Time–frequency (TF)-domain polarization analysis
(PA) methods are widely used as a processing tool to decom-
pose 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 analy-
sis (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 wave-
forms, 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 Mw = 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.