On the use of the autocorrelation function: the constraint of using frequency band-limited signals for monitoring relative velocity changes

Correlations of seismic noise are commonly used to monitor temporal variations of relative seismic velocity in period ranges from 1 s up to 100 s. Of particular interest is the detection of small changes in the order of 0.01–0.1 % in propagation speeds. Measuring such small differences can, however, be significantly biased by temporal variations in the properties of the noise sources within the corresponding frequency band. Using synthetic data, we show that apparent relative velocity variations might appear only due to changes in the amplitude and frequency content caused by source variations. Removing such unwanted effects by applying narrow bandpass filters in the preprocessing restricts the high-resolution analysis of any signal due to Gabor’s uncertainty limit, i.e., the correlation function suffers a limited resolution to time delay estimates for small correlation times, low-frequency ranges, and in narrow frequency bands. Better understanding of spatiotemporal noise source properties and the theoretical limitations of time–frequency analysis is critical for accurate and reliable passive monitoring.