# Noise Attenuation Based on Wave Vector Characteristics
## 4 Application Results and Discussion  
We apply our noise attenuation method to field three-dimensional three-component data acquired from the Xinchang gas field in the Sichuan Basin, Southwest China. The adopted moving window for the suppression of ground roll is 70 ms and that for the suppression of non-ground-roll related noise and random noise is 5-trace and 9 ms. Our method can greatly suppress ground roll, random noise, and other strong coherent noise from the \(Z\)-component (Figure 16); the removed noise is mainly of a wide frequency-band (Figure 17). However, the first arrivals on the \(Z\)-component are also removed, which cause the frequency energy of the seismic primary to occur on the \(Z\)-component frequency spectrum (Figure 17c). On the \(X\)-component (Figures 18 and 19), in addition to ground roll and random noise, noises such as outliers and single frequency interferences are also adequately suppressed. Satisfied filtering results are also found on the \(T\)-component (Figures 20 and 21). Overall, our noise attenuation method greatly improves the S/N of the field multicomponent data, while also maintaining valid signal amplitudes. Figure 15: Instantaneous polarization filtering results. (**a**) Filtered \(Z\)-component; (**b**) filtered \(R\)-component; (**c**) noise filtered out from the \(Z\)-component and (**d**) noise filtered out from the \(R\)-component. Figure 16: Field \(Z\)-component application results. (**a**) Original \(Z\)-component; (**b**) the filtered \(Z\)-component and (**c**) noise removed from the \(Z\)-component. Figure 17: Frequency spectra of field \(Z\)-component application results. (**a**) Original \(Z\)-component; (**b**) filtered \(Z\)-component and (**c**) noise removed from the \(Z\)-component. Figure 18: Field X-component application results. (**a**) Original \(X\)-component; (**b**) filtered \(X\)-component and (**c**) noise removed from the \(X\)-component. Our noise attenuation method is based on the wave vector characteristics of elastic wavefields on all components. The method requires that previous data-processing procedures have not changed the relative amplitude relationships among different components. For example, in bandpass filtering, amplitude scaling, or static correction, all processing parameters for all components should be consistent. Deconvolution should not be performed before using our method, because it will change the shape of the wavelet on different components. Horizontal rotation (\(R\)-\(T\) rotation) will not change the vector amplitudes of elastic wavefields [1], so our method can be implemented before or after horizontal rotation. In this application, the proposed method is implemented before horizontal rotation and the only processing is the exponential gain of the three components on the same scale. Figure 19: Frequency spectra of field \(X\)-component application results. (**a**) Original \(X\)-component; (**b**) filtered \(X\)-component and (**c**) noise removed from the \(X\)-component. Figure 20: Field \(Y\)-component application results. (**a**) Original \(Y\)-component; (**b**) filtered \(Y\)-component and (**c**) noise removed from the \(Y\)-component. In order to ensure the robustness of the algorithm in the proposed method, the sampling rate, recording length, and trace number of each input component are required to be the same. The key loops of the algorithm totally take M \(\times\) N \(\times\) (L1 + L2 + L3) iterations (M: trace number, N: sample number, L1: moving sample number for suppressing ground roll, L2: moving sample number for suppressing random noise, L3: moving trace number for suppressing non-ground-roll related coherent noise). In addition, the seismic data are not required to be transformed into another domain. Therefore, the proposed method is economical in terms of computational cost. Our noise attenuation method is implemented within some certain sizes of moving windows. One moving-time-window size should be close to the maximum apparent period of the valid signal for suppressing ground roll.