Shearlet域稀疏约束地震数据重建

在地震数据处理流程中，通常对不规则的、稀疏的或者缺失的地震数据进行插值处理，通过插值方法来避免多次波的预测错误和成像假频等现象，使地震数据处理更加精准。Shearlet变换是一种多尺度变换，具有最佳的稀疏性、方向性以及局部化特性。将Shearlet变换与基于Landweber加速下降迭代方法结合起来对地震数据进行插值，在保证求解精度的同时提高了计算效率。信号和噪声在Shearlet域具有不同的分布特点，通过阈值法压制随机噪声，可提高算法的抗噪性。此外，采用jitter采样的方式，更好地压制了假频信息。理论和实际地震数据验证了该方法的有效性。

Seismic Data Interpolation Based on Sparse Constraint in Shearlet Domain

Seismic data interpolation for the missing traces forms a crucial step in the seismic processing flow.Interpolation result will affect the subsequent migration imaging and the effect of multiple elimination directly.Shearlet transform is a new multi-scale transform with multi-directions, multi-resolutions,and optimal sparse approximation properties.We propose an accelerate iterative Landweber algorithm for seismic data interpolation based on Shearlet transform,ensuring the precision and improving the computational efficiency at the same time. According to the distribution characteristics of signals and noise,the signal-to-noise ratio could be improved by using a threshold method to suppress random noise,improving the anti-noise capability of our algorithm.Moreover, jittered undersampling is adopted to suppress aliasing.A stylized experiment on synthetic as well as field data show the method is effective and robust.