基于低秩Hankel矩阵分解的地震数据重建  

Reconstruction of Seismic Data based on Low-rank Hankel Matrix Decomposition

作　　者：秦思 田琳 肖兴明 QIN Si;TIAN Lin;XIAO Xing-ming(School of Electronic Engineering,Yili Normal University,Yining,Xinjiang,835000,China;School of Network Security and Information Technology,Yili Normal University,Yining,Xinjiang,835000,China)

机构地区：[1]伊犁师范大学电子工程学院,新疆伊宁835000 [2]伊犁师范大学网络安全与信息技术学院,新疆伊宁835000

出　　处：《新疆师范大学学报(自然科学版)》2025年第3期17-22,共6页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：新疆凝聚态相变与微结构实验室项目(XJDX912Z2413);伊犁师范大学基金资助项目(22XKZZ22);国家自然科学基金项目(61761043)。

摘　　要：物理和经济条件的限制及噪声污染使得地震信号数据缺失,这将影响地震资料的处理和解释,因此进行地震数据重建十分重要。本研究低秩和Hankel矩阵对随机缺失地震数据进行重建:采用快速的低秩Hankel矩阵分解方法在时域直接进行2D重建,将核范数项替换分解成两个矩阵之和,避免SVD计算,加快了计算速度。在求解时,采用交替方向乘子法交替迭代处理,进一步加快计算速度。合成数据和实际地震数据测试均验证了该方法的有效性。该方法在重建精度和信噪比方面相对于f-k域滤波重建方法具有优越性。Reconstruction of seismic data is necessary due to physical and economic constraints and noise contamination,which makes seismic signal data missing,which will affect the subsequent processing and interpretation of seismic data.The low-rank and Hankel matrices are combined to reconstruct the random missing seismic data:a fast low-rank Hankel matrix decomposition method is used to perform the 2D reconstruction directly in the time domain,which decomposes the nuclear norm term substitution into the sum of the two matrices,avoiding the SVD computation,and accelerating the computation speed.In the solution,the alternating direction multiplier method is used for alternating iterative processing to further speed up the computation.Both synthetic data and actual seismic data tests verify the effectiveness of the method.Moreover,the method is superior to the f-k domain filtered reconstruction method in terms of reconstruction accuracy and signal-to-noise ratio.

关 键 词：低秩 HANKEL矩阵 地震数据重建 交替方向乘子法 

分 类 号：P65[天文地球—地质学]