基于Shearlet变换的三维地震数据重建
3D seismic data reconstruction based on Shearlet transform
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摘要: 在地震勘探中,受采集成本或地形环境的限制,地震数据往往存在缺失,因此数据重建是地震数据预处理的关键步骤。本文基于压缩感知理论框架,对合成数据进行二维随机欠采样,将三维地震数据划分为一系列时间切片,随后引入Shearlet稀疏变换,结合凸集投影(POCS)算法逐次对每个时间切片进行数据重建,从而实现了基于Shearlet变换的三维地震数据时间域重建方法。数值试验和实测数据结果表明,相对于Curvelet变换的重建方法,本文所提出的重建方法的信噪比更高,计算速度更快,效果更好。Abstract: Seismic data collected in the field frequently suffer from missing values due to constraints of acquisition cost or terrain. Data reconstruction is a critical step in seismic data preprocessing. Based on the compressed sensing theoretical framework, this study subsampled synthesized data using the 2D random undersampling technique. Then, the 3D seismic data were divided into a series of time slices. By introducing the sparse Shearlet transform and using the convex set projection (POCS) algorithm, this study conducted sequential data reconstruction for various time slices. As a result, a Shearlet transform-based time-domain 3D seismic data reconstruction method was developed. Numerical experiments and measured results demonstrate that the proposed reconstruction method exhibits a higher signal-to-noise ratio, a higher computational speed, and better effects than a Curvelet transform-based approach.
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