# 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  
Different types of seismic waves have different polarization manners during propagation. The surface wave exhibits elliptical polarization characteristics, the P-wave exhibits linear polarization characteristics in the direction of the wave propagation, while the S-wave exhibits linear polarization characteristics perpendicular to the direction of the wave propagation, which provides the theoretical basis for identifying and separating various wave types with their differences in polarization characteristics. Polarization filtering is usually used to separate the body and surface waves in the field of earthquake research [36; 37] and suppress random noise [38; 39], while in exploration seismology, it is mostly used for surface-wave suppression and seldom used for the attenuation of random noise. The earliest method of polarization analysis occurred in the time domain [40]. Thereafter, [PERSON] [41] and [PERSON] et al. [42] conducted detailed studies. The time-domain polarization analysis constructs a covariance matrix using the multi-component seismic data within a certain time window and computes the polarization property of the wave within this time window using the characteristic value and characteristic vector of the constructed covariance matrix. The difficulty with time-domain polarization filtering is the selection of the time-window length because different lengths result in different polarization parameters. Therefore, [PERSON] et al. [43] and [PERSON] [44] proposed to adaptively select the length of the time window according to the instantaneous frequency of the signal; [PERSON] et al. [45], [PERSON] and [PERSON] [46], [PERSON] [23], [PERSON] and [PERSON] [47], and [PERSON] et al. [26] proposed the method of Complex Trace Analysis (CTA) based on the Hilbert transform to obtain the instantaneous polarization properties of the multi-component seismic signals. However, these methods of time-domain polarization analysis cannot differentiate the various wave types that are mutually superposed in time. [PERSON] et al. [48] and [PERSON] et al. [27] proposed the frequency-domain polarization filtering method to differentiate the waves that are superposed in time but with different frequency components. However, the body waves and surface waves would be superposed in both time and frequency; therefore, polarization analysis methods based on a time-frequency transform were developed, including the continuous wavelet transform-based method [28; 49], the discrete wavelet transform-based method [50], and the S transform-based methods [51; 52]. To solve the problem of the inaccurate estimation of the polarization parameter caused by the phase distortion of the conventional wavelet transform coefficient, [PERSON] et al. [53] proposed to use the stationary wavelet packet transform to estimate the instantaneous polarization parameters. Methods of polarization filtering in the time-frequency domain simultaneously use the travel time, frequency, and polarization features of seismic waves, but these methods belong to the single-channel processing mode. Another significant difference between the surface wave and body wave, namely, the apparent velocity, cannot be used. Therefore, [PERSON] et al. [29] proposed to develop a complex seismic data gathering technique by taking the radial component as the real part and the vertical component as the imaginary part, before applying the polarization analysis in the t-f-k- domain for surface-wave attenuation. If the surface wave and body wave are different in either time, frequency, or apparent velocity, the surface waves can be automatically identified and eliminated according to the polarization rate in the t-f-k domain, which fully reflects the advantages of the vector processing method. An example is given here to exhibit the effectiveness of the t-f-k domain polarization filtering method.