Applying statistical analysis to understanding the dynamics of volcanic explosions
Published:January 01, 2006
N. Varley, J. Johnson, M. Ruiz, G. Reyes, K. Martin, 2006. "Applying statistical analysis to understanding the dynamics of volcanic explosions", Statistics in Volcanology, H. M. Mader, S. G. Coles, C. B. Connor, L. J. Connor
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An erupting volcano is a complex system controlled by nonlinear dynamics and hence is difficult to model numerically. Statistical methods can be applied to explain behaviour or to aid the forecasting of future activity. The majority of previous studies have considered large-scale events: large explosive or effusive eruptions, with intervening long periods of repose. This has severely limited the size of the datasets and hence the significance of statistical results. In previous cases a simple Poisson model was applied, but often more sophisticated analysis methods are necessary to model the data. In this study, several statistical techniques are used to describe the data for smaller-scale events from four volcanoes. In each case study the events are relatively frequent explosions; this means that the datasets are large and thus allow a robust statistical analysis. First, time-series analysis is used to identify the presence of clustering or trends in the data. For stationary periods, the data are modelled in a probabilistic fashion, taking the survival function for increasing repose intervals and fitting different distributions to the data. Different types of events are identified, whose repose intervals have different distributions. This implies variation in the physics of the processes involved in the causation of the events. It is shown that activity can be divided into different periods based on the statistics, which can greatly aid in the construction of a model to explain the temporal evolution of eruptive activity. Contrasts between the volcanoes are highlighted, reflecting a variation in certain characteristics of their.
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Statistics in Volcanology
Statistics in Volcanology is a comprehensive guide to modern statistical methods applied in volcanology written by today's leading authorities. The volume aims to show how the statistical analysis of complex volcanological data sets, including time series, and numerical models of volcanic processes can improve our ability to forecast volcanic eruptions. Specific topics include the use of expert elicitation and Bayesian methods in eruption forecasting, statistical models of temporal and spatial patterns of volcanic activity, analysis of time series in volcano seismology, probabilistic hazard assessment, and assessment of numerical models using robust statistical methods. Also provided are comprehensive overviews of volcanic phenomena, and a full glossary of both volcanological and statistical terms.
Statistics in Volcanology is essential reading for advanced undergraduates, graduate students, and research scientists interested in this multidisciplinary field.