We have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space (f-x) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using f-x RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional f-x domain prediction technique. The conventional f-x 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 f-x domain. The shaping regularization in least-square inversion controls the smoothness of the coefficients of f-x 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 f-x domain and time-space domain prediction methods, f-x RNA can be more effective in suppressing random noise and preserving the signals, especially for complex geological structure.

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