基于四元数矩阵分解算法的多分量地震数据矢量重建研究  

Multicomponent seismic data reconstruction via quaternion matrix factorization algorithm

作　　者：孙文博 王艳冬 黄小刚 张洪亮 高建军[3] 王小六 SUN WenBo;WANG YanDong;HUANG XiaoGang;ZHANG HongLiang;GAO JianJun;WANG XiaoLiu(CNOOC Research Institute Co.,Ltd.,Beijing 100028,China;National Engineering ResearchCenter of Offshore Oil and Gas Exploration,Beijing 100028,China;China University of Geosciences(Beijing),School of Geophysics and Information Technology,Beijing 100083,China)

机构地区：[1]中海油研究总院有限责任公司,北京100028 [2]海洋油气勘探国家工程研究中心,北京100028 [3]中国地质大学(北京)地球物理与信息技术学院,北京100083

出　　处：《地球物理学报》2024年第12期4759-4772,共14页Chinese Journal of Geophysics

基　　金：中国海洋石油集团有限公司关键核心技术攻关项目(CNOOC-KJ GJHXJSGG YF 2022-01)资助。

摘　　要：与单分量纯纵波勘探相似,多波多分量地震勘探在数据采集时也会遭遇地震道缺失和不规则采样问题,也需要进行数据规则化重建.然而,对多分量地震数据重建而言,目前普遍采用单分量重建方法逐个分量进行重建,这种标量化做法忽略了各分量之间的非线性关系,破坏了地震波场的矢量结构特征.本文将四元数理论与矩阵分解降秩算法相结合,提出一种基于四元数矩阵分解降秩算法的多分量地震数据矢量规则化重建方法,并将其应用于三分量三维不规则缺失地震道的矢量联合重建.与现有单分量重建方法相比,本文方法能够实现三分量数据的联合重建,且在重建时能有效保持各分量间的非线性正交结构特征,保护波场的矢量特性,此外,该方法是一种非SVD分解类算法,计算成本低.最后,模型数据和实际资料验证了本文方法的有效性和先进性.Similar to the traditional single-component P wave seismic exploration and acquisition,multi-component seismic data acquisition also encounters missing traces and the irregular sampling problems,and also need to do seismic data regularization.However,for the reconstruction of multi-component seismic data,the component-wise reconstruction methods are currently commonly used,where each component is treated independently.These scalar approaches ignore the nonlinear relationship between the components and destroy the vector properties of the seismic wave field.This paper combines quaternion theory with matrix factorization algorithm and proposes a method for multi-component seismic data vector reconstruction based on quaternion matrix factorization algorithm,and applies it to the vector joint reconstruction of 3C-3D irregular missing data.Compared with the existing component-wise reconstruction methods,this proposed method can achieve joint reconstruction of 3C data,and effectively maintain the nonlinear orthogonal structure properties between different components during reconstruction and protect the vector characteristics of the wave field.Moreover,this method is also an SVD-free algorithm with low computational cost.Finally,synthetic data and field data experiments demonstrate the effectiveness and advancement of the presented method.

关 键 词：多分量地震数据 地震数据矢量重建 四元数矩阵分解 低秩矩阵 

分 类 号：P631[天文地球—地质矿产勘探]