Time-domain filtering approach for unambiguous comparison of seismic waveform data

Quantitative comparisons of seismic waveforms are required frequently in seismology. A standard frequency-domain analysis with the Fourier transform was developed for stationary time series, but non-stationary wavelets with finite record length are common in seismology. The Wiener filter is one of data processing schemes proposed for such non-stationary signals, comparing two records directly in the time domain. This study employs the Wiener filter to evaluate the similarity of two waveform records, compared with conventional approaches such as spectral and cross-correlation analyses.

Our first example is on multiple ScS phases of a large deep earthquake. We compared ScS and ScS₂ phases in time windows of 100-200 sec. Their spectral ratio obtained by FFT yields some distorted and unstable features, due to the truncation effect of both ends of the seismograms. In our approach, the Wiener filter is estimated for the two phases, followed by its Fourier transform. Since the resulted filter is generally smooth and zero in both ends, dissimilar to the original records, its raw spectrum is stable and smooth. This helps us to estimate the attenuation factor Q of the mantle between the surface and CMB in a broader range of frequency than the conventional spectral analysis.

The next is on the shear-wave splitting for anisotropic structures. The left figure shows an example seismogram in the caldera of Hakone, Japan, Volcano during its 2015 eruption. Two horizontal components are rotated and time-shifted so that the resulted ones be identical. Cross-correlations of the two records are measured in the domain of rotation angle and time delay, searching for the highest value as the azimuthal anisotropy of its propagation path. Nevertheless, the cross-correlation of waveforms becomes oscillatory with local peaks (the middle figure). In our approach, the Wiener filter should be impulsive if two waveforms were identical, so we introduce a criterion to minimize the spread of Wiener filters. Its distribution in the right figure gives very clear peaks.

Slight discrepancies between the two results were found in some cases. A simple frequency-independent time shift is assumed in the cross-correlation while no phase restrictions are assigned in ours, as its potentiality to retrieve the spatial scale of the anisotropy.