Abstract

The hypothesis of large earthquakes being interrelated at regional distances much greater than the associated rupture lengths and the length of decay for the static stresses was first stated by V. I. Keilis-Borok and L. N. Malinovskaya in the 1960s to be modified later into an algorithm of distant aftershocks. The algorithm has been repeatedly modified; it is considered here for comparatively strong and long seismic responses to initiating large earthquakes (the "Californian version"). The algorithm is applied to Pamir and Tien Shan data whose seismicity is historically represented by two catalogs that overlap in time. This permits the algorithm to be adapted to the one catalog to be then transferred to the other with very slight changes. The version that provides 50 to 75 percent for $\Theta$, the fraction of the space-time alarm volume in the total volume considered, is fairly versatile. The fraction can be made as low as 19 percent while preserving the number of successes (10) out of a total of 11 cases under consideration, but this results in a loss of versatility. The general conclusion is that the statistical significance of the results corroborates the existence of distant aftershocks. The fact that $\Theta$ has such values is explained by the sparsity of distant aftershocks. The high number of successes is achieved by combining distant aftershocks as precursors and events from the background seismicity which reflect the stationary seismicity distribution. The combination of distant aftershocks and the hypothesis of precursory quiescence reduced $\Theta$ considerably but results in a higher number of failures-to-predict.