cross-correlation

It is demonstrated in [Gnyp & Malytskyy, 2023] that only the difference in the intervals between the first P- and S-waves can be used to relocate a cluster of similar earthquakes. The advantage of using only the difference is that it is measured by cross-correlation within a window containing the corresponding arrivals, eliminating the need to know their exact timing. Another advantage is that relative locations can be recovered regardless of source times and, therefore, of often inaccurate arrival picks or velocity models.

The length of the interval between the first P- and S-waves is routinely used as a rough estimator of epicentral distance. We propose an algorithm for the relocation of earthquakes occurring in clusters, based on the simultaneous comparison of a large number of intervals. Variations in the intervals at each station are measured by cross-correlation between the respective portions of records directly and without a reference to any absolute times.