Numerical tools for modelling ground deformation and gravity changes on volcanoes (Invited)

Over the last decades, the volcanology has become increasingly quantitative evolving from an empirical to a more quantitative approach in the study of volcanic processes. As physical volcanology has better defined its methods and objectives, elaborated mathematical models have been devised to track the evolution of eruptive processes based on geophysical observations. Nowadays, numerical tools have replaced simple homogeneous half-space solutions and allow for a more quantitative interpretation of volcano-related geophysical signals. We considered an integrated elastic 3-D model based on Finite Element Method (FEM) to compute ground deformation and gravity changes caused by magmatic sources in volcanic areas. The FEM computations permit to account for the effect of topography and different multi-layered crustal structures constrained by seismic tomography and geological evidences. Comparisons are made between analytical and numerical solutions to estimate the differences caused by these features. Our findings highlight that heterogeneity and topography engender deviations from analytical results in the geophysical changes produced by magmatic sources under elastic conditions. Moreover, in volcanic areas the presence of high temperatures affects the rheological behavior of the Earth's crust that calls for considering anelastic properties of the medium surrounding the magmatic sources. The elastic approximation is generally appropriate for small deformations of crustal materials with temperatures cooler than the brittle-ductile transition. Materials surrounding a long-lived magmatic source are heated significantly and rocks no longer behave in a purely elastic manner. Therefore, the thermal state of the volcanoes can greatly influence the surface deformation field, making the elastic approximation inappropriate to model the observed ground deformation. Thermo-mechanical numerical models are also investigated for evaluating the temperature dependency of the ground deformation, considering viscoelastic and elasto-plastic response of the medium. With this in mind, we present some recent case studies on Etna volcano.