Nonstationary predictive filtering for seismic random noise suppression — A tutorial

Predictive filtering (PF) in the frequency domain is one of the most widely used denoising algorithms in seismic data processing. PF is based on the assumption of linear or planar events in the time-space domain. In traditional PF methods, a predictive filter is fixed across the spatial dimension, which cannot deal with spatial variations in seismic data well. To handle the curved events, the predictive filter is either applied in local windows or extended into a nonstationary version. The regularized nonstationary autoregression (RNAR) method can be treated as a nonstationary extension of traditional PF, in which the predictive filter coefficients are variable in different spatial locations. This highly underdetermined inverse problem is solved by shaping regularization with a smoothness constraint in space. We further extend the RNAR method to the more general case, in which we can apply more constraints to the filter coefficients according to the features of seismic data. First, apart from the smoothness in space, we also apply a smoothing constraint in frequency, considering the coherency of the coefficients in the frequency dimension. Second, we apply a frequency-dependent smoothing radius in the spatial dimension to better take advantage of the nonstationarity of seismic data in the frequency axis and to better deal with noise. The effectiveness of our method is validated using several synthetic and field data examples.