Assimilation of geodetic data for volcanic hazard assessment in near-real time by means of a particle filter

In a perspective of volcanic hazard assessment, it is fundamental to be able to determine as early as possible whether, where and when the magma that has started to propagate from the storage zone will reach the surface. The propagation phase is generally rapid, lasting from a few hours to a few months, but it induces seismicity and deformation signals recorded by continuous sensors and InSAR data. Furthermore, dynamic numerical models can be used to calculate the trajectory and the velocity of magma propagation as a function of the physical properties of the magma and the crust, and the initial conditions (local stress field and magma reservoir location). Data assimilation is a method that combines a dynamic model with current and past observations based on error statistics and predicts the future state of the observed system.This method therefore appears to be an appropriate tool for addressing the need to predict the position and timing of a volcanic eruption based on available models and observations. The particle filter is particularly noteworthy for its ability to handle nonlinear models and non-Gaussian error statistics. This method is based on a representation of the probability density of the dynamic model by a discrete set of model states (particles) and relies on Bayes' theorem. In order to assess the potential of the particle filter for tracking magma propagation at depth, we implemented this assimilation strategy by considering, in two dimensions, the case of magma propagating beneath a caldera in an extensional stress field. The input parameters of the propagation model are the initial position of the magma at depth, its viscosity and driving pressure, the volume of magma injected, the crustal rigidity, and the local stress field characterized by the balance between tectonic extension and caldera unloading. Surface displacements induced by magma propagation are estimated using an Okada dislocation model. We first validate our assimilation strategy with synthetic data in order to take into account geodetic data recorded on volcanic systems in the future.