An inverse cascade explanation for the power-law frequency - area statistics of earthquakes, landslides and wildfires

Bruce D. Malamud, Donald L. Turcotte

Research output: Chapter in Book/Report/Conference proceedingChapter

16 Citations (Scopus)

Abstract

Frequency-magnitude statistics for natural hazards can greatly help in probabilistic hazard assessments. An example is the case of earthquakes, where the generality of it 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-automatamodel 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.

Original languageEnglish
Title of host publicationFRACTAL ANALYSIS FOR NATURAL HAZARDS
EditorsG Cello, BD Malamud
Place of PublicationBATH
PublisherGEOLOGICAL SOC PUBLISHING HOUSE
Pages1-9
Number of pages9
ISBN (Print)1-86239-201-3
Publication statusPublished - 2006
Event32nd International Geological Congress - Florence
Duration: 20 Aug 200428 Aug 2004

Conference

Conference32nd International Geological Congress
CityFlorence
Period20/08/200428/08/2004

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