基于基追踪的位场数据稀疏反演  

Sparse Inversion of Potential Field Data Based on Basis Pursuit

作　　者：叶丽霞 张玉洁[1] Ye Lixia;Zhang Yujie(School of Mathematics and Physics, China University of Geosciences, Wuhan Hubei 430074, China;Key Laboratory of Geological Exploration and Evaluation Ministry of Education, China University of Geosciences, Wuhan Hubei 430074, China)

机构地区：[1]中国地质大学数学与物理学院,湖北武汉430074 [2]中国地质大学地质探测与评估教育部重点实验室,湖北武汉430074

出　　处：《工程地球物理学报》2021年第4期462-470,共9页Chinese Journal of Engineering Geophysics

基　　金：地质探测与评估教育部重点实验室主任基金(编号:GLAB2020ZR13)。

摘　　要：传统的重磁反演方法大多是基于观测数据和模型参数约束的L2范数极小化,利用共轭梯度(Conjugate Gradient,CG)进行物性反演,得到的是分辨率较低的非稀疏解。考虑到大多数地质的情况下,物性分布本身具有稀疏性,本文用压缩感知(Compressed Sensing,CS)技术代替传统的反演方法,提出了基于基追踪的位场数据稀疏反演方法。在反演过程中加入物性上下界约束构建目标函数,然后转化为优化问题,用对数障碍规划算法进行求解。二维模拟数据和真实数据实验表明,本次研究提出的基于对数障碍规划(Logarithmic Barrier Planning,LBP)算法的基追踪反演方法可以获得分辨率高、具有尖锐边界的反演结果,在实际应用中能够取得较好的结果。Traditional gravity and magnetic inversion methods are mostly based on the L2 norm minimization of observation data and model parameter constraints,using conjugate gradient(CG)to perform physical property inversion,and obtain a non-sparse solution with lower resolution.Considering the sparseness of physical property distribution in most geological situations,this paper uses compressed sensing(CS)technology to replace the traditional inversion method,and proposes a sparse inversion method for potential field data based on basis tracking.In the inversion process,the upper and lower bound constraints of physical properties are added to construct the objective function,which is then transformed into an optimization problem,and solved by the logarithmic obstacle programming algorithm.The two-dimensional simulation data and real data experiments show that the basis tracking inversion method based on logarithmic obstacle planning algorithm proposed in this paper can obtain inversion results with high resolution and sharp boundaries,and achieve good results in practical applications.

关 键 词：压缩感知 基追踪 稀疏反演 位场数据 对数障碍规划 

分 类 号：P631[天文地球—地质矿产勘探]