Moving beyond the widely used kinematic models for the deformation sources, we present a new dynamic model to describe the process of injecting magma into an existing magma reservoir. To validate this model, we derive an analytical solution and compare its results to those calculated using the Finite Element Method. A Newtonian fluid characterized by its viscosity, density, and overpressure (relative to the lithostatic value) flows through a vertical conduit, intruding into a reservoir embedded in an elastic domain, leading to an increase in reservoir pressure and time-dependent surface deformation. We apply our injection model to Interferometric Synthetic Aperture Radar (InSAR) data from the ongoing unrest episode at Laguna del Maule (Chile) volcanic field that started in 2007. Using a grid search optimization, we minimize the misfit to the InSAR displacement data and vary the three parameters governing the analytical solution: the characteristic timescale τP for magma propagation, the maximum injection pressure, and the inflection time when the acceleration switches from positive to negative. For a spheroid with semimajor axis a = 6200 m, semiminor axis c = 100 m, located at a depth of 4.5 km in a purely elastic half-space, the best fit to the InSAR displacement data occurs for τP =9.5 years and an injection pressure rising up to 11.5 MPa for 2 years. The volume flow rate increased to 1.2 m3/s for 2 years and then decreased to 0.7 m3/s in 2014. In 7.3 years, at least 187 × 106 m3 of magma was injected.
Keywords: InSAR; ground deformation; magma injection; model; unrest; volcano.