Application of the hereditarian criticality model to the study of the characteristics of the seismic process of the Kuril-Kamchatka island Arc subduction zone

The article presents the results of statistical processing of data from the earthquake catalog of the KBGSRAS 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) within the framework of the earlier presented by the authors hereditarian criticality model. The compound power-law Poisson process in fractional time representation is considered as a model. The use of this model assumes quasi-stationary and quasi-homogeneous regime of the seismic process averaged over time and space during long-term observation. The study of the instability of this process over time is carried out using critical indices, which are determined by the numerical characteristics of the process and depend on the parameter b of the Gutenberg-Richter law. Based on the catalog data, the parameters of the seismic process were found by linear and nonlinear regression: the coefficient b and the exponent of the Caputo fractional derivative $\nu$, by averaging over the magnitude interval in which the power law distribution of recurrence frequencies of events is performed. The significance of the obtained value of the Gutenberg-Richter law parameter b is estimated. Critical indices have been calculated, according to the values of which, and in comparison with the hereditarity parameter $\nu$, the state of the seismic process in the period under consideration is determined.