Noise correlation analysis: the role of the inflection points in the formation of zero-time waves

Abstract

SUMMARY The cross-correlation function (CCF) of seismic noise recorded at two stations often exhibits a prominent burst of energy near zero time. However, the excitation mechanism of such unexpected signals remains unclear. In this study, we demonstrate that this phenomenon arises from constructive interference of body waves radiating from sources near the mid-vertical plane between two receivers. This interference is driven by the occurrence of an inflection point effect in the traveltime difference between waves reaching the two receivers. When noise source distribution is asymmetric, the cumulative effect of such sources results in the generation of zero-time waves. It is noteworthy that a noise source distribution that is either uniform or follows a cosϕ pattern, with ϕ denoting the azimuth from the centre of the receiver pair, can counteract the formation of these waves. Additionally, our investigation reveals that this constructive interference does not occur in the correlation of 2-D surface waves. We used numerical simulation to support our findings. In conclusion, this study offers a theoretical explanation for the emergence of zero-time waves on the CCF and provides efficient means of investigating the extraction of inter-receiver waves with uneven noise source distribution.