## 4 Identification Results to Support Noise Attenuation
Data will be processed by dividing them into data subsets based on a space window with \(nx\) traces. For each data subset \(Seis(i,j)\) with \(nx\) traces (where \(i\) represents the time sample, and \(j\) represents the spatial trace), the following operations will be performed:  
First, the absolute value of each sample is computed. Then, a smoothing filter is applied in the time direction. The resulting smoothed data are denoted as \(A(i,j)\). Second, the reference amplitude trace \(B(i)\) is derived from the smoothed data by computing the median values along the spatial direction. Third, when the raw amplitude exceeds \(m_{a}\) (threshold parameter) times the reference amplitude \(m_{a}B(i)\), the attenuation coefficients are calculated through the reference amplitudes multiplied by the attenuation coefficient, then divided by the amplitude of the smoothed data. \[Coef(i,j)=\left\{ \begin{array}{cl}\frac{B(i)\times\alpha}{A(i,j)}&,Seis(i,j)> B(i)\times m_{a}\\ 1&,Seis(i,j)<B(i)\times m_{a}\end{array} \right. \tag{13}\]  
where \(\alpha\) is the attenuation scale, and \(Coef(i,j)\) is the attenuation coefficient. Figure 12: Synthetic data with added noise. Finally, each sampling point in the raw data is multiplied by its corresponding attenuation coefficient to produce the denoised data \(denoise(i,j)\):  
\[denoise(i,j)=Coef(i,j)\times Seis(i,j) \tag{14}\]  
For the AAA method, the window length \(nx\) was set to 60, the threshold \(m_{a}\) to 2, and the attenuation scale to 1.5. Figure 13 compares the noise attenuation results of the conventional AAA method and the weighting AAA approach. Red arrows indicate the loss of valid signals in the AAA result, highlighting the method's tendency to over-attenuate regions with strong but meaningful reflections. The weighting AAA method, which selectively attenuates only the samples identified as noise, effectively restores most of the lost valid signals and better preserves waveform integrity. This demonstrates the benefit of incorporating noise identification into the attenuation process, especially for strong but geologically significant events. From an SNR perspective, the overall improvement appears limited because blending the denoised data with raw traces reintroduces a small amount of noise. Nevertheless, in practical seismic data processing, preserving valid signals is often more critical than achieving maximal noise suppression, particularly in areas of structural complexity or strong reflectors. Figure 14 shows the migration imaging results. In Figure 14b, noise dominates the section due to the presence of anomalous amplitudes that were not suppressed. In contrast, Figure 14c,d present more coherent reflectors. However, SNR analysis reveals that the image produced by the weighting AAA method achieves better quality. The imaging region in Figure 14 is enlarged, as indicated by the red box. The magnified result is shown in Figure 15. Figure 15 further supports this conclusion by comparing the denoised images against the original noise-free result. Since the velocity model used for imaging is accurate and identical across all datasets, the resulting imaging structures remain the same. As shown in Figure 15, the primary difference between the two denoised datasets lies in the amplitude preservation. With the application of weighting AAA, less amplitude information is lost, resulting in an image that more closely approximates the ideal, noise-free reference. This confirms that the proposed method not only ensures the effect of noise attenuation, but more importantly, safeguards signal fidelity during denoising. Figure 13: Noise attenuation results: (**a**) denoised data by AAA, (**b**) noise removed by AAA, (**c**) denoised data by weighting AAA, (**d**) noise removed by weighting AAA. The red arrows indicate the loss of valid signals caused by the conventional AAA method.