Application of the energy reassignment method to measure accurate Rayleigh and Love wave group velocities from ambient seismic noise cross-correlations

Abstract:

We have collected three-component data from 122 Korean accelerometer stations for the month of December in 2014. We apply similar techniques described by Zha \textit{et al.} (2013) to retrieve accurate station orientation angles, in order to rotate the horizontal component data into the radial and transverse frame of reference, and for subsequent measurement of Love wave group velocity dispersion. We simultaneously normalize all three components of a daily noise record via the frequency-time normalization (FTN) method. Each component is divided by the average signal envelope in an effort to retain relative amplitude information between all three components. Station orientations are found by a grid search for the orientation azimuth which maximizes the coherency between the radial-vertical cross-correlation and the Hilbert transformed vertical-vertical cross-correlation. After measuring orientation angles, we cross-correlate and rotate the data. Typically, the group velocity dispersion curves are measured using the frequency time analysis technique (FTAN), effectively producing spectrograms with significant uncertainty in the time-frequency plane. The spectrogram approach retains only the amplitude information of the short-time Fourier transform (STFT). However, Kodera \textit{et al} (1976) show that by taking into account the phase information, the concepts of instantaneous frequency and group-time delay can be used to compute the first moment of the signal power in the frequency and time domains. During energy reassignment, the signal power calculated using the STFT at a point ($t_0, f_0$) is reassigned to the location of the first moment ($\hat{t}_g,\hat{f}_i$), where $\hat{t}_g$ is the group-time delay and $\hat{f}_i$ is the instantaneous frequency. We apply the method of energy reassignment to produce precise Rayleigh and Love wave group velocity measurements in the frequency range 0.1 - 1.0 Hz. Tests on synthetic data show more accurate retrieval of group velocities at low and high frequencies compared to classic measurement techniques. We regionalize the measurements to make maps of group velocity distributions. The increased accuracy of the measurements provide stronger constraints for the S-velocity structure in the uppermost crust.