A dictionary learning method with atom splitting for seismic footprint suppression

The acquisition footprint causes serious interference with seismic attribute analysis, which severely hinders accurate reservoir characterization. Therefore, acquisition footprint suppression has become increasingly important in industry and academia. We have assumed that the time slice of 3D poststack migration seismic data mainly comprises two components: useful signals and the acquisition footprint. Useful signals describe the spatial distributions of geologic structures with local piecewise smooth morphological features. However, the acquisition footprint often behaves as periodic artifacts in the time-slice domain. In particular, the local morphological features of the acquisition footprint in marine seismic acquisition appear as stripes. Because useful signals and the acquisition footprint have different morphological features, we can train an adaptive dictionary and divide the atoms of the dictionary into two subdictionaries to reconstruct these two components. We have devised an adaptive dictionary learning method for acquisition footprint suppression in the time slice of 3D poststack migration seismic data. To obtain an adaptive dictionary, we use the K-singular value decomposition algorithm to sparsely represent the patches in the time slice of 3D poststack migration seismic data. Each atom of the trained dictionary represents certain local morphological features of the time slice. According to the difference in the variation level between the horizontal and vertical directions, the atoms of the trained dictionary are divided into two types. One type significantly represents the local morphological features of the acquisition footprint, whereas the other type represents the local morphological features of useful signals. Then, these two components are reconstructed using morphological component analysis based on different types of atoms, respectively. Synthetic and field data examples indicate that our method can effectively suppress the acquisition footprint with fidelity to the original data.