Sparsity-promoting approach to polarization analysis of seismic signals in the time-frequency domain

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.