On the measurement of seismic traveltime changes in the time-frequency domain with wavelet cross-spectrum analysis

The spatial distribution of temporal variations in seismic wavespeed is key to understanding the sources and physical mechanisms of various geophysical processes. The imaging of wavespeed changes requires accurate measurements of traveltime delays with both high lapse-time and frequency resolutions. However, traditional methods for time-shift estimation suffer from their limited resolutions. In this paper we propose a new approach, the wavelet method, to measure the traveltime changes in the time-frequency domain. This method is based on wavelet cross-spectrum analysis, and can provide optimal time frequency joint resolution while being computationally efficient. It can deal not only with coda but also dispersive surface waves even in the presence of cycle skipping. Using synthetic coda, we show that the wavelet method can retrieve traveltime shifts more stably and accurately than traditional methods. An application at Salton Sea Geothermal Field indicates that the wavelet method is less affected by spectral smearing and better discriminates dv/v variations at different frequencies. Furthermore, upon investigations on synthetic coda, we illustrate that the bias on dv/v measurements due to changes in source frequency content is likely to be negligible, either with traditional methods or with the new wavelet method. The wavelet method sheds lights on applications of seismic interferometry that aim to locate changes in space.