Two-Dimensional Nonstationary Filtering by Operator Scaling

f-k filtering and Radon transform (RT) are classical methods for processing 2-D seismic signals. They assume that target signal events exhibit specific trajectories in the time-offset domain (linear, parabolic, and hyperbolic) and process them accordingly. In fact, seismic signals are nonstationary, with geometric and dynamic characteristics changing pointwise. This makes that these methods suboptimal for processing such signals. The 2-D nonstationary convolution filtering conducted in the time-space domain allows filter variations point-by-point, adapting to the nonstationarity of seismic signals. However, obtaining the filter factors involves complex calculations, making it not widely applicable. This article proposes an efficient method based on a two-dimensional nonstationary convolution model (TNCM) and termed two-dimensional nonstationary filtering by operator scaling (TNFOS). Leveraging the resemblance among filters, specific filter factors can be easily acquired by extracting and scaling the reference filter factors. Through the cascading of filters, TNFOS effectively fulfills nearly all design requirements for 2-D velocity or dip filtering, enabling the broad implementation of 2-D nonstationary filtering. Using synthetic and field experiments, we tested the efficiency of TNFOS and provided four successful applications in suppressing seismic interference.