Bayesian estimation of magma supply, storage, and eruption rates using a multiphysical volcano model: Kīlauea Volcano, 2000–2012

Abstract

Estimating rates of magma supply to the world's volcanoes remains one of the most fundamental aims of volcanology. Yet, supply rates can be difficult to estimate even at well-monitored volcanoes, in part because observations are noisy and are usually considered independently rather than as part of a holistic system. In this work we demonstrate a technique for probabilistically estimating time-variable rates of magma supply to a volcano through probabilistic constraint on storage and eruption rates. This approach utilizes Bayesian joint inversion of (1) diverse datasets using predictions from a multiphysical volcano model, and (2) independent prior information derived from previous geophysical, geochemical, and geological studies. The solution to the inverse problem takes the form of a probability density function which takes into account uncertainties in observations and prior information, and which we sample using a Markov Chain Monte Carlo algorithm. Applying the technique to Kīlauea Volcano, we develop a model which relates magma flow rates with deformation of the volcano's surface, sulfur dioxide emission rates, lava flow field volumes, and composition of the volcano's basaltic magma. This model accounts for effects and processes mostly neglected in previous supply rate estimates at Kīlauea, including magma compressibility, loss of sulfur to the hydrothermal system, and potential magma storage in the volcano's deep rift zones. We jointly invert data and prior information to estimate rates of supply, storage, and eruption during three recent quasisteady-state periods at the volcano. Results shed new light on the time-variability of magma supply to Kīlauea, which we find to have increased by 35-100% between 2001 and 2006 (from 0.11-0.17 to 0.18-0.28 km 3 /yr), before subsequently decreasing to 0.08-0.12 km 3 /yr by 2012. Changes in supply rate directly impact hazard at the volcano, and were largely responsible for an increase in eruption rate of 60-150% between 2001 and 2006, and subsequent decline by as much as 60% by 2012. We also demonstrate the occurrence of temporal changes in the proportion of Kīlauea's magma supply that is stored versus erupted, with the supply "surge" in 2006 associated with increased accumulation of magma at the summit. Finally, we are able to place some constraints on sulfur concentrations in Kīlauea magma and the scrubbing of sulfur 1

The 2017 Eruption of Erta 'Ale Volcano, Ethiopia: Insights Into the Shallow Axial Plumbing System of an Incipient Mid‐Ocean Ridge

“…If the magma is homogeneous and incompressible, the change in pressure required to sustain pit levels in hydrostatic equilibrium (Δ P ) from the observed changes in pit heights (Δ h ) is Δ P = ρg Δ h , where g is the acceleration due to gravity (9.8 m/s 2 ). For magma density, ρ , we use a value of 2,550–3,100 kg/m 3 (Anderson & Poland, ), using Kilauea volcano, Hawaii, as a close analog of the Erta 'Ale system. We use a large range in density as the gas content in the magma at Erta 'Ale is unknown.…”

Observing eruptions of gas-rich compressible magmas from space

“…Our enhanced understanding of sulfur behaviour in recent years however, has fully reconciled the observations with the presence of a pre-eruptive vapour, first proposed on the basis of observations13 and later confirmed experimentally31 and modelled26. Now a large database of sulfur emissions from volcanoes exists5, but there have been very few attempts2023 to fit these observations into this now well-established theoretical framework for sulfur gas–melt partitioning and none reconciling the geochemical features of the magmatic vapour with the consequences for magma compressibility. This approach clearly has enormous potential for strengthening our constraints on pre-eruptive magma storage conditions.…”

“…The inferred volume change of the reservoir observed syn-eruption, however, is often many times less than the volume of magma erupted at the surface (corrected for density difference). This difference in volume is controlled by the balance between the compressibility of the magma, including that of any exsolved gas phases, and the material properties of the host rock, a feature highlighted by numerous previous studies1151617181920212223. The total mass of exsolved vapour is difficult to quantify independently however, and this lack of understanding leads to a lack of constraint on inferred volume changes from inverse modelling of InSAR observations.…”

Inversion of Surface Deformation Data for Rapid Estimates of Source Parameters and Uncertainties: A Bayesian Approach

“…Geochemistry, Geophysics, Geosystems Anderson & Poland, 2016). This step can also be used to check that PDFs for all chains converge to similar distributions, independently from the chosen initial set of model parameters.…”