基于seislet变换的反假频迭代数据插值方法

许多地震资料处理方法需要完整的数据信息,但是受野外施工条件等因素的影响,观测系统很难记录完整的地震波场,如空间采样率不足和地震道缺失等现象,尤其是缺失的叠前地震数据时常产生空间假频现象,给后续处理流程中很多重要环节带来严重的影响.传统数据插值方法通常很难同时解决数据缺失和空间假频问题,因此开发有效的反空间假频数据插值方法具有重要的意义.本文通过同时改变时间和空间方向采样比例,利用预测误差滤波器的尺度缩放不变性,计算反空间假频地震倾角模式,构建可有效压缩含空间假频不完整地震数据的反假频seislet变换方法,通过压缩感知Bregman迭代算法,对缺失地震数据进行反假频插值.理论模型和实际数据的处理结果验证了基于seislet变换的迭代插值方法可以有效地恢复含有假频的缺失地震信息.

Iterative data interpolation beyond aliasing using seislet transform

Many seismic data processing methods need complete data information. However, an ideal uniform coverage is rarely achieved because of practical and economic constraints, e.g., spatial undersampling and seismic trace missing, especially, missing seismic data always cause spatial aliasing and affect the following data processing workflow. Traditional interpolation methods hardly solve both data missing and spatial aliasing. Therefore, it is important to develop an effective data interpolation technique to realize antialiasing interpolation. In this paper, we rescale both time and spatial axes and use the scale invariance property of prediction-error filter (PEF)s to calculate the antialiasing dip pattern of seismic data. The dip pattern is used to develop antialiasing seislet transform, which compresses missing data with spatial aliasing. By employing the Bregman iterative algorithm belonging to compressive sensing, the proposed method can interpolate the missing information by aliasing. The synthetic and field-data examples demonstrate that the proposed method based on seislet transform and compressive sensing theory is suitable for recovering missing seismic data even with spatial aliasing.