含随机噪声地震数据重建的稀疏反演模型与算法  

Sparse Inversion Models and Methods for Noisy Seismic Data Interpolation

作　　者：朱跃飞 曹静杰 ZHU Yue-fei;CAO Jing-jie(Hebei Key Laboratory of Strategic Critical Mineral Resources,Shijiazhuang 050031,China;Hebei GEO University,Shijiazhuang 050031,China)

机构地区：[1]河北省战略性关键矿产资源重点实验室,河北石家庄050031 [2]河北地质大学地球科学学院,河北石家庄050031

出　　处：《河北地质大学学报》2021年第1期49-57,共9页Journal of Hebei Geo University

基　　金：国家自然科学基金项目(41974166,41674114)资助。

摘　　要：基于稀疏反演思想的凸集投影法是一种常用的重建方法,但是没有阐明求解的反演模型,因此对于其不能求解含噪声数据重建的原因没有深入分析。通过对凸集投影法进行数学算法推导,阐明了其不能解决含噪声数据去噪问题的原因。反演模型的建立及正则参数的选择是决定反演问题成败的关键,文章归纳了基于稀疏变换和矩阵完备理论的地震数据重建模型和算法,分析了几种作为稀疏约束的算子,同时提供了几种正则参数的选择方法。数值试验表明,通过迭代阈值法求解含噪声数据重建问题能够实现含噪声数据的重建和去噪,此外正则参数的选择决定了数据重建和去噪的效果,当正则参数选择合适时才能获得可靠的重建和去噪结果。The convex set projection method based on the sparse inversion idea is a commonly used reconstruction method,but did not clarify the inversion model to be solved,so there is no in-depth analysis of the reason why it cannot solve the reconstruction of noisy data.This paper derives the mathematical algorithm of the convex set projection method and clarifies the reason why it cannot solve the problem of denoising data with noise.The establishment of the inversion model and the selection of regular parameters are the key of determining the success or failure of the inversion problem.The article summarizes seismic data reconstruction models and algorithms based on sparse transformation and matrix complete theory,analyzes several operators as sparse constraints,and provides several methods for selecting regular parameters.Numerical experiments show that the iterative threshold method to solve the noisy data reconstruction problem can achieve the reconstruction and denoising of noisy data.In addition,the choice of regular parameters determines the effect of data reconstruction and denoising.Only when the regular parameters are properly selected can a reliable reconstruction and denoising results be got.

关 键 词：重建 去噪 稀疏反演 算法 正则参数 

分 类 号：P631[天文地球—地质矿产勘探]