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Many complex systems, including sand-pile models, slider-block models, andearthquakes, have been discussed whether they obey the principles ofself-organized criticality. Behavior of these systems can be investigated fromtwo different points of view: interoccurrent behavior in a region and recurrentbehavior at a given point on a fault or at a given fault. The interoccurrentfrequency-size statistics are known to be scale-invariant and obey thepower-law Gutenberg-Richter distribution. This paper investigates the recurrentfrequency-size behavior of characteristic events at a given point on a fault orat a given fault. For this purpose sequences of creep events at a creepingsection of the San Andreas fault are investigated. The applicability of theBrownian passage-time, lognormal, and Weibull distributions to the recurrentfrequency-size statistics of slip events is tested and the Weibull distributionis found to be a best-fit distribution. To verify this result the behaviors ofthe numerical slider-block and sand-pile models are investigated and theapplicability of the Weibull distribution is confirmed. Exponents of thebest-fit Weibull distributions for the observed creep event sequences and forthe slider-block model are found to have close values from 1.6 to 2.2 with thecorresponding aperiodicities of the applied distribution from 0.47 to 0.64.

Recurrent frequency-size distribution of characteristic events