On reproducibility of relative locations of recurrent earthquakes recovered from similarity of their waveforms at a single station

Relative locations of recurrent earthquakes can be recovered from values of cross-correlation coefficients between their waveforms at a single station, provided that an idea of Menke (1999) that the values depend inversely exponentially from separation between the sources is true. An algorithm developed in Gnyp (2013) based on this idea was applied here for recovering relative locations of the two groups of the 2005-2006 recurrent earthquakes in Mukacheve, Ukraine, from the sets of crosscorrelation coefficients between their records at the four local network stations to find out whether the locations were in principle reproducible independently at each of the stations, at epicentral distances from about 6 to 64 km. The resulting sets of locations occurred in good agreement with each other, which may be considered as an experimental evidence for validity of the Menke’s dependence over the corresponding range of distances. The reproducibility of relative locations has been analyzed in terms of existence and uniqueness of the inverse problem’s solution, and in connection with data completeness and the influence of noise on it.