A novel time-domain polarization filter based on a correlation matrix analysis

Abstract

Polarization filters (PFs) are widely used for denoising seismic data. These filters are applied in the fields of seismology, microseismic monitoring, vertical seismic profiling, and subsurface imaging. They are primarily useful to suppress ground roll in seismic reflection data and enhance P- and S-wave arrivals. Traditional implementations of PFs involved the analysis of the covariance matrix or the singular value decomposition (SVD) of a 3C seismogram matrix. The linear polarization level, known as rectilinearity, is expressed as a function of the covariance matrix eigenvalues or by the data matrix singular values. Wavefield records that are linearly polarized are amplified, whereas others are attenuated. Besides the described implementations, we have developed a new time-domain PF based on the analysis of the seismic data correlation matrix. The principal idea is to extend the notion of the correlation coefficient in 3D space. This new filter avoids the need for diagonalization of the covariance matrix or SVD of data matrix, which are often time-consuming. The new implementation facilitates the choice of the rectilinearity threshold: We determine that linear polarization in three dimensions can be represented as three classic 2D correlations. A good linear polarization is detected when a high linear correlation between the three seismogram components is mutually observed. The tuning parameters of the new filter are the length of the time window, the filter order, and the rectilinearity threshold. Tests using synthetic seismograms indicate that optimal results are reached with a filter order that spans between 2 and 4, a rectilinearity threshold between 0.3 and 0.7, and a window length that is equivalent to one to three times the period of the signal wavelet. Compared with covariance-based filters, the new filter can enhance the signal-to-noise ratio by 6–20 dB and reduces computational costs by 25%.