An inverse cascade explanation for the power-law frequency–area statistics of earthquakes, landslides and wildfires
Bruce D. Malamud, Donald L. Turcotte, 2006. "An inverse cascade explanation for the power-law frequency–area statistics of earthquakes, landslides and wildfires", Fractal Analysis for Natural Hazards, G. Cello, B. D. Malamud
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Frequency–magnitude statistics for natural hazards can greatly help in probabilistic hazard assessments. An example is the case of earthquakes, where the generality of a power-law (fractal) frequency–rupture area correlation is a major feature in seismic risk mapping. Other examples of this power-law frequency–size behaviour are landslides and wildfires. In previous studies, authors have made the potential association of the hazard statistics with a simple cellular-automata model that also has robust power-law statistics: earthquakes with slider-block models, landslides with sandpile models, and wildfires with forest-fire models. A potential explanation for the robust power-law behaviour of both the models and natural hazards can be made in terms of an inverse-cascade of metastable regions. A metastable region is the region over which an ‘avalanche’ spreads once triggered. Clusters grow primarily by coalescence. Growth dominates over losses except for the very largest clusters. The cascade of cluster growth is self-similar and the frequency of cluster areas exhibits power-law scaling. We show how the power-law exponent of the frequency–area distribution of clusters is related to the fractal dimension of cluster shapes.
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Fractal Analysis for Natural Hazards
In the Earth sciences, the concept of fractals and scale invariance is well recognized in many natural objects. However, the use of fractals for spatial and temporal analyses of natural hazards has been less used (and accepted) in the Earth sciences. This book brings together 12 contributions that emphasize the role of fractal analyses in natural hazard research, including andslides, wildfires, floods, catastrophic rock fractures and earthquakes. A wide variety of spatial and temporal fractal-related approaches and techniques are applied to ‘natural’ data, experimental data and computer simulations. These approaches include probabilistic hazard analysis, cellular-automata models, spatial analyses, temporal variability, prediction and self-organizing behaviour. The main aims of this volume are (a) to present current research on fractal analyses as applied to natural hazards and (b) to stimulate the curiosity of advanced Earth science students and researchers in the use of fractals analyses for the better understanding of natural hazards.