon变换收敛速率，将贪婪的快速迭代收缩阈值算法(Greedy Fast ISTA，Greedy FISTA) 引入到Radon变换压制多次波的逆问题求解中，构建了一种基于贪婪的快速迭代收缩的混合域快速稀疏时不变Radon变换。与ISTA相比，该方法将前两次的迭代结果加权求和作为当前的迭代起点，通过引入重启条件和收敛条件，使迭代过程中振荡周期减小、计算速度提高。合成数据和实际数据的多次波压制实验表明，相比于ISTA与快速迭代收缩阈值算法(FISTA)，该算法收敛效率有很大提高、精度也略有提升。

Radon transform based on greedy fast iterative shrinkage threshold and its application in multiple suppression

In seismic exploration, multiples seriously affect the interpretation accuracy of seismic data, and effective suppression of multiples is important in seismic data processing. The parabolic Radon transform is a common method to suppress multiples. The iterative shrinkage thresholding algorithm (ISTA) is the most widely used method in the industry to obtain the solution to the inverse problem of the parabolic Radon transform. It has excellent computational accuracy and efficiency, but for massive seismic data, the processing efficiency still needs to be improved. To improve the convergence rate of the parabolic Radon transform, this study proposes greedy fast ISTA (Greedy FISTA) to processing of inversion problem for Radom transform suppressing multiple, and constract an accelerated sparse time-invariant Randon transform in the mixed frequency-time domain based on fast interative shrinkage-thesholding algorithn(SRTGFIS). Unlike ISTA, Greedy FISTA takes the weighted sum of the results of the previous two iterations as the iteration starting point, and it introduces restart conditions and convergence conditions to reduce the oscillation period in the iteration process and accelerate the calculation. The multiple suppression experiments with synthetic and real data show that compared with ISTA and FISTA, the proposed algorithm has a great improvement in convergence efficiency and a slight improvement in convergence accuracy.