基于正交最小二乘的位场数据稀疏反演  

Sparse inversion of potential field data based on Orthogonal Least Squares(OLS)

作　　者：叶丽霞 张玉洁[1,2] 罗重阳 YE LiXia;ZHANG YuJie;LUO ChongYang(School of Mathematics and Physics,China University of Geosciences(Wuhan),Wuhan 430074,China;Key Laboratory of Geological Exploration and Evaluation Ministry of Education,Wuhan 430074,China)

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

出　　处：《地球物理学进展》2023年第6期2611-2621,共11页Progress in Geophysics

基　　金：地质探测与评估教育部重点实验室主任基金和中央高校基本科研业务费(GLAB2020ZR13)联合资助。

摘　　要：传统的重磁反演方法大多数是基于观测数据和模型参数约束的L2范数极小化,然后利用共轭梯度法(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,提出了基于正交最小二乘法(Orthogonal Least Squares, OLS)的物性稀疏反演方法.首先,位场数据可以由核矩阵的列向量线性表出,且物性参数是稀疏的,然后利用OLS算法,将核矩阵的列向量作为一个个原子,根据残差最小选择最相关的列作为选择的原子加以匹配,然后进行迭代求解.模拟数据和真实数据实验表明,本文提出的OLS方法不仅可以快速反演场源的稀疏分布,而且可以获得分辨率高、具有尖锐边界的反演结果,在实际应用中具有较好的效果.Traditional gravity and magnetic inversion methods are mostly based on the minimization of the norm constrained by the observation data and model parameters,and use Conjugate Gradient(CG)to perform physical property inversion,and obtain non-sparse solutions with lower resolution.Taking into account 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 physical properties based on Orthogonal Least Squares(OLS)sparse inversion method.First,the potential field data can be expressed linearly by the column vector of the kernel matrix,and the physical property parameters are sparse,and then using the OLS algorithm,the column vector of the kernel matrix is used as an atom,and the most relevant column is selected according to the minimum residual.The atoms are matched and solved iteratively.Simulation data and real data experiments show that the OLS method proposed in this paper can not only quickly invert the sparse distribution of field sources,but also obtain high-resolution inversion results with sharp boundaries,and has a good effect in practical applications.

关 键 词：压缩感知 正交最小二乘 稀疏反演 位场数据 

分 类 号：P631[天文地球—地质矿产勘探]