Numerical Analysis of Time-Dependent Conduit Magma Flow in Dome-Forming Eruptions With Application to Mount St. Helens 2004–2008

Abstract

Conduit models of volcanic eruptions simulate magma evolution through phase transitions and material changes during ascent. We present a time-dependent one-dimensional model of a chamber-conduit system to examine the temporal evolution of dome-forming eruptions. As magma ascends, volatiles exsolve and may escape vertically through the column or laterally through the conduit walls. Magma solidifies which increases viscosity, leading to a natural transition from viscous flow at depth to frictional sliding along the conduit walls near the surface, resulting in the extrusion of a semisolid plug. The model evaluates time- and depth-dependent pressure, velocity, porosity, and relative amounts of exsolved water to carbon dioxide. Transient effects arise when magma outflux from the chamber appreciably decreases pressure over the magma ascent timescale. For low magma permeability, transient effects increase porosity and velocity relative to steady-state solutions. For high magma permeability, efficient vertical and lateral gas escape depresses porosity and velocity at later times. We use the model to predict three time series data sets from the 2004–2008 eruption of Mount St. Helens: extruded volume, ground deformation, and carbon dioxide emissions. We quantify sensitivity of model predictions to input parameters using the distance-based generalized sensitivity analysis. Chamber volatile content, volume, and excess pressure influence the amplitude of observables, while conduit radius, frictional rate dependence and magma permeability influence temporal evolution. High magma permeability can cause marked departures from exponentially decaying flux and may explain the unique temporal evolution of deformation observed at the only nearby continuous GPS station in operation at the eruption onset.