应用快速POCS算法的非均匀地震数据重建  

Reconstruction of non-uniformly sampled seismic data based on fast POCS algorithm

作　　者：董烈乾 张慕刚 汪长辉 安学勇 郭振兴 范红光 DONG Lieqian;ZHANG Mugang;WANG Changhui;AN Xueyong;GUO Zhenxing;FAN Hongguang(BGP Inc,CNPC,Zhuozhou,Hebei 072750,China)

机构地区：[1]东方地球物理公司,河北涿州072750

出　　处：《石油地球物理勘探》2023年第2期334-339,共6页Oil Geophysical Prospecting

基　　金：中国石油集团东方地球物理勘探有限责任公司重点研发项目“压缩感知地震勘探持续研究”(03-01-2021)资助。

摘　　要：凸集投影(Projection on Convex Sets,POCS)算法已经成功地应用于地震数据重建,灵活且简单。然而该算法要求重构数据必须是在规则网格上进行,由于障碍物等因素导致实际采集数据偏离预设网格点,重构效果不佳,且该算法的收敛速度仅为O(1/k),其中k为迭代次数。针对以上问题,首先构建了非均匀网格地震数据正演模型;然后从快速迭代收缩阈值算法(Fast Iterative Shrinkage Thresholding Algorithm,FISTA)出发,推导并提出了基于曲波变换的快速凸集投影算法(Fast POCS,FPOCS),该算法保留了迭代收缩阈值算法(ISTA)的计算简单性,具有全局收敛速度O(1/k^(2));是一种快速的地震数据重构方法;最后通过模拟和实际数据处理验证了本文方法的有效性。The projection on convex set(POCS)algorithm has been successfully applied to seismic data reconstruction,and it is flexible and simple.However,this algorithm must reconstruct data on a regular grid,and the actual collected data deviate from preset grid points due to obstacles and other factors,which results in poor reconstruction effects.Moreover,the convergence speed of the algorithm is only O(1/k).In order to solve these challenges,this paper builds a forward model of seismic data with non-uniform grids and derives a fast POCS(FPOCS)algorithm based on curvelet transform from the fast iterative shrinkage thresholding algorithm(FISTA).The FPOCS is a fast seismic data reconstruction method,which retains the computational simplicity of ite-rative shrinkage thresholding algorithm(ISTA)and has a global convergence speed of O(1/k^(2)).Finally,the paper demonstrates the effectiveness of the proposed method through simulation and actual data.

关 键 词：地震数据重构 快速凸集投影 快速迭代收缩阈值 曲波变换 

分 类 号：P631[天文地球—地质矿产勘探]