Adaptive prediction filtering in $t$ -$x$ -$y$ domain for random noise attenuation using regularized nonstationary autoregression

2D poststack model

The second example is shown in Figure 7a. The input data are borrowed from Claerbout (2009): a synthetic seismic image containing dipping beds, an unconformity and a fault. Figure 7b shows the same image with Gaussian noise added. The challenge in this example is to account for both nonstationary and event truncations. Figure 8a shows the denoised result using the $f$ -$x$ RNA, which was implemented in each frequency slice. Note that the $f$ -$x$ RNA can eliminate part of noise, but the result shows some artificial events, which are parallel with the events. The difference (Figure 8b) between Figure 7b and Figure 8a also shows the corresponding artifacts. The denoised result and the noise removed using the $t$ -$x$ APF are shown in Figure 8c and Figure 8d, respectively. The APF has 10 (time) $\times$ 10 (space) coefficients for each sample and a 20-sample (time) $\times$ 20-sample (space) smoothing radius. The proposed method eliminates most of random noise and preserves the truncations well.

sigmoid,noise
Figure 7. 2D poststack model (a) and noisy data (b).

sfxrna,sfxnoiz,apfs,apfn
Figure 8. Comparison of nonstationary methods. The denoised result by $f$ -$x$ RNA (a), the noise removed by $f$ -$x$ RNA (b), the denoised result by $t$ -$x$ APF (c), and the noise removed by $t$ -$x$ APF (d).

Adaptive prediction filtering in $t$ -$x$ -$y$ domain for random noise attenuation using regularized nonstationary autoregression