Joint inversions of ground deformation, extrusion flux and gas emissions using physics-based models for the Mount St. Helens 2004-2008 eruption

Abstract:

Physics-based models provide a natural and meaningful way to bring together diverse geophysical and geochemical data from volcanoes. By incorporating these models into quantitative inversions, we can obtain constraints on important properties of the magmatic system that are consistent with these observations. Here we develop a framework for joint inversions of diverse time series data using a physics-based model for dome-forming eruptions. The one-dimensional, time-dependent model simulates magma ascent in a conduit connecting a magma chamber to the surface. During ascent, magma exsolves volatiles and crystallizes, which causes its viscosity to increase. Exsolved gases can escape vertically through the column or laterally through the conduit walls. Time- and depth-dependent magma properties are used to calculate time series of cumulative extruded volume, ground deformation and carbon dioxide emissions. We apply this model to data from the 2004-2008 eruption at 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 (Sambridge 1999, GJI), 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 less than 0.5 with its centroid located at 9–17 km depth. Volume loss from the chamber is 0.20–0.66 km³. Since the model calculates the pressure change during the eruption, we can also constrain 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.