基于非均匀快速傅里叶变换的最小二乘反演地震数据重建

Reconstruction of seismic data with least squares inversion based on nonuniform fast Fourier transform

不规则采样地震数据的重建是地震数据分析处理的重要问题.本文给出了一种基于非均匀快速傅里叶变换的最小二乘反演地震数据重建的方法,在最小二乘反演插值方程中,引入正则化功率谱约束项,通过非均匀快速傅里叶变换和修改周期图的方式,自适应迭代修改约束项,使待插值数据的频谱越来越接近真实的频谱,采用预条件共轭梯度法迭代求解,保证了解的稳定性和收敛速度.理论模型和实际地震数据插值试验证明了本文方法能够去除空间假频,速度快、插值效果好,具有实用价值.

Reconstruction of uneven seismic data is a crucial step of the analyzing and processing of the data. In this paper, a least squares inversion based on nonuniform fast Fourier transform is proposed, which can reconstruct both uneven and alias seismic data. The algorithm of nonuniform fast Fourier transform is used to do Fourier transform of uneven data. An adaptive DFT weighted norm regularization constraint is used during the reconstruction. The inverse problem is solved by the preconditioning conjugate gradient method, which makes the solutions stable and convergence quick. Experimental results on theoretical model and raw uneven seismic data show that the proposed method is fast, efficient and applicable.