Landslides, sandpiles, and self-organized criticality

Power-law distributions of landslides and rockfalls observed under various conditions suggest a relationship of mass movements to self-organized criticality (SOC). The exponents of the distributions show a considerable variability, but neither a unique correlation to the geological or climatic situation nor to the triggering mechanism has been found. Comparing the observed size distributions with models of SOC may help to understand the origin of the variation in the exponent and finally help to distinguish the governing components in long-term landslide dynamics. However, the three most widespread SOC models either overestimate the number of large events drastically or cannot be consistently related to the physics of mass movements. Introducing the process of time-dependent weakening on a long time scale brings the results closer to the observed statistics, so that time-dependent weakening may play a major part in the long-term dynamics of mass movements. 1 Power-law distributions in natural hazards Some natural hazards have been recognized to exhibit scaleinvariant size statistics. Earthquakes are the most prominent example. World-wide monitoring of seismic activity has led to extensive statistics concerning the frequency of earthquake occurrence. Gutenberg and Richter (1954) found that log10 N(m) = a − bm, (1) where N(m) is the number of earthquakes per unit time interval with a magnitude greater than or equal to m, and a and b are parameters. The Gutenberg-Richter law has been supported by an enormous amount of data and has been found to be applicable over a wide range of earthquake magnitudes globally as well as locally. The parameter b slightly varies from region to region, but is generally between about 0.8 Correspondence to: S. Hergarten ([email protected]) and 1.2 (Frohlich and Davis, 1993). In contrast, the parameter a quantifies the regional seismic activity and thus varies strongly. The scale-invariant character of the GutenbergRichter law becomes evident if it is transformed into a statistical distribution of the sizes A of the rupture areas that reads