Two-dimensional Non-stationary Filtering by Operator Scaling

f-k filtering and Radon transform (RT) are classical methods for processing two-dimensional seismic signals. They assume that target signal events exhibit specific trajectories in the time-offset domain (linear, parabolic, hyperbolic) and process them accordingly. In fact, seismic signals are non-stationary, with geometric and dynamic characteristics changing pointwise. This makes these methods suboptimal for processing such signals. Two-dimensional non-stationary convolution filtering conducted in the time-space domain allows filter variations point-by-point, adapting to the non-stationarity of seismic signals. However, obtaining the filter factors involves complex calculations, making it not widely applicable. This paper proposes an efficient method based on a two-dimensional non-stationary convolution model (TNCM), termed two-dimensional non-stationary 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 2D velocity or dip filtering, enabling the broad implementation of two-dimensional non-stationary filtering. Using synthetic and field experiments, we tested the efficiency of TNFOS and provided four successful applications in suppressing seismic interference.