Sparsity-Promoting Approach to Polarization Analysis of Seismic Signals in the Time–Frequency Domain

Time–frequency (TF)-domain polarization analysis (PA) methods are widely used as a processing tool to decompose multicomponent seismic signals. However, as a drawback, they are unable to obtain sufficient resolution to discriminate between overlapping seismic phases, as they generally rely on a low-resolution time–frequency representation (TFR) method. In this article, we present a new approach to the TF-domain PA methods. More precisely, we provide an in-detailed discussion on rearranging the eigenvalue decomposition polarization analysis (EDPA) formalism in the frequency domain to obtain the frequency-dependent polarization properties from the Fourier coefficients owing to the Fourier space orthogonality. Then, by extending the formulation to the TF domain and incorporating sparsity promoting TFR (SP-TFR), we improve the resolution when estimating the TF-domain polarization parameters. Finally, an adaptive SP-TFF is applied to extract and filter different phases of the seismic wave. By processing earthquake waveforms, we show that, by combining amplitude, directivity, and rectilinearity attributes on the sparse TF-domain polarization map of the signal, we are able to extract (or filter) different phases of seismic waves. The SP-TFF method is evaluated on synthetic and real data associated with the source mechanism of the $M_{w}=8.2$ earthquake that occurred in the south-southwest of Tres Picos, Mexico. A discussion on the results is given, verifying the efficiency of the method in separating not only the Rayleigh waves from the Love waves but also in discriminating them from the body and coda waves. The codes and datasets are available at https://github.com/SigProSeismology/SP-TFF, contributing to the geoscience community.