Magma Injection Models to Quantify Reservoir Dynamics at Laguna del Maule Volcanic Field, Chile, between 2007 and 2015.

Moving beyond the widely used kinematic models for the deformation sources, we present new dynamic models to describe the process of injecting magma into an existing magma reservoir. The 3-dimensional numerical models account for a viscoelastic, gravitationally loaded domain with spatially variable rheological properties. A Newtonian fluid characterized by its viscosity, density, and overpressure (relative to the lithostatic value) intrudes into a viscoelastic solid via a conduit leading to the reservoir. Using the Finite Element Method (FEM), we simultaneously solve the coupled quasi-static elastic and Navier-Stokes governing equations for the solid and the fluid, respectively, using the COMSOL Multiphysics software. The fluid and the solid interact through buoyancy and viscoelastic relaxation, leading to time-dependent deformation. To quantify the "strength" of the source, we define the product of the volume change (in cubic meters) and pressure change (in Pascals) as the "volcanic moment" (in Newton-meters or Joules). This quantity serves as a basis for comparing the calculated displacement fields to analytical solutions. After validating our injection model, we apply it to the ongoing episode of unrest at Laguna del Maule (Chile). Since 2007, the volcanic field there has been deforming at an exceptionally high rate, with vertical velocities up to 200 mm/yr, as measured by GPS and Interferometric Synthetic Aperture Radar (InSAR) between 2013 and 2014, as described recently by Le Mével et al. (2015, Geophys. Res. Lett. http://dx.doi.org/10.1002/2015GL064665). We are modeling the geodetic data to analyze the temporal and spatial evolution of the displacement. These models constrain the mass flux of material into the reservoir and thus its impact on the stress in the crust. Our results contribute to understanding the current unrest episode at Laguna del Maule and to assessing geodetic signals at other active volcanoes.