An Application of Voronoi Diagrams to Modeling Earthquake Catalogs

• Activity Number: 386
• Type: Contributed
• Date/Time: Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Christopher Barr*+ and Frederic Paik Schoenberg
• Companies: University of California, Los Angeles and University of California, Los Angeles
• Keywords: Voronoi Diagrams ; Tapered Pareto Distribution ; Earthquakes ; Spatial Statistics ; Stochastic Geometry

Abstract

Following a brief summary of the use of Voronoi diagrams for problems in such diverse fields as astronomy, biology and operations research, some new applications in describing the spatial structure of earthquake epicenters will be introduced. Seismic moments and other properties of earthquakes have long been modeled by the Pareto distribution. Here, a twenty-year catalog of Southern California earthquakes is analyzed, and evidence is provided which suggests numerous properties of Voronoi cells arising from tessellated epicenters follow the tapered Pareto distribution. The findings relate to previous results on the tapered Pareto distribution of earthquake sizes and aftershock distances by a variety of authors including Kagan, Vere-Jones, and Ogata. Additionally, recent work using the tapered Pareto to model wildfire burn regions potentially suggests even broader applications.