Characteristics of the deformation process in the subduction zone of the Kuril-Kamchatka island arc in the aftershock phase based on a fractional model of deformation activity

The article presents the results of calculations of the values of parameters determining the properties of the deformation process, based on data from the earthquake catalog of the Kamchatka Branch of the Federal Research Center «Geophysical Survey of the Russian Academy of Sciences» (KB FRC GS RAS) for the period from 1 January 1962 to 31 December 2002 for the Kuril-Kamchatka island arc subduction zone (area 46$^\circ$–62$^\circ$ N, 158$^\circ$–174$^\circ$ E) in the aftershock phase in within the framework of the fractional model of the deformation process previously presented by the authors. The compound power-law Poisson process in fractional time representation is considered as a model. Aftershocks associated with the mainshock of a given energy are determined based on energy, spatial and temporal criteria.To construct an empirical cumulative distribution function (eCDF) for aftershocks of a fixed class depending on the time before the mainshock, the superposed epoch analysis is applied to sequences of aftershocks for all mainshocks of a given energy in the catalog. The eCDF of the aftershock waiting time are approximated by the Mittag-Leffler function based on the fractional model of the deformation process developed by the authors. The results of calculations of the values of the Mittag-Leffler function parameters for the mainshocks of the classes K < 12.5 showed that the deformation process in the considered zone has the properties of nonstationarity and hereditarity. With an increase in the class of the mainshock, the process can be considered non-stationary standard Poisson process.