# Discussions on the Processing of the Multi-Component Seismic Vector Field
## 2 Multi-Component De-Noising Methods with Respect to the Vector Seismic Field
### The Polarization Filtering Method
The synthetic two-component seismic data are shown in Figure 1 where Figure 1a is the vertical component, and Figure 1b is the radial component. The dominant frequency is 30 Hz for P-waves and 22 Hz for PS-waves. Considering that the frequency range of the ground roll is 5-20 Hz, it shows considerable overlap between the frequency of the PS-waves and the ground roll. The most challenging issue is that the apparent velocities of the ground roll and the reflected wave in far offset are very close. A comparison of the t-f-k domain polarization filtering with the f-k filtering and time-frequency domain polarization filtering would convince that the t-f-k domain polarization filtering performs more effectively. As shown in Figure 1c,d, the results of f-k filtering work well butnot perfectly. The ground roll is not completely removed from the filtered result. Additionally, some body waves appear in the removed noise profiles, as shown in Figure 1e,f; this is because the apparent velocity of these body waves is close to the apparent velocity of the ground roll. Figure 2a,b show the filtered results of the time-frequency polarization filtering. Because the body wave and ground roll overlap both in the time domain and frequency domain, they cannot be effectively separated in the time-frequency domain. The t-f-k polarization filtering is implemented in the t-f-k domain. Three f-k slices (from time 150, 650, and 950 ms) of the t-f-k transform of the gathered complex seismic data are shown in Figure 3a,c,e. These figures show a meaningful phenomenon; the body waves have equal energy while the ground roll has discrepant energy in the positive and negative frequency planes. The ground roll allocated more energy in the positive frequency plane. The f-k slices taken from different times are different from each other; therefore, the computed filtering windows should change with time, as shown in Figure 3b,d,f. With the automatically identified filtering windows, the filtered results of the t-f-k polarization filtering are shown in Figure 4a,b. Furthermore, the removed ground roll is shown in Figure 4c,d. The test results indicate that the t-f-k polarization filtering method can suppress the ground roll effectively and guarantee the body wave does not drop out. Figure 1: _Cont._  
Figure 1: Synthetic two-component shot gathered data. (**a**) Vertical component, (**b**) radial component, (**c**) filtered vertical component, and (**d**) radial component with f-k filtering. The removed noise from the (**e**) vertical component and (**f**) radial component. Figure 2: (**a**) Filtered vertical component (**b**) and radial component with time-frequency polarization filtering. Figure 3: The f-k slices of the t-f-k transform taken from (**a**) 150 ms, (**c**) 650 ms, and (**e**) 950 ms. The computed filtering windows at (**b**) 150 ms, (**d**) 650 ms, and (**f**) 950 ms.  
Figure 4: (**a**) The filtered vertical component (**b**) and radial component with the t-f-k domain polarization filtering method, and (**c**) the removed noise from vertical component and (**d**) the radial component.