New approaches to volcanic time-series analysis
Published:January 01, 2006
The literature on geophysical time-series analysis is so extensive that to review even one topic, such as volcanic tremor series, is a major task (e.g. Konstantinou & Schlindwein 2002). The purpose of this paper is not to attempt such a review but rather to outline some new tools for nonstationary and nonlinear time-series analysis that have been developed and used successfully in other areas of the environmental sciences and appear to have good potential for application in a volcanological or wider geophysical context. These stochastic methods of time-series analysis have the advantage that they all exploit powerful recursive (sequential updating) methods of estimation that facilitate the analysis of data generated by nonstationary and nonlinear systems (e.g. Young 1984).
This paper starts by reviewing briefly some of the model-based methods of time-series analysis, signal extraction and forecasting that have appeared in the statistical and time-series analysis literature over many years and then proceeds to describe in more detail one approach that has attracted considerable interest over the past two decades. This is based on the concept of an ‘unobserved component’ model and it exploits recursive estimation for the purposes of estimating time-variable parameters in nonstationary systems. It is shown that such an approach allows for various, practically useful procedures in time-series analysis: signal extraction; interpolation over gaps in time series; and forecasting or backcasting. It then goes on to outline the basic aspects of input-output time series modelling, considering both discrete-time and continuous-time ‘transfer function’ models that.
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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.