# Noise Attenuation Based on Wave Vector Characteristics
## 1 Introduction  
Multicomponent geophones can fully record the spatial particle motions of elastic wavefields. Using the full vector amplitude information of the elastic wavefield is beneficial for reservoir prediction and fluid detection. Therefore, it is important to maintain the wave vector information of the elastic wavefield during multicomponent data processing [1]. To avoid damaging the vector fidelity of valid seismic signals, multicomponent seismic acquisition usually adopts a single-point non-combination receiving mode [2], which also results in a lower signal-to-noise ratio (S/N) for the multicomponent seismic data. Many existing denoising methods can be directly applied to multicomponent seismic data to improve the S/N; however, most are aimed at single component data. The most appropriate denoising method to apply depends on the valid signal energy and S/N. In most cases, the vertical \(Z\)-component has a higher S/N, while the horizontal component has a poorer S/N. Therefore, conventional denoising methods are not adequate for maintaining vector amplitude information because of the variability of filtering parameters and the variability of signal and noise on each component [3]. Keeping vector amplitude information during denoising remains a challenge to multicomponent seismic data processing. Polarization filtering is a method that separates valid signals from noise by using vector amplitude measured on three-component (3C) records [4; 5]. Polarization filtering has been studied for decades [6; 7; 8; 9; 10; 11], with most studies based on ellipticity or direction filters [3; 4]. For such filtering methods, it is often assumed that ground roll tends to appear as elliptical polarization in the vertical plane, while body waves are linearly polarised in three-dimensional space and random noise is unpolarised [12; 13; 14]. Valid Signals are separated from the noise background based on predefined polarization attributes such as ellipticity or polarization direction. Polarization attributes are usually derived in the time domain or in the frequency (or the time-frequency) domain. In the time domain, most techniques are based on an eigenanalysis of the data matrix constructed within a given moving time window over two-component (2C) or 3C data [12]. One can determine the polarization type according to the semi-major and semi-minor axes of the polarization trajectory given by the eigenvalues of the data covariance matrix [3] or by the eigen images of singular-value decomposition (SVD) on the data matrix [15; 16]. The success of these techniques depends on the selection of the moving window, which is affected by the dominant period, S/N, and polarization type. The problem faced by polarization filtering in the time domain is that valid signals and noise with a similar period arriving in the same time window are hard to decompose [13]. To deal with a wavefield decomposition with different frequency contents, polarization filtering based on frequency attributes has been developed. [PERSON] described a method of estimating the polarization as a function of frequency [17]. [PERSON] et al. devised a multitaper algorithm to determine the polarization of particle motion as a function of frequency and applied it to filter field 3C data [18]. [PERSON] et al. developed the multitaper spectral method of [PERSON] et al. to derive a data-adaptive polarization filter based on the estimation of the spectral density matrix [10; 18]. However, some noise, such as ground roll, always shares a similar frequency band with shear waves. To overcome this problem, polarization-filtering methods in the time-frequency domain are employed rather than those in a real time-series to separate noise and body waves [5; 11; 19; 20; 21; 22; 23; 24]. However, body waves are still hard to distinguish only using instantaneous polarization attributes when significant random noise and extra non-ground-roll related coherent noise occur on all three components [25].