基于压缩感知的地震数据同时规则化和插值方法  

Seismic data regularization and interpolation approach based on compressive sensing principle

作　　者：董烈乾[1] 周恒[1] 桑运云 曾庆芹[1] 范红光 田永庆 DONG LieQian;ZHOU Heng;SANG YunYun;ZENG QingQin;FAN HongGuang;TIAN YongQing(Bureau of Geophysical Prospecting INC.,China National Petroleum Corporation(BGP),Zhuozhou 072750,China)

机构地区：[1]中国石油集团东方地球物理勘探有限责任公司,涿州072750

出　　处：《地球物理学进展》2025年第1期276-284,共9页Progress in Geophysics

摘　　要：地震数据通常期望被放置在规则网格点上进行采集.但实际采集中会由于障碍物等因素的影响,导致采样点偏离预设网格点位置或者造成采样点的缺失.为了同时实现地震数据的偏点规则化与缺失数据的重构,本文基于压缩感知理论提出了一种新的数学模型,该模型基于融合采样算子,三维曲波变换以及快速迭代阈值算法,实现了对偏点数据和缺失数据的同时规则化和重构处理.融合采样算子结合了规则网格点的二值采样算子与纠正偏点的二维重心拉格朗日算子;快速迭代阈值算法可有效解决地震数据缺失反问题并提高算法的计算效率.应用该技术对模型和实际地震数据进行测试,验证了该方法在改善地震数据品质的优越性.Seismic samples are typically designed on a perfect Cartesian grid.However,field constructions can disrupt the sampling geometry,resulting in the samples missing or off-the-grid.Our research goals are to simultaneously regularize off-the-grid samples and interpolate missing data for 3D seismic data under the framework of compressive sensing,which combines a 3D curvelet transform,a fast iterative threshold algorithm,and a merging sampling operator.The new sampling operator combines a binary mask with a barycentric Lagrangian operator for simultaneous interpolation and regularization.The fast iterative threshold algorithm is helpful to improve the interpolation accuracy and efficiency while solving the ill-posed problem.Finally,we demonstrate the effectiveness of the proposed approach by simulated and field datasets.

关 键 词：压缩感知 融合采样 重心拉格朗日 快速迭代阈值 数据规则化和插值 

分 类 号：P631[天文地球—地质矿产勘探]