Error Diagrams and Temporal Correlations in a Fracture Model with Characteristic and Power-Law Distributed Avalanches

TL;DR

This study investigates error diagrams in a fracture model exhibiting both characteristic and power-law avalanche regimes, revealing differences in predictability and temporal correlations, with implications for seismology.

Contribution

It introduces an analysis of error diagrams in a fracture model with dual regimes, highlighting differences in forecasting large avalanches and identifying temporal correlations.

Findings

Distinct regimes show different predictability for large avalanches

Power-law regime exhibits non-trivial temporal correlations

Results have implications for earthquake forecasting

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.