Physics‐based models of ground deformation and extrusion rate at effusively erupting volcanoes

[1] We present a model of effusive silicic volcanic eruptions which relates magma chamber and conduit physics to time‐dependent data sets, including ground deformation and extrusion rate. The model involves a deflating chamber which supplies Newtonian magma through a cylindrical conduit. Solidification is approximated as occurring at fixed depth, producing a solid plug that slips along its margins with rate‐dependent friction. Changes in tractions acting on the chamber and conduit walls are used to compute surface deformations. Given appropriate material properties and initial conditions, the model predicts the full evolution of an eruption, allowing us to examine the dependence of observables on initial chamber volume, overpressure, and volatile content. Employing multiple data sets in combination with a physics‐based model allows for better constraints on these parameters than is possible using kinematic idealizations. Modeling posteruptive deformation provides an improved constraint on the rate of influx into the magma chamber from deeper sources. We compare numerical results to analytical approximations and to data from the 2004–2008 eruption of Mount St. Helens. For nominal parameters the balance between magma chamber pressure and frictional resistance of the solid plug controls the evolution of the eruption, with little contribution from the fluid magma below the idealized crystallization depth. While rate‐dependent plug friction influences the time‐ dependent evolution of the eruption, it has no control on the final chamber pressure or extruded volume.