基于降秩和稀疏联合约束的地震数据同时重建和去噪

Simultaneous reconstruction and denoising of seismic data based on rank reduction and sparsity constraints

野外地震数据包含各种随机噪声干扰,且存在不规则道缺失现象,为了不影响后续资料处理,需要对其进行同时重建和去噪。目前大部分同时重建和去噪方法都是基于单一稀疏约束和降秩约束,尽管稀疏约束具有高效性优点,但对各种数据缺乏适应性,而降秩约束可以自适应不同数据,但计算成本较高。为了充分利用不同约束条件的优势,本文提出一种基于联合约束的地震数据同时重建和去噪方法:选用基于傅立叶变换的凸集投影算法(POCS)作为稀疏约束,阻尼多道奇异谱分析(DMSSA)作为降秩约束,在此过程中,还需使用截断奇异值分解(TSVD)算法和指数阈值公式。理论和实际数据的处理结果表明,本方法在联合约束条件下,能够从时间和空间上考虑地震资料的相关性并利用起来,比单一约束方法能在更少的迭代次数下取得更高的信噪比。

Field seismic data contain various random noise and irregular channel missing.Their simultaneous reconstruction and denoising is necessary for subsequent data processing.Currently,most simultaneous reconstruction and denoising methods only use a single sparsity or rank reduction constraint.The sparsity constraint exhibits high efficiency but lacks adaptability to various data.In contrast,the rank reduction constraint can adapt to various data but shows a high computational cost.To take a full advantage of different constraints,this study proposed a method for simultaneous reconstruction and denoising of seismic data based on combined constraints.This method regards projection onto convex sets(POCS)based on Fourier transform as the sparsity constraint,and damped multichannel singular spectrum analysis(DMSSA)as the rank reduction constraint.It employs the truncated singular value decomposition(TSVD)algorithm and the exponential threshold equation,fully utilizing the high computational efficiency of the sparsity constraint and the strong adaptability of the rank reduction constraint.As indicated by the processing results of theoretical and field data,this method based on combined constraints can consider and utilize the spatio-temporal correlations of seismic data,achieving higher signal-to-noise ratios via fewer iterations compared to methods based on a single constraint.