Non-stationary predictive filtering for seismic random noise suppression - A tutorial

Predictive filtering in the frequency domain is one of the most widely used denoising algorithms in the seismic data processing workflow. Predictive filtering is based on the assumption of linear/planar events in the time-space domain. In traditional predictive filtering method, the predictive filter is fixed across the spatial dimension, which cannot deal with the spatial variation of seismic data well. To handle the curving events, the predictive filter is either applied in local windows or extended to a non-stationary version. The regularized non-stationary autoregression (RNAR) method can be treated as a non-stationary extension of the traditional predictive filtering, where the predictive filter coefficients are variable in different space locations. The highly under-determined inverse problem is solved by shaping regularization with a smoothness constraint in space. We further extend the RNAR method to a more general case, where 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. Secondly, we apply a frequency dependent smoothing radius along the space dimension to better take advantage of the non-stationarity of seismic data in the frequency axis, and to better deal with noise. The proposed method is validated via several synthetic and field data examples.