Poisson-distributed patterns of explosive eruptive activity

Cruz‐Reyna, Servando De la

doi:10.1007/bf00278206

Cited by 101 publications

(47 citation statements)

References 26 publications

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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 ). An exhaustive list of the available literature on this subject is beyond the scope of this paper, and the above references only attempt to illustrate the diversity of methods that have been applied to the volcanic eruption sequences.…”

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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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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“…De la Cruz-Reyna (1991) proposed a general load-and-discharge model, where the 'energy' of the volcano increases at a constant rate between eruptions. An eruption occurs when this exceeds a threshold H, during which the stored energy drops to a lower threshold L. If the threshold H is constant, the repose will be proportional to the energy of the preceding eruption, which is the time-predictable model.…”

Section: Time-predictable Modelsmentioning

confidence: 99%

Models for Temporal Volcanic Hazard

Bebbington

2013

SIV

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In estimating hazard from a currently quiescent volcano, the most basic quantity of interest is the likelihood of an eruption in some defined time horizon. Starting with the dichotomy of stationarity (where the average future level of activity is equal to the average level of past activity) or non-stationarity, we outline several classes of stochastic models that can be used to forecast future onsets. Renewal models, including the simple Poisson process and mixtures, are compared with models that incorporate volumes of past eruptions, and models that include a trend in the activity level. The mathematical formulations are supplemented by Matlab programs that fit the models using maximum likelihood. Tests are provided for whether a particular model is consistent with the data, and for identifying the best model from those considered. The philosophy behind assumptions and the limitations of each class of models are discussed, and suggestions for further exploration are given. The models are illustrated on a data set of VEI > 1 eruptions from Mt Ruapehu (New Zealand) since 1860.

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“…We thus analyze the eruptive records using a scaling logarithmic relationship between the magnitude VEI (Volcanic Explosivity Index; Newhall and Self, 1982) and the eruption occurrence rate for each magnitude category VEI. This relationship (De la Cruz-Reyna, 1991De la Cruz-Reyna and Carrasco-Núñez, 2002) provides a criterion to estimate the most probable magnitude of eruptions to which no VEI has been assigned. Although Table 1.…”

Section: El Chichón Volcanomentioning

confidence: 99%

Hazard estimates for El Chichón volcano, Chiapas, México: a statistical approach for complex eruptive histories

Mendoza-Rosas¹,

Cruz‐Reyna²

2010

Nat. Hazards Earth Syst. Sci.

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Abstract. The El Chichón volcano (Chiapas, México) most recent eruption occurred in 1982 causing the worst volcanic disaster in the recorded history of Mexico. Prior to the eruption, El Chichón volcano was not considered a very hazardous volcano, a perception mostly caused by the low eruption rate of the past eruptions. The correct assessment of volcanic hazard is the first step to prevent a disaster. In this paper, we analyze two periods of the reported eruptive history of El Chichón volcano during the Holocene, searching for the eruption rates of different VEI magnitude categories and testing their time dependence. One period accounting the eruptions of the last 3707 years before the last eruption (BLE) is assumed to be complete, with no missing relevant events. More scarce information of a period extending to 7772 years BLE is then added. We then apply the Non-Homogeneous Generalized Pareto-Poisson Process (NHGPPP), and the Mixture of Exponentials Distribution (MOED) methods to estimate the volcanic hazard of El Chichón considering both periods. The results are compared with the probabilities obtained from the homogeneous Poisson and Weibull distributions. In this case the MOED and the Weibull distribution are rather insensitive to the inclusion of the extended period. In contrast, the NHGPPP is strongly influenced by the extended period.

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Poisson-distributed patterns of explosive eruptive activity

Cited by 101 publications

References 26 publications

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

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

Models for Temporal Volcanic Hazard

Hazard estimates for El Chichón volcano, Chiapas, México: a statistical approach for complex eruptive histories

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