Markov Models of Repose-Period Patterns of Volcanoes

Wickman, Frans E.

doi:10.1007/978-3-642-66146-4_11

Cited by 70 publications

(60 citation statements)

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“…1 to 7, ESM1). None of the datasets is well fit by an exponential distribution, rejecting the hypothesis of a homogeneous Poisson process controlling explosions, meaning that these systems are not controlled by random failure modes and constant eruption hazard rates (Wickman, 1966). Instead, most of our datasets are well described by log-logistic, log-normal, Weibull and gamma models (Table 3).…”

Section: Discussionmentioning

confidence: 79%

Quantifying unsteadiness and dynamics of pulsatory volcanic activity

Domínguez

Pioli

Bonadonna

et al. 2016

Earth and Planetary Science Letters

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Available online xxxx Editor: T.A. MatherKeywords: explosions pulsatory activity magma viscosity repose interval source dynamics eruptive style Pulsatory eruptions are marked by a sequence of explosions which can be separated by time intervals ranging from a few seconds to several hours. The quantification of the periodicities associated with these eruptions is essential not only for the comprehension of the mechanisms controlling explosivity, but also for classification purposes. We focus on the dynamics of pulsatory activity and quantify unsteadiness based on the distribution of the repose time intervals between single explosive events in relation to magma properties and eruptive styles. A broad range of pulsatory eruption styles are considered, including Strombolian, violent Strombolian and Vulcanian explosions. We find a general relationship between the median of the observed repose times in eruptive sequences and the viscosity of magma given by η ≈ 100 · t median . This relationship applies to the complete range of magma viscosities considered in our study (10 2 to 10 9 Pa s) regardless of the eruption length, eruptive style and associated plume heights, suggesting that viscosity is the main magma property controlling eruption periodicity. Furthermore, the analysis of the explosive sequences in terms of failure time through statistical survival analysis provides further information: dynamics of pulsatory activity can be successfully described in terms of frequency and regularity of the explosions, quantified based on the log-logistic distribution.A linear relationship is identified between the log-logistic parameters, μ and s. This relationship is useful for quantifying differences among eruptive styles from very frequent and regular mafic events (Strombolian activity) to more sporadic and irregular Vulcanian explosions in silicic systems. The time scale controlled by the parameter μ, as a function of the median of the distribution, can be therefore correlated with the viscosity of magmas; while the complexity of the erupting system, including magma rise rate, degassing and fragmentation efficiency, can be also described based on the log-logistic parameter s, which is found to increase from regular mafic systems to highly variable silicic systems. These results suggest that the periodicity of explosions, quantified in terms of the distribution of repose times, can give fundamental information about the system dynamics and change regularly across eruptive styles (i.e., Strombolian to Vulcanian), allowing for direct comparison and quantification of different types of pulsatory activity during these eruptions.

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Section: Discussionmentioning

confidence: 79%

Quantifying unsteadiness and dynamics of pulsatory volcanic activity

Domínguez

Pioli

Bonadonna

et al. 2016

Earth and Planetary Science Letters

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“…Some of the earliest, (Wickman, 1965(Wickman, , 1976Reyment, 1969;Klein, 1982) employed stochastic principles to analyze eruption patterns. Further studies included transition probabilities of Markov chains (Carta et al, 1981;Aspinall et al, 2006;Bebbington, 2007), Bayesian analysis of volcanic activity (Ho, 1990;Solow, 2001;Newhall and Hoblitt, 2002;Ho et al, 2006;Marzocchi et al, 2008), homogeneous and non-homogeneous Poisson process applied to volcanic series (De la Cruz-Reyna, 1991;426 A. T. Mendoza-Rosas and S. De la Cruz-Reyna: A simple and precise assessment of the volcanic hazard 1996a, b), geostatistical hazard-estimation methods (Jaquet et al, 2000;Jaquet and Carniel, 2006), a mixture of Weibull distributions (Turner et al, 2008) and non-homogeneous statistics to link geological and historical eruption time series (Mendoza-Rosas and De la ).…”

Section: Introductionmentioning

confidence: 99%

A mixture of exponentials distribution for a simple and precise assessment of the volcanic hazard

Mendoza-Rosas¹,

Cruz‐Reyna²

2009

Nat. Hazards Earth Syst. Sci.

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Abstract. The assessment of volcanic hazard is the first step for disaster mitigation. The distribution of repose periods between eruptions provides important information about the probability of new eruptions occurring within given time intervals. The quality of the probability estimate, i.e., of the hazard assessment, depends on the capacity of the chosen statistical model to describe the actual distribution of the repose times. In this work, we use a mixture of exponentials distribution, namely the sum of exponential distributions characterized by the different eruption occurrence rates that may be recognized inspecting the cumulative number of eruptions with time in specific VEI (Volcanic Explosivity Index) categories. The most striking property of an exponential mixture density is that the shape of the density function is flexible in a way similar to the frequently used Weibull distribution, matching long-tailed distributions and allowing clustering and time dependence of the eruption sequence, with distribution parameters that can be readily obtained from the observed occurrence rates. Thus, the mixture of exponentials turns out to be more precise and much easier to apply than the Weibull distribution. We recommended the use of a mixture of exponentials distribution when regimes with well-defined eruption rates can be identified in the cumulative series of events. As an example, we apply the mixture of exponential distributions to the repose-time sequences between explosive eruptions of the Colima and Popocatépetl volcanoes, México, and compare the results obtained with the Weibull and other distributions.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

A quantitative model for the time‐size distribution of eruptions

Marzocchi

Zaccarelli

2006

J. Geophys. Res.

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[1] The modeling of the statistical distribution of eruptive frequency and volume provides basic information to assess volcanic hazard and to constrain the physics of the eruptive process. We analyze eruption catalogs from volcanoes worldwide in order to find ''universal'' relationships and peculiarities linked to different eruptive styles. In particular, we test (1) the Poisson process hypothesis in the time domain, looking for significant clustering of events or the presence of almost regular recurrence times, (2)

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Markov Models of Repose-Period Patterns of Volcanoes

Cited by 70 publications

References 0 publications

Quantifying unsteadiness and dynamics of pulsatory volcanic activity

Quantifying unsteadiness and dynamics of pulsatory volcanic activity

A mixture of exponentials distribution for a simple and precise assessment of the volcanic hazard

A quantitative model for the time‐size distribution of eruptions

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