Substituting smoothing with low-rank decomposition - Applications to least-squares reverse time migration of simultaneous source and incomplete seismic data

Seismic migration can be formulated as an inverse problem, the model of which can be iteratively inverted via the least-squares migration framework instead of approximated by applying the adjoint operator to the observed data. Least-squares reverse time migration (LSRTM) has attracted more and more attention in modern seismic imaging workflows because of its exceptional performance in obtaining high-resolution true-amplitude seismic images and the fast development of the computational capability of modern computing architecture. However, due to a variety of reasons, e.g., insufficient shot coverage and data sampling, the image from least-squares inversion still contains a large amount of artifacts. This phenomenon results from the ill-posed nature of the inverse problem. In traditional LSRTM, the minimum least-squares energy of the model is used as a constraint to regularize the inverse problem. Considering the residual noise caused by the smoothing operator in traditional LSRTM, we regularize the model using a powerful low-rank decomposition operator, which can better suppress the migration artifacts in the image during iterative inversion. We evaluate in detail the low-rank decomposition operator and the way to apply it along the geologic structure of seismic reflectors. We comprehensively analyze the performance of our algorithm in attenuating crosstalk noise caused by simultaneous source acquisition and migration artifacts caused by insufficient space sampling via two synthetic examples and one field data example. Our results indicate that compared to the conventional smoothing operator, our low-rank decomposition operator can help obtain a cleaner LSRTM image and obtain a slightly better edge-preserving performance.