The global magnitude–frequency relationship for large explosive volcanic eruptions

Rougier, Jonathan; Sparks, R. S. J.; Cashman, Katharine V.; Brown, Sarah K.

doi:10.1016/j.epsl.2017.11.015

Cited by 56 publications

(70 citation statements)

References 37 publications

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“…A more nuanced approach also considers eruptions that are smaller than supereruptions, which can be incorporated in the exceedance probability of supereruptions by assuming a smooth magnitude-frequency curve. This raises the exceedance probability of supereruptions to 5:9 × 10 −5 (Rougier et al, 2018b).…”

Section: Implications For National Scale Risk Assessmentmentioning

confidence: 99%

Confidence in Risk Assessments

Rougier

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Risk is assessed with varying degrees of confidence, and the degree of confidence is relevant to the risk manager. The paper proposes an operational framework for representing confidence, based on an expert's current beliefs about how her beliefs might be different in the future. Two modelling simplifications, ‘no unknown unknowns’ and a homogeneous Poisson process, make this framework trivial to apply. This is illustrated for assessing an exceedance probability for a large event, with volcanic risk as a specific example. The paper ends with a discussion about risk and confidence assessments for national scale risk assessment, including several further illustrations.

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Section: Implications For National Scale Risk Assessmentmentioning

confidence: 99%

Confidence in Risk Assessments

Rougier

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…The VEI scale combines a series of parameters to define an eruption magnitude, and provides a direct relationship with the volume of erupted magma, which varies with VEI according to a logarithmic scale to account for the many orders of magnitude variations from small up to colossal eruptions (Table 1 ). The Methods include a discussion on the use of the VEI scale to characterize eruption size, compared to the use of the Magnitude scale 15 adopted by other authors 11 , 15 – 17 . There are 9517 individual eruptions with reported VEI in the joined GVP+LaMEVE database (from here on, simply referred to as the database, described in the Methods), spanning the entire VEI scale over a time extending back to more than 2 Ma BP (millions of years Before Present, conventionally identified with 1950 AD).…”

Section: Introductionmentioning

confidence: 99%

Global time-size distribution of volcanic eruptions on Earth

Papale

2018

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Volcanic eruptions differ enormously in their size and impacts, ranging from quiet lava flow effusions along the volcano flanks to colossal events with the potential to affect our entire civilization. Knowledge of the time and size distribution of volcanic eruptions is of obvious relevance for understanding the dynamics and behavior of the Earth system, as well as for defining global volcanic risk. From the analysis of recent global databases of volcanic eruptions extending back to more than 2 million years, I show here that the return times of eruptions with similar magnitude follow an exponential distribution. The associated relative frequency of eruptions with different magnitude displays a power law, scale-invariant distribution over at least six orders of magnitude. These results suggest that similar mechanisms subtend to explosive eruptions from small to colossal, raising concerns on the theoretical possibility to predict the magnitude and impact of impending volcanic eruptions.

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“…The calculated timescales and volumes are comparable with natural volcanic values (e.g., Pyle, ) and span the full range between small mafic eruptions (e.g., Strombolian type) to the largest magnitude eruptions (e.g., caldera‐forming eruptions and flood basalts). The time needed for an instability to develop allows melt to accumulate in large layers and corresponds to a dormant period (e.g., Rougier et al, ; Sheldrake et al, ), whereas the instability may destabilize the system and produce a period of unrest or an eruption. Additionally, successive instabilities without eruption could yield larger accumulated volumes (e.g., Sparks & Cashman, ).…”

Section: Discussionmentioning

confidence: 99%

The Gravitational Stability of Lenses in Magma Mushes: Confined Rayleigh‐Taylor Instabilities

2018

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In the current paradigm, magma primarily exists in the crust as a crystalline mush containing distributed melt lenses. If a melt-rich (or fluid) lens is less dense than the overlying mush, then Rayleigh-Taylor (RT) instabilities will develop and could evolve into spheroids of ascending melt. Due to contrasting melt-mush rheologies, the theoretical RT instability wavelength can be orders of magnitude larger than the magmatic system. We explored how this confinement affects the gravitational stability of melt lenses through laboratory experiments with pairs of liquids with one layer much thinner and up to 2.2 ⋅ 10 5 times less viscous than the other; we extended the viscosity ratio to 10 6 with linear stability analysis. We found the growth rate of a bounded RT instability is approximately Δ gD 6 2 , where Δ is the difference in density between the fluids, g is gravity, D is the container diameter, and 2 is the viscosity of the thicker viscous layer. This differs from the unbounded case, where the growth rate also depends on the thickness and viscosity of the thin, low-viscosity layer. Applying the results to melt lenses in magmatic mushes, we find that for the ranges of expected rheologies, the timescales for development of the instability, and the volumes of packets of rising melt generated span very wide ranges. They are comparable with the frequencies and sizes of volcanic eruptions and episodes of unrest and so suggest that RT instabilities in mush systems can cause episodic volcanism. Key Points:• Melt-mush Rayleigh-Taylor instabilities are generally laterally confined, which reduces the growth rate • The confined instability growth rate only depends on the mush viscosity, melt lens diameter, and density difference • Mush rheology is a key control on size and frequency of eruptions related to buoyancy instabilities

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The global magnitude–frequency relationship for large explosive volcanic eruptions

Cited by 56 publications

References 37 publications

Confidence in Risk Assessments

Confidence in Risk Assessments

Global time-size distribution of volcanic eruptions on Earth

The Gravitational Stability of Lenses in Magma Mushes: Confined Rayleigh‐Taylor Instabilities

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