Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary. They may exhibit stationarity on a short timescale but eventually alter their behavior in time and space. We propose a 2D t-x adaptive prediction filter (APF) and further extend this to a 3D t-x-y version for random noise attenuation based on regularized nonstationary autoregression (RNA). Instead of using patching, a popular method for handling nonstationarity, we obtain smoothly nonstationary APF coefficients by solving a global regularized least-squares problem. We use shaping regularization to control the smoothness of the coefficients of APF. 3D space-noncausal t-x-y APF uses neighboring traces around the target traces in the 3D seismic cube to predict noise-free signal, so it provides more accurate prediction results than the 2D version. In comparison with other denoising methods, such as frequency-space deconvolution, time-space prediction filter, and frequency-space RNA, we test the feasibility of our method in reducing seismic random noise on three synthetic datasets. Results of applying the proposed method to seismic field data demonstrate that nonstationary t-x-y APF is effective in practice.
This reproducible paper is the first direct contribution from Jilin University, China.