基于非均匀Fourier变换的地震数据重建方法研究

不规则采样地震数据会对地震数据的多道处理造成严重影响，将非均匀Fourier变换和贝叶斯参数反演方法相结合，对不规则空间带限地震数据进行反演重建.对每一个频率依据最小视速度确定出重建数据的带宽，然后从不规则地震数据中估计出重建数据的空间Fourier系数.将不规则地震数据重建视为信息重建的地球物理反演问题，运用贝叶斯参数反演理论来估计Fourier系数.在反演求解时，使用共轭梯度算法，以保证求解的稳定性，加快解的收敛速度.理论模型和实际资料处理验证了本方法的有效性和实用性.

Study on reconstruction of seismic data based on nonuniform Fourier transform

The uneven seismic data impose serious impact on multi-trace processing algorithms, leading to suboptimal processing and imaging results. Reconstruction of uneven seismic data can be considered as a geophysical inverse problem. In this paper, a new reconstruction method based on non-uniform Fourier transform and Bayesian parameter estimation theory is proposed. The main idea of the method is calculating the band width depending on the minimum apparent velocity for each temporal frequency and estimating the Fourier spectrum from the uneven seismic data. Regarding to this inverse problem, it is solved by the conjugate gradient method for the stable solution and quick convergence. Examples on synthetic as well as on field data show that the proposed method is efficient and applicable.