On the measurement of relative phase velocity changes for ballistic wave seismic monitoring

SUMMARY The temporal variations in seismic wave velocity provide critical insights into the sources and physical mechanisms underlying diverse geophysical processes. While traditional approaches rely on measuring coda wave traveltime shifts to estimate velocity changes, the increasing availability of dense seismic networks has shifted attention towards ballistic waves for seismic velocity monitoring. Current methodologies for measuring ballistic wave time-shifts predominantly employ the wavelet-transform technique, which, despite its proven reliability for coda wave analysis, introduces non-negligible biases in ballistic wave monitoring due to the spectral leakage effect. To address this limitation, we propose a novel frequency-domain approach that estimates time-shifts at each frequency, leveraging the characteristics of invariant phase shifts of ballistic waves along lag time. This method offers enhanced computational efficiency and simplicity in phase shift measurements compared to the time–frequency domain analysis. The phase velocity change is subsequently determined through a linear regression of phase time-shifts along the offset. Synthetic tests validate the superior stability and accuracy of our method in estimating ballistic wave phase velocity changes. We further apply this approach to extract surface wave relative phase velocity changes from field data. Our results bring a robust and efficient method for measuring relative phase velocity changes in ballistic wave seismic monitoring.