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Authors: Marzocchi, W.* 
Zaccarelli, L.* 
Title: A quantitative model for the time-size distribution of eruptions
Issue Date: 2006
Series/Report no.: / 111 (2006)
DOI: 10.1029/2005JB003709
Keywords: quantitative model
Subject Classification04. Solid Earth::04.08. Volcanology::04.08.08. Volcanic risk 
Abstract: The statistical modeling of the time-size distribution of volcanic eruptions is a fundamental tool to understand better the physics of the eruptive process, and to make reliable forecasts [Newhall and Hoblitt, 2002; Connor et al., 2003; Marzocchi et al., 2004a; Sparks and Aspinall, 2004]. Eruption forecasting is commonly associated to different timescales (short-, intermediate-, and long-term; see definition by Newhall and Hoblitt [2002]). Regardless of the time frame, the statistical modeling of the past behavior of a volcano is a key ingredient for quantitative forecasting (usually, but not necessarily, over long time intervals) when the volcano has an almost stationary state (for instance, it is dormant). In this case, monitoring data are not particularly informative of the future evolution of the system, at least until the volcano becomes restless and/or changes its stationary state. Hereinafter, the terms ‘‘eruption forecasting’’ and ‘‘volcanic hazard’’ refer to this stationary case. [3] The main difficulties in providing a general model of eruptive activity are linked to the existence of different types of volcanic activity, to the paucity of eruptive data for most volcanoes, and to the intrinsic complexity of eruptive processes. As a consequence, most of the past papers devoted to this issue are focused on single (or very few) volcanoes [e.g., Wickman, 1976; Klein, 1982; Burt et al., 1994; Bebbington and Lai, 1996; Marzocchi, 1996; Connor et al., 2003; Gusev et al., 2003; Sandri et al., 2005] where detailed eruptive catalogs exist. This approach limits the generality of the results. We cannot know if the behavior of the volcano analyzed represents a generic feature of a specific type of volcanism, or if it is peculiar of the volcano itself. Under this perspective, part of the different statistical distributions found by analyzing single eruptive catalogs can be explained by the existence of some peculiarities in volcanic activity. [4] One way to overcome this drawback, which we use here, is to perform a common analysis on data from several volcanoes. In particular, we test the Poisson hypothesis in the time domain, and the reliability of time-size distributions such as the time predictable model and size predictable model. The results obtained are then used to build a quantitative model of the statistical time-size distribution for some classes of volcanic activities that can be used for volcanic hazard assessment.
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