Relocating earthquakes in clusters based on variations in the intervals between their first P- and S-waves

Abstract

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. In the current version of the algorithm, it is assumed that the size of the cluster is much smaller than the distance to the stations; the azimuths of the stations, as well as the angles of the emergence of the first P- and S-waves, are more or less accurately known for at least one (reference) earthquake; and the rays of the first waves lie in the vertical plane that contains the earthquake and the station. Under these assumptions, the relationship between the locations and the variations in the intervals becomes purely geometrical and linear, and the corresponding system can easily be solved. A series of synthetic experiments with different numbers and configurations of stations, levels of noise in the observed data, sparse data, and inaccuracies in azimuths and angles of emergence have demonstrated the stable and reliable performance of the algorithm and its potential applicability to real data. Due to the large number of constraints on each location, the algorithm can be used primarily in the case of small earthquakes or sparse networks when a large portion of data is missing. It can be used independently, to validate the locations determined by other methods, or be integrated into them, thereby improving their reliability by providing a large number of additional constraints.