基于非均匀曲波变换的高精度地震数据重建

High accurate seismic data reconstruction based on non-uniform curvelet transform

在野外数据采集过程中,空间非均匀采样下的地震道缺失现象经常出现,为了不影响后续资料处理,必须进行高精度数据重建.然而大多数常规方法只能对空间均匀采样下的地震缺失道进行重建,而对于非均匀采样的地震数据则无能为力.为此本文在以往多尺度多方向二维曲波变换的基础上,首先引入非均匀快速傅里叶变换,建立均匀曲波系数与空间非均匀采样下地震缺失道数据之间的规则化反演算子,在L1最小范数约束下,使用线性Bregman方法进行反演计算得到均匀曲波系数,最后再进行均匀快速离散曲波反变换,从而形成基于非均匀曲波变换的高精度地震数据重建方法.该方法不仅可以重建非均匀带假频的缺失数据,而且具有较强的抗噪声能力,同时也可以将非均匀网格数据归为到任意指定的均匀采样网格.理论与实际数据的处理表明了该方法重建效果远优于非均匀傅里叶变换方法,可以有效地指导复杂地区数据采集设计及重建.

During the field data acquisition, we often face the challenge of non-uniformly sampled data with missing seismic traces. In order not to affect the subsequent data processing, the high accurate data reconstruction must be carried out. However, most conventional data reconstruction methods can only handle the uniform sampled data with missing traces, and they will fail to reconstruct for non-uniformly sampled data. In this paper, based on the 2D Curvelet transform of the multi-scale and multi-direction, the non-uniform fast Fourier transform is introduced, and the regularization inversion of operator between the curvelet coefficient and non-uniformly sampled traces is established under the L1 norm constraint, then uniform curvelet coefficient can be calculated by using the inversion algorithm of the linearized Bregman method. Finally, we can adopt the standard the curvelet inverse transform for the uniform curvelet coefficient, and high accurate reconstruction method based on the 2D non-uniform Curvelet transform is formed. This method introduced here not only reconstruct non-uniformly sampled, aliased data or noisy data with missing traces, but also can be capable of reconstructing any subset of observed data on a nonuniform grid to a specified uniform grid. The reconstructed results for synthetic and real data indicate that this proposed method shows significant improvement over the non-uniform Fourier transform-based reconstruction method, and it can guide seismic data acquisition and reconstruction effectively for complex areas.