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

Abstract

Time-frequency (TF)-domain polarization analysis (PA) methods are widely used as a processing tool to decompose multi-component 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 paper, 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 time-frequency representation (SP-TFR), we alleviate the limited resolution when estimating the TFdomain polarization parameters. The final details of the technique are to apply an adaptive sparsity-promoting time-frequency filtering (SP-TFF) 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 Mw = 8.2 earthquake that occurred in the southsouthwest of Tres Picos, Mexico. A detailed discussion on the results of these experiments is given, approving the efficiency of the technique in separating not only the Rayleigh from the Love waves but also to discriminate them from the body and coda waves.

Applications of Time‐Frequency Domain Polarization Filtering to InSight Seismic Data

“…A mother wavelet specifically imitating the shape of the SEIS data glitches could for example, provide an even better identification and isolation of glitches than the one that we obtained with the S‐transform. Additionally, we anticipate that recent developments in high‐resolution time‐frequency transforms such as the synchrosqueezing method (Daubechies et al., 2011) or sparsity‐promoting time‐frequency representations (Mohammadigheymasi et al., 2022) may help to obtain a more localized time‐frequency representations that enhance the characterization and suppression of, for example, the imprint of the lander resonances.…”