In the past few decades, the expansion of both ground and satellite-based earth observation systems, as well as advances in laboratory techniques, have increased the quantity and quality of volcanological data. Since these observations are produced by common physical processes, integrating multiple coeval datasets into a joint analysis resolves more details of the underlying volcanic systems. This requires a conceptualization of the volcanic system that predicts observations given appropriate input parameters ? ?a forward model?. Previous studies that applied physics-based forward models with quantitative inversions of ground deformation, magma flux and other data were able to reveal considerably more about volcanic systems than traditional techniques. However, these forward models have remained overly simplified relative to state-of-the-art theoretical modeling of volcanic eruptions.

In this project, we advanced models of dome-forming volcanic eruptions by including processes ignored or over-simplified in earlier work (see figure).  Specifically, we include gradual, pressure-dependent crystallization as magma ascends from the magma chamber to the surface. At the same time, we explicitly model permeable gas escape from the volcanic conduit. The model is then applied to quantitative joint inversions using data from the 2004-2008 dome-forming eruption at Mount St. Helens. Results from this project have been published in two papers with another currently in review.  

We first tested the effect of these additional processes on the steady-state governing equations. Modeling at steady-state assumes that pressure driving the eruption decreases slowly, and that properties in the conduit do not vary in time.  Due to pressure-dependent crystallization, viscosity increases by many orders of magnitude as magma ascends which leads to a natural transition from viscous flow to frictional sliding on the conduit margin. The modeled erupted mass flux depends strongly on wall rock and magma permeabilities due to their impact on magma density. Using this physics-based model in a Bayesian inversion, we link data sets from Mount St. Helens such as extrusion flux and earthquake depths with petrological data to estimate unknown parameters, including the magma chamber pressure and water content, magma permeability constants, conduit radius, and friction along the conduit walls. Even with this relatively simple model and limited data, we obtain improved constraints on important model parameters:  the magma chamber had low (<5 wt%) total water content and that the magma permeability scale is well constrained at ∼ 10^−11.4 m² to reproduce observed dome rock porosities.

Moving beyond the steady-state system, we developed code to study the temporal evolution of the chamber-conduit system.  In this case, as magma exits the crustal reservoir, the pressure decreases which causes the overall velocity to decline. Gas escape becomes more important particularly at shallow depth, which greatly retards flow and could explain how an eruption might end. We use the model to predict three time series from the 2004-2008 eruption of Mount St. Helens: 1) extruded volume, 2) ground displacements from GPS measurements,  and 3) carbon dioxide emissions.  We find that chamber volatile content, volume and excess pressure influence the amplitude of observables, while conduit radius, frictional rate-dependence and magma permeability scale influence temporal evolution. Therefore, including both the amplitude and temporal evolution of eruptions can be useful for estimating system parameters.

Using this time-dependent model, we performed joint inversions of the three time series datasets from the 2004-2008 eruption of Mount St. Helens to estimate essential system parameters, including chamber geometry, pressure, volatile content and material properties. The model parameter space is first sampled using the neighborhood search algorithm, then the resulting ensemble of models is resampled to generate posterior probability density functions (PDFs) of the parameters. We find models that fit all three datasets well. Posterior PDFs suggest an elongate chamber with aspect ratio(width/height) less than 0.5 with its centroid located at 9?17 km depth. Volume loss from the chamber is 0.20?0.66 km³. We also constrain the magma chamber volume to 64 and 256 km³. At the top of the chamber, total (dissolved and exsolved) water contents are 5.0-6.4 wt% and total carbon dioxide contents are 1560-3891 ppm, giving a porosity of 5.3-16.6% depending on the conduit length. Observed dome porosities (<40%) constrain the magma permeability to 10^-17?10^-15 m² such that the magma loses sufficient volatiles before reaching the surface. Insights into this variety of system parameters would not have been possible with standard discipline-specific modeling.

This project has advanced both physics-based modeling of volcanic systems and techniques for quantitative joint inversions. In the long term, the results from this study will be helpful in designing better models and data analysis frameworks for volcanic hazard analysis.

Last Modified: 08/10/2020
Modified by: Paul Segall