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