Random noise attenuation using f-x regularized nonstationary autoregression

Abstract

We have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space ([Formula: see text]) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using [Formula: see text] RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional [Formula: see text] domain prediction technique. The conventional [Formula: see text] domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data. The new method does not require windowing strategies in spatial direction. We implement the algorithm by an iterated scheme using the conjugate-gradient method. We constrain the coefficients of nonstationary autoregression (NA) to be smooth along space and frequency in the [Formula: see text] domain. The shaping regularization in least-square inversion controls the smoothness of the coefficients of [Formula: see text] RNA. There are two key parameters in the proposed method: filter length and radius of shaping operator. Tests on synthetic and field data examples showed that, compared with [Formula: see text] domain and time-space domain prediction methods, [Formula: see text] RNA can be more effective in suppressing random noise and preserving the signals, especially for complex geological structure.