Wavefield Separation and Signal Enhancement in the Stockwell Transform Domain and Applications to Local and Regional Seismic Data

Summary Because of the nonstationary character and frequency dependence of seismic recordings, the signals and noise that make up those recordings are effectively dealt with in the time-frequency domain. Popular tools used to transform time series into time-frequency domains include the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT). The Stockwell transform (ST) is a less known time-frequency transform that contains some elements of both STFT and CWT; compared with the others, the power of ST lies in the frequency-dependent resolution it provides. To leverage that advantage, we implemented polarization filtering and non-linear thresholding techniques in the ST domain. We are able to successfully enhance linearly polarized P and S signals and suppress elliptically polarized Rg waves when jointly exploiting the linearity and directionality properties of particle motion in the polarization filter. Conversely, the ellipticity parameter from analysis of the complex polarization matrix obtained from analytic seismograms is used to suppress P and S signals and enhance Rg waves. However, polarization filtering also enhances polarized noise; and, for that reason, it results in low signal-to-noise ratios (SNRs) in some cases. We demonstrate that polarized noise that persists after polarization filtering can be successfully removed with non-linear ST thresholding, improving the SNR further and allowing an effective exploitation of the different phases. For a dataset comprising approximately 2,700 waveforms, applying polarization filtering followed by thresholding resulted in a median SNR improvement of ~8.8 dB compared to the raw data. In contrast, thresholding alone improved the median SNR by ~6.7 dB, while polarization or frequency filtering alone yielded a more modest improvement of only ~0.3–1.3 dB.