Eur. Phys. J. B 34, 489-494 (2003)
https://doi.org/10.1140/epjb/e2003-00248-6

Error diagrams and temporal correlations in a fracture model with characteristic and power-law distributed avalanches

¹ Departamento de Física Teórica, Universidad de Zaragoza, Zaragoza 50009, Spain
² Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Zaragoza 50009, Spain
³ Departamento de Ciencias de la Tierra, Universidad de Zaragoza, Zaragoza 50009, Spain

Received: 16 April 2003
Published online: 9 September 2003

Abstract

Forecasting failure events is one of the most important problems in fracture mechanics and related sciences. In this paper, we use the Molchan scheme to investigate the error diagrams in a fracture model which has the notable advantage of displaying two completely different regimes according to the heterogeneity of the system. In one regime, a characteristic event is observed while for the second regime a power-law spectrum of avalanches is obtained reminiscent of self-organized criticality. We find that both regimes are different when predicting large avalanches and that, in the second regime, there are non-trivial temporal correlations associated to clustering of large events. Finally, we extend the discussion to seismology, where both kinds of avalanche size distributions can be seen.