## 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 language | English |
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Title of host publication | FRACTAL ANALYSIS FOR NATURAL HAZARDS |

Editors | G Cello, BD Malamud |

Place of Publication | BATH |

Publisher | GEOLOGICAL SOC PUBLISHING HOUSE |

Pages | 1-9 |

Number of pages | 9 |

ISBN (Print) | 1-86239-201-3 |

Publication status | Published - 2006 |

Event | 32nd International Geological Congress - Florence Duration: 20 Aug 2004 → 28 Aug 2004 |

### Conference

Conference | 32nd International Geological Congress |
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City | Florence |

Period | 20/08/2004 → 28/08/2004 |