A new wavelet-based approach to measure time- and frequency-dependent seismic velocity variations

Temporal variations of relative seismic velocity (dv/v) in different frequency bands provide information about the stress or strain perturbations at different depth and can be measured from earthquake doublets or ambient noise cross-correlations. Calculating dv/v in the traditional way, that is, the moving-window cross-spectrum analysis, faces several challenges. First, the frequency bands must be sufficiently broad to allow reliable phase-shift regressions and robust measurements of travel-time difference, limiting the frequency resolution and therefore the depth resolution. Second, measurements of multiple frequency bands require repeating the calculation multiple times, increasing the computational cost. Here we present an approach to measure dv/v using wavelet transforms, which allows the use of adaptive time windows at different frequencies and gives the phase shift in the whole time-frequency domain all at once. Synthetic tests and real data applications using coda as well as direct waves demonstrate that this new method can accurately and quickly retrieve the velocity changes in various frequency bands. It allows us to improve the depth localization of the source of velocity change in the shallow crust.