Physics-based conduit models of dome extrusion: Steady-state solutions applied to the Mount St. Helens 2004-2008 eruption

Physics-based models of volcanic eruptions allow us to integrate diverse volcanological datasets to constrain important parameters of magmatic systems and to track its evolution during ascent. We have extended the 1D cylindrical conduit model of Anderson and Segall [2011] to include equilibrium crystallization, and vertical and lateral gas loss from the magma. Excess pressure in the magma chamber drives Newtonian flow until the viscous resistance to flow exceeds the rate-dependent frictional strength on the conduit wall, when magma transitions from viscous to plug flow. We investigate steady-state solutions to compare with the quasi-steady dome growth phase of Mount St. Helens between March and December 2005, and take magma chamber pressure, initial water content, permeability, conduit radius and friction coefficient as unknown model parameters. By including crystallization and gas loss, we can link physical datasets such as ground deformation and extrusion flux with petrological and gas flux data. Specifically, the model parameters influence dome rock porosity estimated from hand samples, extrusion rate from photogrammetry, plug depth from drumbeat earthquakes, and crystallization pressure from petrologic data. Model sensitivity tests show that changes that promote higher shear stress along the conduit walls, such as higher chamber pressure and conduit radius, as well as changes that retain more gas in the system, such as higher water content and percolation threshold, tend to increase dome porosity and exit velocity. Changes in permeability produce non-monotonic behavior in the predicted data due to the competing processes of gas exsolution and gas loss. Using this physics-based model in a Bayesian inversion, we estimate probability density functions of the model parameters and their correlations. Future work will investigate the time-dependent system, allowing us to incorporate time-evolving geodetic and eruption rate data into the inversion.