Complex seismic wavefield interpolation based on the Bregman iteration method in the sparse transform domain

In seismic prospecting, field conditions and other factors hamper the recording of the complete seismic wavefield; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent high-precision data processing workflow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefield and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefield. Model and field data tests demonstrate that the Bregman iteration method based on the H-curve north in the sparse transform domain can effectively reconstruct missing complex wavefield data.