Journal of Conference Abstracts

Self-organized Criticality and the Scale Invariance

Mikhail Shnirman (shnir@mitp.rssi.ru) & Elena Blanter (blanter@ium.ips.ras.ru)

International Institute of Earthquake, Prediction Theory and Mathematical Geophysics, Varshavskoe sh., 79 korp 2, Moscow, 113556, Russia

A mixed hierarchical system of defects with heterogenious conditions of destruction is considered. The model exhibits three kinds of behavior: stability, catastrophe and scale invariance. In the area of stability the probability of a defect tends to zero when its size grows; the system demonstrate the increasing strengths of large scales. The catastrophic behavior is characterized by increasing probabilities of defects of large scales, tending to unity for high levels of the system, that may be associated with a complete destruction of the system. Two kinds of scale invariance are obtained: stable and unstable ones. The stable scale invariance represents the traditional form of the self-organized criticality with a unity slope of the magnitude-frequency relationship. The linear form of the magnitude-frequency relation with different slopes different from unity is also observed inside both areas of stability and catastrophe. Phase transitions between various kinds of system behavior are obtained in the model. Possible applications of results to the earthquake prediction are discussed.