Bayesian Inversion using Physics-based Models Applied to Dome Extrusion at Mount St. Helens 2004-2008

Abstract:

Physics-based models of volcanic eruptions have grown more sophisticated over the past few decades. These models, combined with Bayesian inversion, offer the potential of integrating diverse geological and geophysical datasets to better understand volcanic systems. Using a Markov Chain Monte Carlo (MCMC) algorithm with a physics-based conduit model, we invert data from the 2004-2008 dome-forming eruption at Mount St. Helens, USA. We extend the 1D cylindrical conduit model of Anderson and Segall [2011] to include vertical and lateral gas loss from the magma, as well as equilibrium crystallization. The melt viscosity increases strongly with crystal content. Magma permeability obeys the Kozeny-Carman law with a threshold porosity. Excess pressure in the magma chamber drives Newtonian flow of magma upwards until the viscous resistance to flow exceeds the rate-dependent frictional strength on the conduit wall, at which point the magma transitions from viscous flow to plug flow.

We investigate the steady-state solutions for lava dome growth between March and December 2005, in which magma chamber pressure, initial water content, permeability and friction parameters are unknown model parameters. These parameters are constrained by: dome rock porosity, extrusion rate from photogrammetry, plug depth from drumbeat earthquakes, and crystallization pressure from petrologic studies. Posterior probability density functions (PDFs) reveal the constraints on the model parameters and their correlations. Assuming lithostatic normal stress on the plug, low coefficients of friction (0.1-0.3) are required to allow extrusion at the observed rate while maintaining reasonable magma chamber pressures. Lower effective normal stress or melt viscosity could allow for larger friction coefficients. Future work will investigate the time-dependent system, thereby allowing us to incorporate time-evolving geodetic and eruption rate data into the inversion.